Showing 1–50 of 230 results for author: Aoki, H

Flat bands in condensed-matter systems -- perspective for magnetism and superconductivity

Authors: Hideo Aoki

Abstract: There is a recent upsurge of interests in flat bands in condensed-matter systems and the consequences for magnetism and superconductivity. This article highlights the physics, where peculiar quantum-mechanical mechanisms for the physical properties such as flatband ferromagnetism and flatband superconductivity that arise when the band is not trivially flat but has a strange Hilbert space with non-… ▽ More There is a recent upsurge of interests in flat bands in condensed-matter systems and the consequences for magnetism and superconductivity. This article highlights the physics, where peculiar quantum-mechanical mechanisms for the physical properties such as flatband ferromagnetism and flatband superconductivity that arise when the band is not trivially flat but has a strange Hilbert space with non-orthogonalisable Wannier states, which goes far beyond just the diverging density of states. Peculiar wavefunctions come from a quantum-mechanical interference and entanglement. Interesting phenomena become even remarkable when many-body interactions are introduced, culminating in flatband superconductivity as well as flatband ferromagnetism. Flatband physics harbours a very wide range physics indeed, extending to non-equilibrium physics in laser illumination, where Floquet states for topologcial superconductivity is promoted in flatbands. While these are theoretically curious, possible candidates for the flatband materials are beginning to emerge, which is also described. These provide a wide and promising outlook. △ Less

Submitted 14 October, 2025; originally announced October 2025.

Comments: 63 pages, 43 figures

Journal ref: Contemporary Physics (2025)

Emergent Fano-Feshbach resonance in two-band superconductors with an incipient quasi-flat band: Enhanced critical temperature evading particle-hole fluctuations

Authors: Hiroyuki Tajima, Hideo Aoki, Andrea Perali, Antonio Bianconi

Abstract: In superconductivity, a surge of interests in enhancing $T_{\rm c}$ is ever mounting, where a recent focus is toward multi-band superconductivity. In $T_{\rm c}$ enhancements specific to two-band cases, especially around the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover considered here, we have to be careful about how quantum fluctuations affect the many-body states,… ▽ More In superconductivity, a surge of interests in enhancing $T_{\rm c}$ is ever mounting, where a recent focus is toward multi-band superconductivity. In $T_{\rm c}$ enhancements specific to two-band cases, especially around the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover considered here, we have to be careful about how quantum fluctuations affect the many-body states, i.e., particle-hole fluctuations suppressing the pairing for attractive interactions. Here we explore how to circumvent the suppression by examining multichannel pairing interactions in two-band systems. With the Gor'kov-Melik-Barkhudarov (GMB) formalism for particle-hole fluctuations in a continuous space, we look into the case of a deep dispersive band accompanied by an incipient heavy-mass (i.e., quasi-flat) band. We find that, while the GMB corrections usually suppress $T_{\rm c}$ significantly, this in fact competes with the enhanced pairing arising from the heavy band, with the trade-off leading to a peaked structure in $T_{\rm c}$ against the band-mass ratio when the heavy band is incipient. The system then plunges into a strong-coupling regime with the GMB screening vastly suppressed. This occurs prominently when the chemical potential approaches the bound state lurking just below the heavy band, which can be viewed as a Fano-Feshbach resonance, with its width governed by the pair-exchange interaction. The diagrammatic structure comprising particle-particle and particle-hole channels is heavily entangled, so that the emergent Fano-Feshbach resonance dominates all the channels, suggesting a universal feature in multiband superconductivity. △ Less

Submitted 28 March, 2024; v1 submitted 9 February, 2024; originally announced February 2024.

Comments: 12 pages, 9 figures, Accepted version for Physical Review B

Journal ref: Phys. Rev. B 109, L140504 (2024)

Exact continuum theory of anti-Klein tunneling in bilayer graphene

Authors: P. A. Maksym, H. Aoki

Abstract: Exact conditions for anti-Klein transmission zeros are found analytically with a 4-component continuum approach which includes trigonal warping. Anti-Klein tunneling occurs at oblique incidence on steps and barriers with soft and hard walls as well as in the known case of normal incidence on a hard step. The necessary energy and angle of incidence depend on the crystallographic orientation of the… ▽ More Exact conditions for anti-Klein transmission zeros are found analytically with a 4-component continuum approach which includes trigonal warping. Anti-Klein tunneling occurs at oblique incidence on steps and barriers with soft and hard walls as well as in the known case of normal incidence on a hard step. The necessary energy and angle of incidence depend on the crystallographic orientation of the step or barrier. At normal incidence on an armchair step in unbiased bilayer graphene, anti-Klein tunneling occurs because both the continuum and the tight binding Hamiltonians are invariant under layer and site interchange. At oblique incidence, anti-Klein tunneling is valley-dependent even in the absence of trigonal warping. An experimental arrangement that functions both as a detector of anti-Klein tunneling and a valley polarizer is suggested. There are cases where anti-Klein tunneling occurs in the 4-component theory but not in the 2-component approximation. △ Less

Submitted 16 June, 2023; originally announced June 2023.

Comments: 16 pages, 10 figures

Sub-cycle multidimensional spectroscopy of strongly correlated materials

Authors: V. Valmispild, E. Gorelov, M. Eckstein, A. Lichtenstein, H. Aoki, M. Katsnelson, M. Ivanov, O. Smirnova

Abstract: Strongly correlated solids are extremely complex and fascinating quantum systems, where new states continue to emerge, especially when interaction with light triggers interplay between them. In this interplay, sub-laser-cycle electron response is particularly attractive as a tool for ultrafast manipulation of matter at PHz scale. Here we introduce a new type of non-linear multidimensional spectros… ▽ More Strongly correlated solids are extremely complex and fascinating quantum systems, where new states continue to emerge, especially when interaction with light triggers interplay between them. In this interplay, sub-laser-cycle electron response is particularly attractive as a tool for ultrafast manipulation of matter at PHz scale. Here we introduce a new type of non-linear multidimensional spectroscopy, which allows us to unravel the sub-cycle dynamics of strongly correlated systems interacting with few-cycle infrared pulses and the complex interplay between different correlated states evolving on the sub-femtosecond time-scale. We demonstrate that single particle sub-cycle electronic response is extremely sensitive to correlated many-body dynamics and provides direct access to many body response functions. For the two-dimensional Hubbard model under the influence of ultra-short, intense electric field transients, we demonstrate that our approach can resolve pathways of charge and energy flow between localized and delocalized many-body states on the sub-cycle time scale and follow the creation of a highly correlated state surviving after the end of the laser pulse. Our findings open a way towards a regime of imaging and manipulating strongly correlated materials at optical rates, beyond the multi-cycle approach employed in Floquet engineering, with the sub-cycle response being a key tool for accessing many body phenomena. △ Less

Submitted 10 March, 2023; v1 submitted 9 August, 2022; originally announced August 2022.

Comments: 10 pages, 4, figures, Methods (5 pages), Supplementary information (4 figures, 4 pages)

Superconductivity enhanced by pair fluctuations between wide and narrow bands

Authors: Changming Yue, Hideo Aoki, Philipp Werner

Abstract: Full or empty narrow bands near the Fermi level are known to enhance superconductivity by promoting scattering processes and spin fluctuations. Here, we demonstrate that doublon-holon fluctuations in systems with half-filled narrow bands can similarly boost the superconducting $T_c$. We study the half-filled attractive bilayer Hubbard model on the square lattice using dynamical mean-field theory.… ▽ More Full or empty narrow bands near the Fermi level are known to enhance superconductivity by promoting scattering processes and spin fluctuations. Here, we demonstrate that doublon-holon fluctuations in systems with half-filled narrow bands can similarly boost the superconducting $T_c$. We study the half-filled attractive bilayer Hubbard model on the square lattice using dynamical mean-field theory. The band structure of the noninteracting system contains a wide band formed by bonding orbitals and a narrow band formed by antibonding orbitals, with bandwidths tunable by the inter-layer hopping. The shrinking of the narrow band can lead to a substantial increase in the superconducting order parameter and phase stiffness in the wide band. At the same time, the coupling to the wide band allows the narrow band to remain superconducting -- and to reach the largest order parameter -- in the flat band limit. We develop an anomalous worm sampling method to study superconductivity in the limit of vanishing effective hopping. By analyzing the histogram of the local eigenstates, we clarify how the interplay between different interaction terms in the bonding/antibonding basis promotes pair fluctuations and superconductivity. △ Less

Submitted 29 July, 2022; v1 submitted 25 July, 2022; originally announced July 2022.

Comments: 7+12 pages, 4+7 figures

Nematicity-enhanced superconductivity in systems with a non-Fermi liquid behavior

Authors: Sharareh Sayyad, Motoharu Kitatani, Abolhassan Vaezi, Hideo Aoki

Abstract: We explore the interplay between nematicity~(spontaneous breaking of the sixfold rotational symmetry), superconductivity, and non-Fermi liquid behavior in partially flat-band models on the triangular lattice. A key result is that the nematicity (Pomeranchuk instability), which is driven by many-body effect and stronger in flat-band systems, enhances superconducting transition temperature in a syst… ▽ More We explore the interplay between nematicity~(spontaneous breaking of the sixfold rotational symmetry), superconductivity, and non-Fermi liquid behavior in partially flat-band models on the triangular lattice. A key result is that the nematicity (Pomeranchuk instability), which is driven by many-body effect and stronger in flat-band systems, enhances superconducting transition temperature in a systematic manner on the $T_{\rm c}$ dome. There, a $s_{x^2+y^2} - d_{x^2-y^2} - d_{xy}$-wave symmetry, in place of the conventional $d_{x^2-y^2}$-wave, governs the nematicity-enhanced pairing with a sharp rise in the $T_{\rm c}$ dome on the filling axis. When the sixfold symmetry is spontaneously broken, the pairing becomes more compact in real space than in the case when the symmetry is enforced. These are accompanied by a non-Fermi character of electrons in the partially flat bands with many-body interactions. △ Less

Submitted 3 April, 2023; v1 submitted 27 October, 2021; originally announced October 2021.

