Showing 1–50 of 76 results for author: Ikeda, R

Electromagnetic Responses of Vortex Lattices in Unconventional Superconductors

Authors: Ryusuke Ikeda, Yuto Yokota

Abstract: The electro-magnetic responses of ordered vortex lattices in unconventional superconductors are studied in a high field approximation. In the cases with a vortex lattice formed within the lowest Landau level of the superconducting order parameter (OP) such as a conventional s-wave paired system with a single OP and a nonchiral spin triplet paired one with multiple components of OPs, the va… ▽ More The electro-magnetic responses of ordered vortex lattices in unconventional superconductors are studied in a high field approximation. In the cases with a vortex lattice formed within the lowest Landau level of the superconducting order parameter (OP) such as a conventional s-wave paired system with a single OP and a nonchiral spin triplet paired one with multiple components of OPs, the vanishing of the superfluid stiffness for a gauge field disturbance perpendicular to the applied uniform magnetic field is found to be ensured only for the vortex lattice structures minimizing the free energy. The notion of the vanishing superfluid stiff ness ensured by minimization of the free energy is found to be satisfied in a more complex d-wave pairing case where the vortex lattice in lower fields has an anisotropic structure de viated from the six-fold hexagonal symmetry. Interestingly, such an anisotropy in the vortex lattice structure of a d-wave paired superconductor is reflected not in the resulting vortex flow conductivities obtained after minimizing the free energy but in the elastic energy describing the harmonic fluctuation around the vortex lattice state. Relevance of the obtained results to the vortex pinning effects are discussed. △ Less

Submitted 25 October, 2025; originally announced October 2025.

Comments: 24 pages, 4 figures

High harmonic generation reflecting the sub-cycle evolution of the Mott transition under a mid-infrared electric field

Authors: Ryohei Ikeda, Yuta Murakami, Daiki Sakai, Tatsuya Miyamoto, Toshimitsu Ito, Hiroshi Okamoto

Abstract: Solids in an intense laser field show high-harmonic generation (HHG), which can provide information on carrier dynamics and band structures in weakly correlated systems. In strongly correlated systems, a laser field can induce a transition between the various electronic phases formed by the entanglement of charge, spin, and orbital degrees of freedom via carrier generation. The HHG accompanying th… ▽ More Solids in an intense laser field show high-harmonic generation (HHG), which can provide information on carrier dynamics and band structures in weakly correlated systems. In strongly correlated systems, a laser field can induce a transition between the various electronic phases formed by the entanglement of charge, spin, and orbital degrees of freedom via carrier generation. The HHG accompanying this process should contain information on the nonequilibrium electronic-state dynamics along the oscillating field - an aspect that remains unresolved to date. Here, we show that an intense mid