Comments: 6+18 pages, 5+26 figures

Journal ref: J. Phys.: Condens. Matter 35 245605 (2023)

Floquet topological $d+id$ superconductivity induced by chiral many-body interactions

Authors: Sota Kitamura, Hideo Aoki

Abstract: We study how a $d$-wave superconductivity is changed when illuminated by circularly-polarised light (CPL) in the repulsive Hubbard model in the strong-coupling regime. We adopt the Floquet formalism for the Gutzwiller-projected effective Hamiltonian with the time-periodic Schrieffer-Wolff transformation. We find that CPL induces a topological superconductivity with a $d+id$ pairing, which arises f… ▽ More We study how a $d$-wave superconductivity is changed when illuminated by circularly-polarised light (CPL) in the repulsive Hubbard model in the strong-coupling regime. We adopt the Floquet formalism for the Gutzwiller-projected effective Hamiltonian with the time-periodic Schrieffer-Wolff transformation. We find that CPL induces a topological superconductivity with a $d+id$ pairing, which arises from the chiral spin coupling and the three-site term generated by the CPL. The latter term remains significant even for low frequencies and low intensities of the CPL. This is clearly reflected in the obtained phase diagram against the laser intensity and temperature for various frequencies red-detuned from the Hubbard $U$, with the transient dynamics also examined. The phenomenon revealed here can open a novel, dynamical way to induce a topological superconductivity. △ Less

Submitted 2 March, 2022; v1 submitted 31 August, 2021; originally announced August 2021.

Comments: 13 pages, 6 figures

Journal ref: Commun. Phys. 5, 174 (2022)

Resonant pair-exchange scattering and BCS-BEC crossover in a system composed of dispersive and heavy incipient bands: a Feshbach analogy

Authors: Kazunari Ochi, Hiroyuki Tajima, Kei Iida, Hideo Aoki

Abstract: We theoretically show that a two-band system with very different masses harbors a resonant pair scattering that leads to novel pairing properties, as highlighted by the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. Most importantly, the interband pair-exchange coupling induces an effective intraband attraction in each band, enhancing the superfluidity/superconducti… ▽ More We theoretically show that a two-band system with very different masses harbors a resonant pair scattering that leads to novel pairing properties, as highlighted by the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. Most importantly, the interband pair-exchange coupling induces an effective intraband attraction in each band, enhancing the superfluidity/superconductivity. The effect, a kind of Suhl-Kondo mechanism, is specifically enhanced when the second band has a heavy mass and is incipient (lying close to, but just above, the chemical potential, $μ$), which we call a resonant pair scattering. By elucidating the dependence of the effective interactions and gap functions on $μ$, we can draw an analogy between the resonant pair scattering and the Feshbach resonance. △ Less

Submitted 10 November, 2021; v1 submitted 29 July, 2021; originally announced July 2021.

Comments: 11 pages, 8 figures

Journal ref: Phys. Rev. Research 4, 013032 (2022)

Magnetic structures and phase transitions of A-site Ordered Double-Perovskite SmBaMn2O6

Authors: Ryoji Kiyanagi, Shigeki Yamada, Hiroshi Aoki, Hajime Sagayama, Taketo Moyoshi, Akiko Nakao, Takahisa Arima

Abstract: Magnetic structures and the relationship between spin and charge-orbital orderings of an A-site ordered double-perovskite manganite SmBaMn2O6, an anticipated multiferroic material, were investigated by means of neutron diffraction. The spin arrangement in MnO2 planes perpendicular to the c axis is revealed to be the same as that in the A-site disordered half-doped manganites CE-type but the stacki… ▽ More Magnetic structures and the relationship between spin and charge-orbital orderings of an A-site ordered double-perovskite manganite SmBaMn2O6, an anticipated multiferroic material, were investigated by means of neutron diffraction. The spin arrangement in MnO2 planes perpendicular to the c axis is revealed to be the same as that in the A-site disordered half-doped manganites CE-type but the stacking pattern is found to be different displaying a unique twofold period. The temperature dependence of the superlattice magnetic and nuclear reflections clarifies that the antiferromagnetic spin ordering occurs at a temperature slightly lower than the temperature at which a rearrangement of the charge-orbital orderings occurs. The result evidences that the rearrangement leads the spin ordering. The intensities of the magnetic reflections are found to change across Tf = 10 K, suggesting a spin-flop by 90 [deg.] while keeping the Mn spin ordering pattern unchanged. △ Less

Submitted 12 July, 2021; v1 submitted 8 July, 2021; originally announced July 2021.

Comments: 11 pages, 5 figures

Emergence of spin-orbit coupled ferromagnetic surface state derived from Zak phase in a nonmagnetic insulator FeSi

Authors: Yusuke Ohtsuka, Naoya Kanazawa, Motoaki Hirayama, Akira Matsui, Takuya Nomoto, Ryotaro Arita, Taro Nakajima, Takayasu Hanashima, Victor Ukleev, Hiroyuki Aoki, Masataka Mogi, Kohei Fujiwara, Atsushi Tsukazaki, Masakazu Ichikawa, Masashi Kawasaki, Yoshinori Tokura

Abstract: A chiral compound FeSi is a nonmagnetic narrow-gap insulator, exhibiting peculiar charge and spin dynamics beyond a simple band-structure picture. Those unusual features have been attracting renewed attention from topological aspects. Although a signature of surface conduction was indicated according to size-dependent resistivity in bulk crystals, its existence and topological properties remain el… ▽ More A chiral compound FeSi is a nonmagnetic narrow-gap insulator, exhibiting peculiar charge and spin dynamics beyond a simple band-structure picture. Those unusual features have been attracting renewed attention from topological aspects. Although a signature of surface conduction was indicated according to size-dependent resistivity in bulk crystals, its existence and topological properties remain elusive. Here we demonstrate an inherent surface ferromagnetic-metal state of FeSi thin films and its strong spin-orbit-coupling (SOC) properties through multiple characterizations of the two-dimensional (2D) conductance, magnetization and spintronic functionality. Terminated covalent-bonding orbitals constitute the polar surface state with momentum-dependent spin textures due to Rashba-type spin splitting, as corroborated by unidirectional magnetoresistance measurements and first-principles calculations. As a consequence of the spin-momentum locking, non-equilibrium spin accumulation causes magnetization switching. These surface properties are closely related to the Zak phase of the bulk band topology. Our findings propose another route to explore noble-metal-free materials for SOC-based spin manipulation. △ Less

Submitted 26 April, 2021; originally announced April 2021.

Comments: 22 pages, 6 figures, supplementary materials

Robust Zero Modes in Disordered Two-Dimensional Honeycomb Lattice with Kekulé Bond Ordering

Authors: Tohru Kawarabayashi, Yuya Inoue, Ryo Itagaki, Yasuhiro Hatsugai, Hideo Aoki

Abstract: Robustness of zero-modes of two-dimensional Dirac fermions is examined numerically for the honeycomb lattice in the presence of Kekulé bond ordering. The split $n=0$ Landau levels in a magnetic field as well as the zero-modes generated by topological defects in the Kekulé ordering are shown to exhibit anomalous robustness against disorder when the chiral symmetry is respected. Robustness of zero-modes of two-dimensional Dirac fermions is examined numerically for the honeycomb lattice in the presence of Kekulé bond ordering. The split $n=0$ Landau levels in a magnetic field as well as the zero-modes generated by topological defects in the Kekulé ordering are shown to exhibit anomalous robustness against disorder when the chiral symmetry is respected. △ Less

Submitted 31 January, 2021; originally announced February 2021.

Comments: 11 pages, 9 figures, submitted to the proceedings of Localisation 2020

Journal ref: Annals of Physics 435 (2021) 168440

Superconducting mechanism for the cuprate Ba$_2$CuO$_{3+δ}$ based on a multiorbital Lieb lattice model

Authors: Kimihiro Yamazaki, Masayuki Ochi, Daisuke Ogura, Kazuhiko Kuroki, Hiroshi Eisaki, Shinichi Uchida, Hideo Aoki

Abstract: For the recently discovered cuprate superconductor $\mathrm{Ba_{2}CuO_{3+δ}}$, we propose a lattice structure which resembles the model considered by Lieb to represent the vastly oxygen-deficient material. We first investigate the stability of the Lieb-lattice structure, and then construct a multiorbital Hubbard model based on first-principles calculation. By applying the fluctuation-exchange appr… ▽ More For the recently discovered cuprate superconductor $\mathrm{Ba_{2}CuO_{3+δ}}$, we propose a lattice structure which resembles the model considered by Lieb to represent the vastly oxygen-deficient material. We first investigate the stability of the Lieb-lattice structure, and then construct a multiorbital Hubbard model based on first-principles calculation. By applying the fluctuation-exchange approximation to the model and solving the linearized Eliashberg equation, we show that $s$-wave and $d$-wave pairings closely compete with each other, and, more interestingly, that the intra-orbital and inter-orbital pairings coexist. We further show that, if the energy of the $d_{3z^2-r^2}$ band is raised to make it "incipient" with the lower edge of the band close to the Fermi level within a realistic band filling regime, $s\pm$-wave superconductivity is strongly enhanced. We reveal an intriguing relation between the Lieb model and the two-orbital model for the usual K$_2$NiF$_4$ structure where a close competition between $s-$ and $d-$wave pairings is known to occur. The enhanced superconductivity in the present model is further shown to be related to an enhancement found previously in the bilayer Hubbard model with an incipient band. △ Less

Submitted 5 September, 2020; v1 submitted 9 March, 2020; originally announced March 2020.

Comments: 19 pages, 20 figures; references and figures updated

Journal ref: Phys. Rev. Research 2, 033356 (2020)

Optical imprinting of superlattices in two-dimensional materials

Authors: Hwanmun Kim, Hossein Dehghani, Hideo Aoki, Ivar Martin, Mohammad Hafezi

Abstract: We propose an optical method of shining circularly polarized and spatially periodic laser fields to imprint superlattice structures in two-dimensional electronic systems. By changing the configuration of the optical field, we synthesize various lattice structures with different spatial symmetry, periodicity, and strength. We find that the wide optical tunability allows one to tune different proper… ▽ More We propose an optical method of shining circularly polarized and spatially periodic laser fields to imprint superlattice structures in two-dimensional electronic systems. By changing the configuration of the optical field, we synthesize various lattice structures with different spatial symmetry, periodicity, and strength. We find that the wide optical tunability allows one to tune different properties of the effective band structure, including Chern number, energy bandwidths, and band gaps. The in situ tunability of the superlattice gives rise to unique physics ranging from the topological transitions to the creation of the flat bands through the kagome superlattice, which can allow a realization of strongly correlated phenomena in Floquet systems. We consider the high-frequency regime where the electronic system can remain in the quasiequilibrium phase for an extended amount of time. The spatiotemporal reconfigurability of the present scheme opens up possibilities to control light-matter interaction to generate novel electronic states and optoelectronic devices. △ Less

Submitted 5 October, 2020; v1 submitted 30 December, 2019; originally announced December 2019.

Comments: 5+5 pages, 4+2 figures

Journal ref: Phys. Rev. Research 2, 043004 (2020)

Theoretical possibilities for flat-band superconductivity

Authors: Hideo Aoki

Abstract: One novel arena for designing superconductors with high $T_C$ is the flat-band systems. A basic idea is that flat bands, arising from quantum mechanical interference, give unique opportunities for enhancing $T_C$ with (i) many pair-scattering channels between the dispersive and flat bands, and (ii) an even more interesting situation when the flat band is topological and highly entangled. Here we c… ▽ More One novel arena for designing superconductors with high $T_C$ is the flat-band systems. A basic idea is that flat bands, arising from quantum mechanical interference, give unique opportunities for enhancing $T_C$ with (i) many pair-scattering channels between the dispersive and flat bands, and (ii) an even more interesting situation when the flat band is topological and highly entangled. Here we compare two routes, which comprise a multi-band system with a flat band coexisting with dispersive ones, and a one-band case with a portion of the band being flat. Superconductivity can be induced in both cases when the flat band or portion is "incipient" (close to, but away from, the Fermi energy). Differences are, for the multi-band case, we can exploit large entanglement associated with topological states, while for the one-band case a transition between different (d and p) wave pairings can arise. These hint at some future directions. △ Less

Submitted 24 March, 2020; v1 submitted 9 December, 2019; originally announced December 2019.

Comments: 6 pages, 5 figures, Proc. Int. Conf. "Superstripes 2019"

Journal ref: Journal of Superconductivity and Novel Magnetism 33, 2341 (2020)

Complete Spin and Valley Polarization by Total External Reflection from Potential Barriers in Bilayer Graphene and Monolayer Transition Metal Dichalcogenides

Authors: P. A. Maksym, H. Aoki

Abstract: It is shown that potential barriers in bilayer graphene (BLG) and monolayer transition metal dichalcogenides (TMDs) can split a valley unpolarized incident current into reflected and transmitted currents with opposite valley polarization. Valley asymmetric transmission inevitably occurs because of the low symmetry of the total Hamiltonian and when total external reflection occurs the transmission… ▽ More It is shown that potential barriers in bilayer graphene (BLG) and monolayer transition metal dichalcogenides (TMDs) can split a valley unpolarized incident current into reflected and transmitted currents with opposite valley polarization. Valley asymmetric transmission inevitably occurs because of the low symmetry of the total Hamiltonian and when total external reflection occurs the transmission is 100% valley polarized in BLG and 100% spin and valley polarized in TMDs, except for exponentially small corrections. By adjusting the potential, 100% polarization can be obtained regardless of the crystallographic orientation of the barrier. A valley polarizer can be realized by arranging for a collimated beam of carriers to be incident on a barrier within the range of angles for total external reflection. The transmission coefficients of barriers with a relative rotation of $\pmπ/3$ are related by symmetry. This allows two barriers to be used to demonstrate that the current is valley polarized. A soft-walled potential is used to model the barrier and the method used to find the transmission coefficients is explained. In the case of monolayer TMDs, a 4-band k.p Hamiltonian is used and the k.p parameters are obtained by fitting to ab-initio band structures. △ Less

Submitted 9 September, 2021; v1 submitted 8 November, 2019; originally announced November 2019.

Comments: 21 pages, 16 figures; merged paper and supplemental material; updated references

Journal ref: Phys. Rev. B 104, 155401 (2021)

Model construction and a possibility of cuprate-like pairing in a new d9 nickelate superconductor (Nd,Sr)NiO2

Authors: Hirofumi Sakakibara, Hidetomo Usui, Katsuhiro Suzuki, Takao Kotani, Hideo Aoki, Kazuhiko Kuroki

Abstract: Effective models are constructed for a newly discovered superconductor (Nd,Sr)NiO2, which has been considered as a possible nickelate analogue of the cuprates owing to the d9 electron configuration. Estimation of the effective interaction, which turns out to require a multiorbital model that takes account of all the orbitals involved on the Fermi surface, shows that the effective interactions are… ▽ More Effective models are constructed for a newly discovered superconductor (Nd,Sr)NiO2, which has been considered as a possible nickelate analogue of the cuprates owing to the d9 electron configuration. Estimation of the effective interaction, which turns out to require a multiorbital model that takes account of all the orbitals involved on the Fermi surface, shows that the effective interactions are significantly larger than in the cuprates. A fluctuation exchange study for the model indicates that dx2-y2-wave superconductivity is likely to occur as in the cuprates, where the transition temperature in the nickelate can be lower from the cuprates due to the larger interaction and narrower bandwidth. △ Less

Submitted 4 September, 2019; v1 submitted 30 August, 2019; originally announced September 2019.

Comments: Contains three figures in the main text. Version 1 and 2 are essentially the same, except that Fig. S3-S5 are newly added in the supplemental material

Journal ref: Phys. Rev. Lett. 125, 077003 (2020)

Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions

Authors: Tohru Kawarabayashi, Hideo Aoki, Yasuhiro Hatsugai

Abstract: The doubling of massless Dirac fermions on two-dimensional lattices is theoretically studied. It has been shown that the doubling of massless Dirac fermions on a lattice with broken chiral symmetry is topologically protected even when the Dirac cone is tilted. This is due to the generalized chiral symmetry defined for lattice systems, where such models can be generated by a deformation of the chir… ▽ More The doubling of massless Dirac fermions on two-dimensional lattices is theoretically studied. It has been shown that the doubling of massless Dirac fermions on a lattice with broken chiral symmetry is topologically protected even when the Dirac cone is tilted. This is due to the generalized chiral symmetry defined for lattice systems, where such models can be generated by a deformation of the chiral-symmetric lattice models. The present paper shows for two-band lattice models that this is a general way to produce systems with the generalized chiral symmetry in that such systems can always be transformed back to a lattice model with the conventional chiral symmetry. We specifically show that the number of zero modes is an invariant of the transformation, leading to the topological protection à la Nielsen-Ninomiya of the doubling of tilted and massless Dirac fermions in two dimensions. △ Less

Submitted 10 April, 2019; originally announced April 2019.

Comments: 5 pages, 3 figures, ICPS 2018

Journal ref: Phys. Status Solidi B, 1800524 (2019)

Pairing and non-Fermi liquid behavior in partially flat-band systems

Authors: Sharareh Sayyad, Edwin W. Huang, Motoharu Kitatani, Mohammad-Sadegh Vaezi, Zohar Nussinov, Abolhassan Vaezi, Hideo Aoki

Abstract: While multiband systems are usually considered for flat-band physics, here we study one-band models that have flat portions in the dispersion to explore correlation effects in the 2D repulsive Hubbard model in an intermediate coupling regime. The FLEX+DMFT~(the dynamical mean-field theory combined with the fluctuation exchange approximation) is used to show that we have a crossover from ferromagne… ▽ More While multiband systems are usually considered for flat-band physics, here we study one-band models that have flat portions in the dispersion to explore correlation effects in the 2D repulsive Hubbard model in an intermediate coupling regime. The FLEX+DMFT~(the dynamical mean-field theory combined with the fluctuation exchange approximation) is used to show that we have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied, which triggers a crossover from triplet to singlet pairings with a peculiar filling dependence that is dominated by the size of the flat region in the dispersion. A curious manifestation of the flat part appears as larger numbers of nodal lines associated with pairs extended in real space. We further detect non-Fermi liquid behavior in the momentum distribution function, frequency dependence of the self-energy and spectral function. These indicate correlation physics peculiar to flat-band systems. △ Less

Submitted 11 December, 2019; v1 submitted 23 March, 2019; originally announced March 2019.

Comments: 7+2 pages

Journal ref: Phys. Rev. B 101, 014501 (2020)

SO(4) FLEX+DMFT formalism with SU(2)$\otimes$SU(2)-symmetric impurity solver for superconductivity in the repulsive Hubbard model

Authors: Sharareh Sayyad, Naoto Tsuji, Massimo Capone, Hideo Aoki

Abstract: Here we have developed a FLEX+DMFT formalism, where the symmetry properties of the system are incorporated by constructing a SO(4) generalization of the conventional fluctuation-exchange approximation (FLEX) coupled self-consistently to the dynamical mean-field theory (DMFT). Along with this line, we emphasize that the SO(4) symmetry is the lowest group-symmetry that enables us to investigate supe… ▽ More Here we have developed a FLEX+DMFT formalism, where the symmetry properties of the system are incorporated by constructing a SO(4) generalization of the conventional fluctuation-exchange approximation (FLEX) coupled self-consistently to the dynamical mean-field theory (DMFT). Along with this line, we emphasize that the SO(4) symmetry is the lowest group-symmetry that enables us to investigate superconductivity and antiferromagnetism on an equal footing. We have imposed this by decomposing the electron operator into auxiliary fermionic and slave-boson constituents that respect SU(2)$_{\rm spin}\otimes$SU(2)$_{η{\rm spin}}$. This is used not in a mean-field treatment as in the usual slave-boson formalisms, but instead in the DMFT impurity solver with an SU(2)$_{\rm spin}\otimes$SU(2)$_{η{\rm spin}}$ hybridization function to incorporate the FLEX-generated bath information into DMFT iterations. While there have been attempts such as the doublon-less SU(2) slave-boson formalism, the present "full-SU(2)" slave-boson formalism is expected to provide a new platform for addressing the underlying physics for various quantum orders, which compete with each other and can coexist. △ Less

Submitted 13 March, 2019; originally announced March 2019.

Comments: 12+15 pages

Momentum-dependent relaxation dynamics of the doped repulsive Hubbard model

Authors: Sharareh Sayyad, Naoto Tsuji, Abolhassan Vaezi, Massimo Capone, Martin Eckstein, Hideo Aoki

Abstract: We study the dynamical behavior of doped electronic systems subject to a global ramp of the repulsive Hubbard interaction. We start with formulating a real-time generalization of the fluctuation-exchange approximation. Implementing this numerically, we investigate the weak-coupling regime of the Hubbard model both in the electron-doped and hole-doped regimes. The results show that both local and n… ▽ More We study the dynamical behavior of doped electronic systems subject to a global ramp of the repulsive Hubbard interaction. We start with formulating a real-time generalization of the fluctuation-exchange approximation. Implementing this numerically, we investigate the weak-coupling regime of the Hubbard model both in the electron-doped and hole-doped regimes. The results show that both local and nonlocal (momentum-dependent) observables evolve toward a thermal state, although the temperature of the final state depends on the ramp duration and the chemical doping. We further reveal a momentum-dependent relaxation rate of the distribution function in doped systems, and trace back its physical origin to the anisotropic self-energies in the momentum space. △ Less

Submitted 28 November, 2018; originally announced November 2018.

Comments: 10 pages, 11 figures

Journal ref: Phys. Rev. B 99, 165132 (2019)

Superconductivity arising from layer-differentiation in multi-layer cuprates

Authors: Kazutaka Nishiguchi, Shingo Teranishi, Koichi Kusakabe, Hideo Aoki

Abstract: In order to theoretically identify the factors governing superconductivity in multi-layer cuprates, a three-layer Hubbard model is studied with the two-particle self-consistent (TPSC) approach so as to incorporate electron correlations. The linearized Eliashberg equation is then solved for the gap function in a matrix form to resolve the role of outer CuO$_2$ planes (OPs) and inner plane (IP). We… ▽ More In order to theoretically identify the factors governing superconductivity in multi-layer cuprates, a three-layer Hubbard model is studied with the two-particle self-consistent (TPSC) approach so as to incorporate electron correlations. The linearized Eliashberg equation is then solved for the gap function in a matrix form to resolve the role of outer CuO$_2$ planes (OPs) and inner plane (IP). We show that OPs dominate IP in the $d_{x^{2}-y^{2}}$-wave superconductivity, while IP dominates in the antiferromagnetism. This comes from an electron correlation effect in that the correlation makes the doping rates different between OPs and IP (i.e., a self-doping effect), which occurs in intermediate and strong correlation regimes. Namely, the antiferromagnetic fluctuations in IP are stronger due to a stronger electron correlation, which simultaneously reduces the quasiparticle density of states in IP with a suppressed $d_{x^{2}-y^{2}}$-wave superconductivity. Intriguingly, while the off-diagonal (inter-layer) elements in the gap function matrix are tiny, {\it inter-layer pair scattering} processes are in fact at work in enhancing the superconducting transition temperature $T_{\text{c}}$ through the inter-layer Green's functions. This actually causes the trilayer system to have higher $T_{\text{c}}$ than the single-layer in a weak- and intermediate-coupling regimes. This picture holds for a range of the on-site Hubbard repulsion $U$ that contains those estimated for the cuprates. The present result is qualitatively consistent with nuclear magnetic resonance experiments in multi-layer cuprates superconductors. △ Less

Submitted 24 October, 2018; v1 submitted 12 June, 2018; originally announced June 2018.

Comments: 10 pages, 8 figures, to be submitted in Physical Review B

Journal ref: Phys. Rev. B 98, 174508 (2018)

Why the critical temperature of high-$T_{\rm c}$ cuprate superconductors is so low: The importance of the dynamical vertex structure

Authors: Motoharu Kitatani, Thomas Schäfer, Hideo Aoki, Karsten Held

Abstract: To fathom the mechanism of high-temperature ($T_{\rm c}$) superconductivity, the dynamical vertex approximation (D$Γ$A) is evoked for the two-dimensional repulsive Hubbard model. After showing that our results well reproduce the cuprate phase diagram with a reasonable $T_{\rm c}$ and dome structure, we keep track of the scattering processes that primarily affect $T_{\rm c}$. We find that local par… ▽ More To fathom the mechanism of high-temperature ($T_{\rm c}$) superconductivity, the dynamical vertex approximation (D$Γ$A) is evoked for the two-dimensional repulsive Hubbard model. After showing that our results well reproduce the cuprate phase diagram with a reasonable $T_{\rm c}$ and dome structure, we keep track of the scattering processes that primarily affect $T_{\rm c}$. We find that local particle-particle diagrams significantly screen the bare interaction at low frequencies, which in turn suppresses antiferromagnetic spin fluctuations and hence the pairing interaction. Thus we identify dynamical vertex corrections as one of the main oppressors of $T_{\rm c}$, which may provide a hint toward higher $T_{\rm c}$'s. △ Less

Submitted 25 January, 2019; v1 submitted 18 January, 2018; originally announced January 2018.

Comments: 6+5 pages, 5+6 figures

Journal ref: Phys. Rev. B 99, 041115 (2019)

Higgs mode in the d-wave superconductor Bi2Sr2CaCu2O8+x driven by an intense terahertz pulse

Authors: Kota Katsumi, Naoto Tsuji, Yuki I. Hamada, Ryusuke Matsunaga, John Schneeloch, Ruidan D. Zhong, Genda. D. Gu, Hideo Aoki, Yann Gallais, Ryo Shimano

Abstract: We investigated the terahertz (THz)-pulse driven nonlinear response in the d-wave cuprate superconductor Bi2Sr2CaCu2O8+x (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We have observed an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is strongly enhanced below Tc. The corresponding third-order nonlinear effect exhibits bo… ▽ More We investigated the terahertz (THz)-pulse driven nonlinear response in the d-wave cuprate superconductor Bi2Sr2CaCu2O8+x (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We have observed an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is strongly enhanced below Tc. The corresponding third-order nonlinear effect exhibits both A1g and B1g symmetry components, which are decomposed from polarization-resolved measurements. Comparison with a BCS calculation of the nonlinear susceptibility indicates that the A1g component is associated with the Higgs mode of the d-wave order parameter. △ Less

Submitted 13 November, 2017; originally announced November 2017.

Comments: 14 pages, 4 figures + supplemental material

Journal ref: Phys. Rev. Lett. 120, 117001 (2018)

New class of flat-band models on tetragonal and hexagonal lattices: Gapped versus crossing flat bands

Authors: Tatsuhiro Misumi, Hideo Aoki

Abstract: We propose a new class of tight-binding models where a flat band is either gapped from or crossing right through a dispersive band on two-band (i.e., two sites/unit cell) tetragonal and honeycomb lattices. By imposing a condition on the hopping parameters for generic models with up to third-neighbor hoppings, we first obtain models having a rigorously flat band isolated from a dispersive band with… ▽ More We propose a new class of tight-binding models where a flat band is either gapped from or crossing right through a dispersive band on two-band (i.e., two sites/unit cell) tetragonal and honeycomb lattices. By imposing a condition on the hopping parameters for generic models with up to third-neighbor hoppings, we first obtain models having a rigorously flat band isolated from a dispersive band with a gap, which accommodate both rank-reducing and non-rank-reducing of the Hamiltonian. The class of models include Tasaki's flat-band models, but the present model has a nonzero flat-band energy, whose gap from the dispersive band is controllable as well. We then modify the models by appropriately changing the second- or third-neighbor hoppings, leading to a new class of two-dimensional lattices where a (slightly warped) flat band pierces a dispersive one. As with the known flat-band models, the connectivity condition is satisfied in the present models, so that we have unusual, unorthogonalizable Wannier orbitals. We have also shown that the present flat-band model can be extended to three (or higher) dimensions. Implications on possible high-$T_{C}$ superconductivity are discussed when a repulsive electron-electron interaction is introduced, where the flat band is envisaged to be utilized as intermediate states in pair scattering processes. △ Less

Submitted 19 October, 2017; v1 submitted 17 August, 2017; originally announced August 2017.

Comments: 13 pages, 14 figures; typos corrected, references added, version to appear in PRB

Journal ref: Phys. Rev. B 96, 155137 (2017)

Possible high-$T_c$ superconductivity due to incipient narrow bands originating from hidden ladders in Ruddlesden-Popper compounds

Authors: Daisuke Ogura, Hideo Aoki, Kazuhiko Kuroki

Abstract: We introduce a concept of hidden ladders for the bilayer Ruddlesden-Popper type compounds: While the crystal structure is bilayer, $d_{xz}$ ($d_{yz}$) orbitals in the relevant $t_{2g}$ sector of the transition metal form a two-leg ladder along $x$ ($y$), since the $d_{xz}$ ($d_{yz}$) electrons primarily hop along the leg direction $x$ ($y$) on top of the rung $z$ direction. We predict that Sr$_3$M… ▽ More We introduce a concept of hidden ladders for the bilayer Ruddlesden-Popper type compounds: While the crystal structure is bilayer, $d_{xz}$ ($d_{yz}$) orbitals in the relevant $t_{2g}$ sector of the transition metal form a two-leg ladder along $x$ ($y$), since the $d_{xz}$ ($d_{yz}$) electrons primarily hop along the leg direction $x$ ($y$) on top of the rung $z$ direction. We predict that Sr$_3$Mo$_2$O$_7$ and Sr$_3$Cr$_2$O$_7$ are candidates for the hidden-ladder material with a right position of $E_F$, from a first-principles band calculation. Based on the analysis of Eliashberg equation for these systems, we propose a possible occurrence of high temperature superconductivity in these materials arising from the interband pair scattering processes between the wide and "incipient" narrow bands on the ladder. △ Less

Submitted 17 November, 2017; v1 submitted 6 June, 2017; originally announced June 2017.

Comments: 8 pages, 7 figures, published version

Journal ref: Phys. Rev. B 96, 184513 (2017)

Probing and controlling spin chirality in Mott insulators by circularly polarized laser

Authors: Sota Kitamura, Takashi Oka, Hideo Aoki

Abstract: Scalar spin chirality, a three-body spin correlation that breaks time-reversal symmetry, is revealed to couple directly to circularly polarized laser. This is shown by the Floquet formalism for the periodically driven repulsive Hubbard model with a strong-coupling expansion. A systematic derivation of the effective low-energy Hamiltonian for a spin degree of freedom reveals that the coupling const… ▽ More Scalar spin chirality, a three-body spin correlation that breaks time-reversal symmetry, is revealed to couple directly to circularly polarized laser. This is shown by the Floquet formalism for the periodically driven repulsive Hubbard model with a strong-coupling expansion. A systematic derivation of the effective low-energy Hamiltonian for a spin degree of freedom reveals that the coupling constant for scalar spin chirality can become significant for a situation in which the driving frequency and the on-site interaction are comparable. This implies that the scalar chirality can be induced by circularly polarized lights, or that it can be used conversely for probing the chirality in Mott insulators as a circular dichroism. △ Less

Submitted 5 July, 2017; v1 submitted 13 March, 2017; originally announced March 2017.

Comments: 10 pages, 8 figures

Journal ref: Phys. Rev. B 96, 014406 (2017)

Polarization-resolved terahertz third-harmonic generation in a superconductor NbN: dominance of Higgs mode beyond the BCS approximation

Authors: Ryusuke Matsunaga, Naoto Tsuji, Kazumasa Makise, Hirotaka Terai, Hideo Aoki, Ryo Shimano

Abstract: Recent advances in time-domain terahertz (THz) spectroscopy have unveiled that resonantly-enhanced strong THz third-harmonic generation (THG) mediated by the collective Higgs amplitude mode occurs in s-wave superconductors, where charge-density fluctuations (CDF) have also been shown to contribute to the nonlinear third-order susceptibility. It has been theoretically proposed that the nonlinear re… ▽ More Recent advances in time-domain terahertz (THz) spectroscopy have unveiled that resonantly-enhanced strong THz third-harmonic generation (THG) mediated by the collective Higgs amplitude mode occurs in s-wave superconductors, where charge-density fluctuations (CDF) have also been shown to contribute to the nonlinear third-order susceptibility. It has been theoretically proposed that the nonlinear responses of Higgs and CDF exhibit essentially different polarization dependences. Here we experimentally discriminate the two contributions by polarization-resolved intense THz transmission spectroscopy for a single-crystal NbN film. The result shows that the resonant THG in the transmitted light always appears in the polarization parallel to that of the incident light with no appreciable crystal axis dependence. When we compare this with the theoretical calculation here with the BCS approximation and the dynamical mean-field theory for a model of NbN constructed from first principles, the experimental result strongly indicates that the Higgs mode rather than the CDF dominates the THG resonance in NbN. A possible mechanism for this is discussed such as the retardation effect in the phonon-mediated pairing interaction beyond BCS. △ Less

Submitted 8 March, 2017; v1 submitted 8 March, 2017; originally announced March 2017.

Journal ref: Phys. Rev. B 96, 020505 (2017)

Electric Properties of Dirac Fermions Captured into 3D Nanoporous Graphene Networks

Authors: Yoichi Tanabe, Yoshikazu Ito, Katsuaki Sugawara, Daisuke Hojo, Mikito Koshino, Takeshi Fujita, Tsutomu Aida, Xiandong Xu, Khuong Kim Huynh, Hidekazu Shimotani, Tadafumi Adschiri, Takashi Takahashi, Katsumi Tanigaki, Hideo Aoki, Mingwei Chen

Abstract: Graphene, as a promising material of post-silicon electronics, opens a new paradigm for the novel electronic properties and device applications. On the other hand, the 2D feature of graphene makes it technically challenging to be integrated into 3D transistors with a sufficient processor capacity. Although there are many attempts to assemble 2D graphene into 3D structures, the characteristics of m… ▽ More Graphene, as a promising material of post-silicon electronics, opens a new paradigm for the novel electronic properties and device applications. On the other hand, the 2D feature of graphene makes it technically challenging to be integrated into 3D transistors with a sufficient processor capacity. Although there are many attempts to assemble 2D graphene into 3D structures, the characteristics of massless Dirac fermions cannot be well preserved in these materials for transistor applications. Here we report a high-performance graphene transistor by utilizing 3D nanoporous graphene which is comprised of an interconnected single graphene sheet and a commodious open porosity to infuse an ionic liquid for a tunable electronic state by applying electric fields. The 3D nanoporous graphene transistor, with high carrier mobility of 5000-7500 cm$^2$V$^{-1}$s$^{-1}$, exhibits two to three orders of magnitude higher electric conductance and capacitance than those of 2D graphene devices, along with preserved ambipolor electronic nature of Dirac cones. Moreover, the 3D graphene networks with Dirac fermions turn out to exhibit a unique nonlinear Hall resistance in a wide range of the gate voltages. The high quality 3D nanoporous graphene EDLT may open a new field for utilizing Dirac fermions in 3D network structures for various fundamental and practical applications. △ Less

Submitted 17 December, 2016; originally announced December 2016.

Comments: 25 page, 11 Figures, 1 Tables

Journal ref: Advanced Materials 28, 10304 (2016)

Lattice realization of the generalized chiral symmetry in two dimensions

Authors: T. Kawarabayashi, H. Aoki, Y. Hatsugai

Abstract: While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a continuous low-energy Hamiltonian. Here we show that the generalized chiral symmetry can be rigorously defined for lattice fermions as well. A key concept is a conti… ▽ More While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a continuous low-energy Hamiltonian. Here we show that the generalized chiral symmetry can be rigorously defined for lattice fermions as well. A key concept is a continuous "algebraic deformation" of Hamiltonians, which generates lattice models with the generalized chiral symmetry from those with the conventional chiral symmetry. This enables us to explicitly express zero modes of the deformed Hamiltonian in terms of that of the original Hamiltonian. Another virtue is that the deformation can be extended to non-uniform systems, such as fermion-vortex systems and disordered systems. Application to fermion vortices in a deformed system shows how the zero modes for the conventional Dirac fermions with vortices can be extended to the tilted case. △ Less

Submitted 9 December, 2016; v1 submitted 23 September, 2016; originally announced September 2016.

Comments: 11 pages, 10 figures

Journal ref: Phys. Rev. B 94, 235307 (2016)

Interplay of Pomeranchuk instability and superconductivity in the two-dimensional repulsive Hubbard model

Authors: Motoharu Kitatani, Naoto Tsuji, Hideo Aoki

Abstract: Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and d-wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the four-fold symmetric Fermi surface becomes unstable against a spontaneous distortion into two-fol… ▽ More Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and d-wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the four-fold symmetric Fermi surface becomes unstable against a spontaneous distortion into two-fold near the van Hove filling, where the symmetry of superconductivity coexisting with the Pomeranchuk distorted Fermi surface is modified from the d-wave pairing to (d+s)-wave. By systematically shifting the position of van Hove filling with varied second- and third-neighbor hoppings, we find that the transition temperature $T_{\rm c}^{\rm PI}$ of Pomeranchuk instability is more sensitively affected by the position of van Hove filling than the superconducting $T_{\rm c}^{\rm SC}$. This implies that the filling region for strong Pomeranchuk instability and that for strong superconducting fluctuations can be separated, and Pomeranchuk instability can appear even if the peak of $T_c^{\rm PI}$ is lower than the peak of $T_c^{\rm SC}$. An interesting observation is that the Fermi surface distortion can enhance the superconducting $T_{\rm c}^{\rm SC}$ in the overdoped regime, which is explained with a perturbation picture for small distortions. △ Less

Submitted 7 February, 2017; v1 submitted 19 September, 2016; originally announced September 2016.

Comments: 8 pages, 5 figures

Journal ref: Phys. Rev. B 95, 075109 (2017)

Superconductivity in repulsively interacting fermions on a diamond chain: flat-band induced pairing

Authors: Keita Kobayashi, Masahiko Okumura, Susumu Yamada, Masahiko Machida, Hideo Aoki

Abstract: To explore whether a flat-band system can accommodate superconductivity, we consider repulsively interacting fermions on the diamond chain, a simplest quasi-one-dimensional system that contains a flat band. Exact diagonalization and the density-matrix renormalization group (DMRG) are used to show that we have a significant binding energy of a Cooper pair with a long-tailed pair-pair correlation in… ▽ More To explore whether a flat-band system can accommodate superconductivity, we consider repulsively interacting fermions on the diamond chain, a simplest quasi-one-dimensional system that contains a flat band. Exact diagonalization and the density-matrix renormalization group (DMRG) are used to show that we have a significant binding energy of a Cooper pair with a long-tailed pair-pair correlation in real space when the total band filling is slightly below $1/3$, where the dispersive band interacts with the flat band that is empty but close to $E_F$. Pairs selectively formed across the outer sites of the diamond chain are responsible for the pairing correlation. At exactly $1/3$-filling an insulating phase emerges, where the entanglement spectrum indicates the particles on the outer sites are highly entangled and topological. These come from a peculiarity of the flat band in which "Wannier orbits" are not orthogonalizable. △ Less

Submitted 28 October, 2016; v1 submitted 30 July, 2016; originally announced August 2016.

Comments: Phys. Rev. B, to be published

Journal ref: Physical Review B, 94, 214501 (2016)

Nonlinear light-Higgs coupling in superconductors beyond BCS: Effects of the retarded phonon-mediated interaction

Authors: Naoto Tsuji, Yuta Murakami, Hideo Aoki

Abstract: We study the contribution of the Higgs amplitude mode on the nonlinear optical response of superconductors beyond the BCS approximation by taking into account the retardation effect in the phonon-mediated attractive interaction. To evaluate the vertex correction in nonlinear optical susceptibilities that contains the effect of collective modes, we propose an efficient scheme which we call the "dot… ▽ More We study the contribution of the Higgs amplitude mode on the nonlinear optical response of superconductors beyond the BCS approximation by taking into account the retardation effect in the phonon-mediated attractive interaction. To evaluate the vertex correction in nonlinear optical susceptibilities that contains the effect of collective modes, we propose an efficient scheme which we call the "dotted DMFT" based on the nonequilibrium dynamical mean-field theory (nonequilibrium DMFT) to go around the difficulty of solving the Bethe-Salpeter equation and analytical continuation. The vertex correction is represented by the derivative of the self-energy with respect to the external driving field, which is self-consistently determined by the differentiated ("dotted") DMFT equations. We apply the method to the Holstein model, a prototypical electron-phonon-coupled system, to calculate the susceptibility for the third-harmonic generation including the vertex correction. The results show that, in sharp contrast to the BCS theory, the Higgs mode can contribute to the third-harmonic generation for general polarization of the laser field with an order of magnitude comparable to the contribution from the pair breaking or charge density fluctuations. The physical origin is traced back to the nonlinear resonant light-Higgs coupling, which has been absent in the BCS approximation. △ Less

Submitted 29 November, 2016; v1 submitted 15 June, 2016; originally announced June 2016.

Journal ref: Phys. Rev. B 94, 224519 (2016)

Optical Evidence of Itinerant-Localized Crossover of $4f$ Electrons in Cerium Compounds

Authors: Shin-ichi Kimura, Yong Seung Kwon, Yuji Matsumoto, Haruyoshi Aoki, Osamu Sakai

Abstract: Cerium (Ce)-based heavy-fermion materials have a characteristic double-peak structure (mid-IR peak) in the optical conductivity [$σ(ω)$] spectra originating from the strong conduction ($c$)--$f$ electron hybridization. To clarify the behavior of the mid-IR peak at a low $c$-$f$ hybridization strength, we compared the $σ(ω)$ spectra of the isostructural antiferromagnetic and heavy-fermion Ce compou… ▽ More Cerium (Ce)-based heavy-fermion materials have a characteristic double-peak structure (mid-IR peak) in the optical conductivity [$σ(ω)$] spectra originating from the strong conduction ($c$)--$f$ electron hybridization. To clarify the behavior of the mid-IR peak at a low $c$-$f$ hybridization strength, we compared the $σ(ω)$ spectra of the isostructural antiferromagnetic and heavy-fermion Ce compounds with the calculated unoccupied density of states and the spectra obtained from the impurity Anderson model. With decreasing $c$-$f$ hybridization intensity, the mid-IR peak shifts to the low-energy side owing to the renormalization of the unoccupied $4f$ state, but suddenly shifts to the high-energy side owing to the $f$-$f$ on-site Coulomb interaction at a slight localized side from the quantum critical point (QCP). This finding gives us information on the change in the electronic structure across QCP. △ Less

Submitted 30 June, 2016; v1 submitted 16 May, 2016; originally announced May 2016.

Comments: 6 pages, 4 figures. To appear in JPSJ (Letters)

Journal ref: J. Phys. Soc. Jpn. 85, 083702 (2016)

Damping of the Collective Amplitude Mode in Superconductors with Strong Electron-Phonon Coupling

Authors: Y. Murakami, P. Werner, N. Tsuji, H. Aoki

Abstract: We study the effect of strong electron-phonon interactions on the damping of the Higgs amplitude mode in superconductors by means of non-equilibrium dynamical mean-field simulations of the Holstein model. In contrast to the BCS dynamics, we find that the damping of the Higgs mode strongly depends on the temperature, becoming faster as the systen approaches the transition temperature. The damping a… ▽ More We study the effect of strong electron-phonon interactions on the damping of the Higgs amplitude mode in superconductors by means of non-equilibrium dynamical mean-field simulations of the Holstein model. In contrast to the BCS dynamics, we find that the damping of the Higgs mode strongly depends on the temperature, becoming faster as the systen approaches the transition temperature. The damping at low temperatures is well described by a power-law, while near the transition temperature the damping shows exponential-like behavior. We explain this crossover by a temperature-dependent quasiparticle lifetime caused by the strong electron- phonon coupling, which smears the superconducting gap edge and makes the relaxation of the Higgs mode into quasiparticles more efficient at elevated temperatures. We also reveal that the phonon dynamics can soften the Higgs mode, which results in a slower damping. △ Less

Submitted 18 September, 2016; v1 submitted 27 April, 2016; originally announced April 2016.

Comments: 7 pages,6 figures

Journal ref: Phys. Rev. B 94, 115126 (2016)

$η$-pairing superfluid in periodically-driven fermionic Hubbard model with strong attraction

Authors: Sota Kitamura, Hideo Aoki

Abstract: We propose a novel possibility of dynamically changing the pairing of superconductors from $s$ wave to $η$ pairing (where the pairs condense at the Brillouin-zone corner momenta) by driving the system with ac fields. We consider a periodically-driven attractive Hubbard model in the strong-coupling regime, and show that the pair-hopping and pair-repulsion terms in the effective Hamiltonian in the F… ▽ More We propose a novel possibility of dynamically changing the pairing of superconductors from $s$ wave to $η$ pairing (where the pairs condense at the Brillouin-zone corner momenta) by driving the system with ac fields. We consider a periodically-driven attractive Hubbard model in the strong-coupling regime, and show that the pair-hopping and pair-repulsion terms in the effective Hamiltonian in the Floquet formalism are drastically renormalized in different manners between the two terms, which can change the ground states from an $s$-wave superconductivity to an $η$-pairing superconductivity or a charge-ordered phase. While in isolated systems such as cold atoms a simple quench scheme would not realize the dynamical phase transition into $η$ pairing, we show that there are pathways that realize the dynamical transition, where the field amplitude is varied via a charge-ordered phase as an intermediate state. △ Less

Submitted 10 November, 2016; v1 submitted 24 November, 2015; originally announced November 2015.

Comments: 10 pages, 9 figures

Journal ref: Phys. Rev. B 94, 174503 (2016)

Multiple amplitude modes in strongly-coupled phonon-mediated superconductors

Authors: Yuta Murakami, Philipp Werner, Naoto Tsuji, Hideo Aoki

Abstract: We study collective amplitude modes of the superconducting order parameter in strongly-coupled electron-phonon systems described by the Holstein model using the nonequilibrium dynamical mean-field theory with the self-consistent Migdal approximation as an impurity solver. The frequency of the Higgs amplitude mode is found to coincide with the superconducting gap even in the strongly-coupled (beyon… ▽ More We study collective amplitude modes of the superconducting order parameter in strongly-coupled electron-phonon systems described by the Holstein model using the nonequilibrium dynamical mean-field theory with the self-consistent Migdal approximation as an impurity solver. The frequency of the Higgs amplitude mode is found to coincide with the superconducting gap even in the strongly-coupled (beyond BCS) regime. Besides the Higgs mode, we unravel another collective mode involving the dynamics of both the phonons and the superconducting order parameter. The frequency of this mode, higher than twice the renormalized phonon frequency in the superconducting phase, is shown to reflect a strong electron-mediated phonon-phonon interaction. Both types of collective excitations contribute to time-resolved photoemission spectra after a strong laser pump as vertex corrections to produce resonance peaks, which allows one to distinguish them from quasiparticle excitations. △ Less

Submitted 15 June, 2017; v1 submitted 19 November, 2015; originally announced November 2015.

Comments: 11pages, 11figures published version

Journal ref: Phys. Rev. B 93, 094509 (2016)

Theory of light-induced resonances with collective Higgs and Leggett modes in multiband superconductors

Authors: Yuta Murotani, Naoto Tsuji, Hideo Aoki

Abstract: We theoretically investigate coherent optical excitations of collective modes in two-band BCS superconductors, which accommodate two Higgs modes and one Leggett mode corresponding, respectively, to the amplitude and relative-phase oscillations of the superconducting order parameters associated with the two bands. We find, based on a mean-field analysis, that each collective mode can be resonantly… ▽ More We theoretically investigate coherent optical excitations of collective modes in two-band BCS superconductors, which accommodate two Higgs modes and one Leggett mode corresponding, respectively, to the amplitude and relative-phase oscillations of the superconducting order parameters associated with the two bands. We find, based on a mean-field analysis, that each collective mode can be resonantly excited through a nonlinear light-matter coupling when the doubled frequency of the driving field coincides with the frequency of the corresponding mode. Among the two Higgs modes, the higher-energy one exhibits a sharp resonance with light, while the lower-energy mode has a broadened resonance width. The Leggett mode is found to be resonantly induced by a homogeneous ac electric field because the leading nonlinear effect generates a potential offset between the two bands that couples to the relative phase of the order parameters. The resonance for the Leggett mode becomes sharper with increasing temperature. All of these light-induced collective modes along with density fluctuations contribute to the third-harmonic generation. We also predict an experimental possibility of optical detection of the Leggett mode. △ Less

Submitted 13 December, 2016; v1 submitted 18 November, 2015; originally announced November 2015.

Comments: 12 pages, 7 figures

Journal ref: Phys. Rev. B 95, 104503 (2017)

Dirac electrons on three-dimensional graphitic zeolites --- a scalable mass gap

Authors: Mikito Koshino, Hideo Aoki

Abstract: A class of graphene wound into three-dimensional periodic curved surfaces ("graphitic zeolites") is proposed and their electronic structures are obtained to explore how the massless Dirac fermions behave on periodic surfaces. We find in the tight-binding model that the low-energy band structure around the charge neutrality point is dominated by the topology (cubic or gyroid) of the periodic surfac… ▽ More A class of graphene wound into three-dimensional periodic curved surfaces ("graphitic zeolites") is proposed and their electronic structures are obtained to explore how the massless Dirac fermions behave on periodic surfaces. We find in the tight-binding model that the low-energy band structure around the charge neutrality point is dominated by the topology (cubic or gyroid) of the periodic surface as well as by the spatial period $L$ in modulo 3 in units of the lattice constant. In both of cubic and gyroid cases the Dirac electrons become massive around the charge neutrality point, where the band gap is shown to scale as $1/L$ within each mod-3 class. Wave functions around the gap are found to have amplitudes sharply peaked around the topological defects that are required to deform the graphene sheet into a three-dimensional periodic surface, and this is shown to originate from non-trivial Bloch phases at $K$ and $K'$ points of the original graphene. △ Less

Submitted 1 December, 2015; v1 submitted 9 November, 2015; originally announced November 2015.

Comments: 5 pages, 6 figures

Journal ref: Phys. Rev. B 93, 041412(R) (2016)

Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators

Authors: Takahiro Mikami, Sota Kitamura, Kenji Yasuda, Naoto Tsuji, Takashi Oka, Hideo Aoki

Abstract: We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hamiltonian on the projected zero-photon subspace in the Floquet theory, reproducing the quasienergies and eigenstates of the original Floquet Hamiltonian up to desired order in $1/ω$, with $ω$ being the frequency of the dri… ▽ More We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hamiltonian on the projected zero-photon subspace in the Floquet theory, reproducing the quasienergies and eigenstates of the original Floquet Hamiltonian up to desired order in $1/ω$, with $ω$ being the frequency of the drive. The advantage of the BW method is that it is not only efficient in deriving higher-order terms, but even enables us to write down the whole infinite series expansion, as compared to the van Vleck degenerate perturbation theory. The expansion is also free from a spurious dependence on the driving phase, which has been an obstacle in the Floquet-Magnus expansion. We apply the BW expansion to various models of noninteracting electrons driven by circularly polarized light. As the amplitude of the light is increased, the system undergoes a series of Floquet topological-to-topological phase transitions, whose phase boundary in the high-frequency regime is well explained by the BW expansion. As the frequency is lowered, the high-frequency expansion breaks down at some point due to band touching with nonzero-photon sectors, where we find numerically even more intricate and richer Floquet topological phases spring out. We have then analyzed, with the Floquet dynamical mean-field theory, the effects of electron-electron interaction and energy dissipation. We have specifically revealed that phase transitions from Floquet-topological to Mott insulators emerge, where the phase boundaries can again be captured with the high-frequency expansion. △ Less

Submitted 1 May, 2016; v1 submitted 2 November, 2015; originally announced November 2015.

Comments: 26 pages, 19 figures

Journal ref: Phys. Rev. B 93, 144307 (2016)

First-Principles Design of a Half-Filled Flat Band of the Kagome Lattice in Two-Dimensional Metal-Organic Frameworks

Authors: Masahiko G. Yamada, Tomohiro Soejima, Naoto Tsuji, Daisuke Hirai, Mircea Dincă, Hideo Aoki

Abstract: We design from first principles a new type of two-dimensional metal-organic frameworks (MOFs) using phenalenyl-based ligands to exhibit a half-filled flat band of the kagome lattice, which is one of the lattice family that shows Lieb-Mielke-Tasaki's flat-band ferromagnetism. Among various MOFs, we find that $\textit{trans}$-Au-THTAP(trihydroxytriaminophenalenyl) has such an ideal band structure, w… ▽ More We design from first principles a new type of two-dimensional metal-organic frameworks (MOFs) using phenalenyl-based ligands to exhibit a half-filled flat band of the kagome lattice, which is one of the lattice family that shows Lieb-Mielke-Tasaki's flat-band ferromagnetism. Among various MOFs, we find that $\textit{trans}$-Au-THTAP(trihydroxytriaminophenalenyl) has such an ideal band structure, where the Fermi energy is adjusted right at the flat band due to unpaired electrons of radical phenalenyl. The spin-orbit coupling opens a band gap giving a non-zero Chern number to the nearly flat band, as confirmed by the presence of the edge states in first-principles calculations and by fitting to the tight-binding model. This is a novel and realistic example of a system in which a nearly flat band is both ferromagnetic $\textit{and}$ topologically non-trivial. △ Less

Submitted 26 July, 2016; v1 submitted 1 October, 2015; originally announced October 2015.

Comments: 6+7 pages, 3+5 figures, 0+1 table; the phonon dispersion added; the final submitted version to appear in PRB-RC

Journal ref: Phys. Rev. B 94, 081102(R) (2016)

Electronic structure of helicoidal graphene: massless Dirac particles on a curved surface with a screw symmetry

Authors: Masataka Watanabe, Hisato Komatsu, Naoto Tsuji, Hideo Aoki

Abstract: Massless Dirac particles on the helicoid are theoretically investigated. With its possible application being helical graphene, we explore how the peculiarities of Dirac particles appear on the curved, screw-symmetric surface. The zweibein is used to derive the massless Dirac equation on the helicoid, as well as general curved surfaces. Bound states of massless Dirac electrons are shown to be absen… ▽ More Massless Dirac particles on the helicoid are theoretically investigated. With its possible application being helical graphene, we explore how the peculiarities of Dirac particles appear on the curved, screw-symmetric surface. The zweibein is used to derive the massless Dirac equation on the helicoid, as well as general curved surfaces. Bound states of massless Dirac electrons are shown to be absent on the helicoid, and then the scattering probabilities and the phase shifts on the surface are obtained from numerically calculated wave functions. We find the local density of states and the phase shifts idiosyncratic especially around the axis of the helicoid. Bound states of massive Dirac electrons on the surface are also shown to be absent as an extension of the above result on massless Dirac electrons. △ Less

Submitted 23 October, 2015; v1 submitted 19 May, 2015; originally announced May 2015.

Comments: 9 pages, 11 figures

Journal ref: Phys. Rev. B 92, 205425 (2015)

FLEX+DMFT approach to the $d$-wave superconducting phase diagram of the two-dimensional Hubbard model

Authors: Motoharu Kitatani, Naoto Tsuji, Hideo Aoki

Abstract: The dynamical mean-field theory (DMFT) combined with the fluctuation exchange (FLEX) method, namely FLEX+DMFT, is an approach for correlated electron systems to incorporate both local and non-local long-range correlations in a self-consistent manner. We formulate FLEX+DMFT in a systematic way starting from a Luttinger-Ward functional, and apply it to study the $d$-wave superconductivity in the two… ▽ More The dynamical mean-field theory (DMFT) combined with the fluctuation exchange (FLEX) method, namely FLEX+DMFT, is an approach for correlated electron systems to incorporate both local and non-local long-range correlations in a self-consistent manner. We formulate FLEX+DMFT in a systematic way starting from a Luttinger-Ward functional, and apply it to study the $d$-wave superconductivity in the two-dimensional repulsive Hubbard model. The critical temperature ($T_c$) curve obtained in the FLEX+DMFT exhibits a dome structure as a function of the filling, which has not been clearly observed in the FLEX approach alone. We trace back the origin of the dome to the local vertex correction from DMFT that renders a filling dependence in the FLEX self-energy. We compare the results with those of GW+DMFT, where the $T_c$-dome structure is qualitatively reproduced due to the same vertex correction effect, but a crucial difference from FLEX+DMFT is that $T_c$ is always estimated below the Néel temperature in GW+DMFT. The single-particle spectral function obtained with FLEX+DMFT exhibits a double-peak structure as a precursor of the Hubbard bands at temperature above $T_c$. △ Less

Submitted 19 August, 2015; v1 submitted 19 May, 2015; originally announced May 2015.

Comments: 8 pages, 7 figures

Journal ref: Phys. Rev. B 92, 085104(2015)

Interaction-Driven Topological Insulator in Fermionic Cold Atoms on an Optical Lattice: A Design with a Density Functional Formalism

Authors: Sota Kitamura, Naoto Tsuji, Hideo Aoki

Abstract: We design an interaction-driven topological insulator for fermionic cold atoms in an optical lattice, that is, we pose the question of whether we can realize in a continuous space a spontaneous symmetry breaking induced by the inter-atom interaction into a topological Chern insulator. Such a state, sometimes called a "topological Mott insulator", has yet to be realized in solid-state systems, sinc… ▽ More We design an interaction-driven topological insulator for fermionic cold atoms in an optical lattice, that is, we pose the question of whether we can realize in a continuous space a spontaneous symmetry breaking induced by the inter-atom interaction into a topological Chern insulator. Such a state, sometimes called a "topological Mott insulator", has yet to be realized in solid-state systems, since this requires, in the tight-binding model, large offsite interactions on top of a small onsite interaction. Here we overcome the difficulty by introducing a spin-dependent potential, where a spin-selective occupation of fermions in $A$ and $B$ sublattices makes the onsite interaction Pauli-forbidden, while a sizeable inter-site interaction is achieved by a shallow optical potential with a large overlap between neighboring Wannier orbitals. This puts the system away from the tight-binding model, so that we adopt the density functional theory for cold-atoms, here extended to accommodate non-collinear spin structures emerging in the topological regime, to quantitatively demonstrate the phase transition to the topological Mott insulator. △ Less

Submitted 22 July, 2015; v1 submitted 12 November, 2014; originally announced November 2014.

Comments: 5+8 pages, 3+3 figures

Journal ref: Phys. Rev. Lett. 115, 045304 (2015)

Flat bands in Weaire-Thorpe model and silicene

Authors: Y. Hatsugai, K. Shiraishi, H. Aoki

Abstract: In order to analytically capture and identify peculiarities in the electronic structure of silicene, Weaire-Thorpe(WT) model, a standard model for treating three-dimensional (3D) silicon, is applied to silicene with the buckled 2D structure. In the original WT model for four hybridized $sp^3$ orbitals on each atom along with inter-atom hopping, the band structure can be systematically examined in… ▽ More In order to analytically capture and identify peculiarities in the electronic structure of silicene, Weaire-Thorpe(WT) model, a standard model for treating three-dimensional (3D) silicon, is applied to silicene with the buckled 2D structure. In the original WT model for four hybridized $sp^3$ orbitals on each atom along with inter-atom hopping, the band structure can be systematically examined in 3D, where flat (dispersionless) bands exist as well. For examining silicene, here we re-formulate the WT model in terms of the overlapping molecular-orbital (MO) method which enables us to describe flat bands away from the electron-holesymmetric point. The overlapping MO formalism indeed enables us to reveal an important difference: while in 3D the dipersive bands with cones are sandwiched by doubly-degenerate flat bands, in 2D the dipersive bands with cones are sandwiched by triply-degenerate and non-degenerate (nearly) flat bands, which is consistent with the original band calculation by Takeda and Shiraishi. Thus emerges a picture for why the whole band structure of silicene comprises a pair of dispersive bands with Dirac cones with each of the band touching a nearly flat (narrow) band at $Γ$. We can also recognize that, for band engineering, the bonds perpendicular to the atomic plane are crucial, and that a ferromagnetism or structural instabilities are expected if we can shift the chemical potential close to the flat bands. △ Less

Submitted 30 January, 2015; v1 submitted 29 October, 2014; originally announced October 2014.

Comments: 13 pages, 3 figures (final version) to appear in NJP

Journal ref: New J. Phys. 17 025009 (2015)

Survival of sharp $n=0$ Landau levels in massive tilted Dirac fermions: Protection by generalized chiral operator

Authors: Yasuhiro Hatsugai, Tohru Kawarabayashi, Hideo Aoki

Abstract: Anomalously sharp (delta-function-like) $n=0$ Landau level in the presence of disorder is usually considered to be a manifestation of the massless Dirac fermions in magnetic fields. This property persists even when the Dirac cone is tilted, which has been shown by Kawarabayashi et al. [Phys. Rev. B {\bf 83}, 153414 (2011)] to be a consequence of a "generalized chiral symmetry". Here we pose a ques… ▽ More Anomalously sharp (delta-function-like) $n=0$ Landau level in the presence of disorder is usually considered to be a manifestation of the massless Dirac fermions in magnetic fields. This property persists even when the Dirac cone is tilted, which has been shown by Kawarabayashi et al. [Phys. Rev. B {\bf 83}, 153414 (2011)] to be a consequence of a "generalized chiral symmetry". Here we pose a question whether this property will be washed out when the tilted Dirac fermion becomes massive. Surprisingly, the levels persist to be delta-function-like, although the mass term that splits $n=0$ Landau levels may seem to degrade the anomalous sharpness. This has been shown both numerically for a tight-binding model, and analytically in terms of the Aharonov-Casher argument extended to the massive tilted Dirac fermions. A key observation is that, while the generalized chiral symmetry is broken by the mass term, the $n=0$ Landau level remains to accommodate eigenstates of the generalized chiral operator, resulting in the robustness against chiral-symmetric disorders. Mathematically, the conventional and generalized chiral operators are related with each other via a non-unitary transformation, with which the split, nonzero-energy $n=0$ wave functions of the massive system are just gauge-transformed zero-mode wave functions of the massless system. A message is that the chiral symmetry, rather than a simpler notion of the sublattice symmetry, is essential for the robustness of the $n=0$ Landau level. △ Less

Submitted 30 January, 2015; v1 submitted 23 October, 2014; originally announced October 2014.

Comments: 13 pages, 7 figures (final version) to apper in Phys. Rev. B

Journal ref: Phys. Rev. B 91, 085112 (2015)

Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation

Authors: Yuta Murakami, Philipp Werner, Naoto Tsuji, Hideo Aoki

Abstract: We study the relaxation of the Holstein model after a sudden switch-on of the interaction by means of the nonequilibrium dynamical mean field theory, with the self-consistent Migdal approximation as an impurity solver. We show that there exists a qualitative change in the thermalization dynamics as the interaction is varied in the weak-coupling regime. On the weaker interaction side of this crosso… ▽ More We study the relaxation of the Holstein model after a sudden switch-on of the interaction by means of the nonequilibrium dynamical mean field theory, with the self-consistent Migdal approximation as an impurity solver. We show that there exists a qualitative change in the thermalization dynamics as the interaction is varied in the weak-coupling regime. On the weaker interaction side of this crossover, the phonon oscillations are damped more rapidly than the electron thermalization timescale, as determined from the relaxation of the electron momentum distribution function. On the stronger interaction side, the relaxation of the electrons becomes faster than the phonon damping. In this regime, despite long-lived phonon oscillations, a thermalized momentum distribution is realized temporarily. The origin of the thermalization crossover found here is traced back to different behaviors of the electron and phonon self-energies as a function of the electron-phonon coupling. In addition, the importance of the phonon dynamics is demonstrated by comparing the self-consistent Migdal results with those obtained with a simpler Hatree-Fock impurity solver that neglects the phonon self-energy. The latter scheme does not properly describe the evolution and thermalization of isolated electron-phonon systems. △ Less

Submitted 27 October, 2014; v1 submitted 31 July, 2014; originally announced July 2014.

Comments: 13 pages, 11 figures, minor changes

Journal ref: Phys. Rev. B 91, 045128 (2015)

Fermi Surface Properties, Metamgnetic Transition and Quantum Phase Transition of CeRu$_2$Si$_2$ and Its Alloys Probed by the dHvA Effect--Fermi Surface Studies on the Itinerant and Localized Dichotomy of $f$ Electron Nature

Authors: Haruyoshi Aoki, Noriaki Kimura, Taichi Terashima

Abstract: This article describes the Fermi surface properties of CeRu$_2$Si$_2$ and its alloy systems CeRu$_2$(Si$_x$Ge$_{1-x}$)$_2$ and Ce$_x$La$_{1-x}$Ru$_2$Si$_2$ studied by the de Haas - van Alphen (dHvA) effect. We pay particular attention to how the Fermi surface properties and the f electron state change with magnetic properties, in particular how they change associated with metamagnetic transition a… ▽ More This article describes the Fermi surface properties of CeRu$_2$Si$_2$ and its alloy systems CeRu$_2$(Si$_x$Ge$_{1-x}$)$_2$ and Ce$_x$La$_{1-x}$Ru$_2$Si$_2$ studied by the de Haas - van Alphen (dHvA) effect. We pay particular attention to how the Fermi surface properties and the f electron state change with magnetic properties, in particular how they change associated with metamagnetic transition and quantum phase transition. After summarizing the important physical properties of CeRu$_2$Si$_2$, we present the magnetic phase diagrams of CeRu$_2$(Si$_x$Ge$_{1-x}$)$_2$ and Ce$_x$La$_{1-x}$Ru$_2$Si$_2$ as a function of temperature, magnetic field and concentration $x$. From the characteristic features of the magnetic phase diagram, we argue that the ferromagnetic interaction in addition to the anitferromagnetic interaction and the Kondo effect is responsible for the magnetic properties and that the metamagnetic transitions in these systems are relevant to the ferromagnetic interaction. We summarize the Fermi surface properties of CeRu$_2$Si$_2$ in fields below the metamagnetic transition where the f electron state is now well understood theoretically as well as experimentally. We present experimental results in fields above the metamagnetic transitions in CeRu$_2$(Si$_x$Ge$_{1-x}$)$_2$ and Ce$_x$La$_{1-x}$Ru$_2$Si$_2$ as well as CeRu$_2$Si$_2$ to show that the Fermi surface properties above the metamagnetic transitions are significantly different from those below in many important aspects. We argue that the Fermi surface properties above the metamagnetic transitions are not appropriately described in terms of either itinerant or localized f electron. The experimental results in fields below the metamagnetic transitions in CeRu$_2$(Si$_x$Ge$_{1-x}$)$_2$ and Ce$_x$La$_{1-x}$Ru$_2$Si$_2$ are presented to discuss the f electron state in the ground state. The Fermi surface properties of ... △ Less

Submitted 10 April, 2014; originally announced April 2014.

Comments: 106 pages, 46 figures

Journal ref: J. Phys. Soc. Jpn. 83 (2014) 072001

Theory of Anderson pseudospin resonance with Higgs mode in superconductors

Authors: Naoto Tsuji, Hideo Aoki

Abstract: A superconductor illuminated by an ac electric field with frequency $Ω$ is theoretically found to generate a collective precession of Anderson's pseudospins, and hence a coherent amplitude oscillation of the order parameter, with a doubled frequency $2Ω$ through a nonlinear light-matter coupling. We provide a fundamental theory, based on the mean-field formalism, to show that the induced pseudospi… ▽ More A superconductor illuminated by an ac electric field with frequency $Ω$ is theoretically found to generate a collective precession of Anderson's pseudospins, and hence a coherent amplitude oscillation of the order parameter, with a doubled frequency $2Ω$ through a nonlinear light-matter coupling. We provide a fundamental theory, based on the mean-field formalism, to show that the induced pseudospin precession resonates with the Higgs amplitude mode of the superconductor at $2Ω=2Δ$ with $2Δ$ being the superconducting gap. The resonant precession is accompanied by a divergent enhancement of the third-harmonic generation (THG). By decomposing the THG susceptibility into the bare one and vertex correction, we find that the enhancement of the THG cannot be explained by individual quasiparticle excitations (pair breaking), so that the THG serves as a smoking gun for an identification of the collective Higgs mode. We further explore the effect of electron-electron scattering on the pseudospin resonance by applying the nonequilibrium dynamical mean-field theory to the attractive Hubbard model driven by ac electric fields. The result indicates that the pseudospin resonance is robust against electron correlations, although the resonance width is broadened due to electron scattering, which determines the lifetime of the Higgs mode. △ Less

Submitted 13 August, 2015; v1 submitted 10 April, 2014; originally announced April 2014.

Journal ref: Phys. Rev. B 92, 064508 (2015)

Orbital mixture effect on the Fermi surface-$T_c$ correlation in the cuprate superconductors --- bilayer vs single layer

Authors: Hirofumi Sakakibara, Katsuhiro Suzuki, Hidetomo Usui, Satoaki Miyao, Isao Maruyama, Koichi Kusakabe, Ryotaro Arita, Hideo Aoki, Kazuhiko Kuroki

Abstract: By constructing $d_{x^2-y^2}-d_{z^2}$ two-orbital models from first principles, we have obtained a systematic correlation between the Fermi surface warping and the evaluated $T_c$ for various bilayer as well as single-layer cuprates. This reveals that smaller mixture of the $d_{z^2}$ orbital component on the Fermi surface leads to both of larger Fermi surface warping and higher $T_c$. The theoreti… ▽ More By constructing $d_{x^2-y^2}-d_{z^2}$ two-orbital models from first principles, we have obtained a systematic correlation between the Fermi surface warping and the evaluated $T_c$ for various bilayer as well as single-layer cuprates. This reveals that smaller mixture of the $d_{z^2}$ orbital component on the Fermi surface leads to both of larger Fermi surface warping and higher $T_c$. The theoretical correlation strikingly resembles a systematic plot for the experimentally observed $T_c$ against the Fermi surface warping due to Pavarini {\it et al.} [Phys. Rev. Lett. {\bf 87}, 047003 (2001)], and the present result unambiguously indicates that the $d_{z^2}$ mixture is a key factor that determines $T_c$ in the cuprates. △ Less

Submitted 3 June, 2014; v1 submitted 11 March, 2014; originally announced March 2014.

Comments: 7pages, 3 figures

Journal ref: Phys. Rev. B 89 224505(2014)

Polarization as a topological quantum number in graphene

Authors: Hideo Aoki, Yasuhiro Hatsugai

Abstract: Graphene, with its quantum Hall topological (Chern) number reflecting the massless Dirac particle, is shown to harbor yet another topological quantum number. This is obtained by combining Streda's general formula for the polarization associated with a second topological number in the Diophantine equation for the Hofstadter problem, and the adiabatic continuity, earlier shown to exist between the s… ▽ More Graphene, with its quantum Hall topological (Chern) number reflecting the massless Dirac particle, is shown to harbor yet another topological quantum number. This is obtained by combining Streda's general formula for the polarization associated with a second topological number in the Diophantine equation for the Hofstadter problem, and the adiabatic continuity, earlier shown to exist between the square and honeycomb lattices by Hatsugai et al. Specifically, we can regard, from the adiabatic continuity, graphene as a ``simulator" of square lattice with half flux quantum per unit cell, which implies that the polarization topological numbers in graphene in weak magnetic fields is 1/2 per Dirac cone for the energy region between the van Hove singularities, signifying a new quantum number characterizing graphene. △ Less

Submitted 6 March, 2014; originally announced March 2014.

Comments: 2 figures

Journal ref: Phys. Rev. B 90, 045206 (2014)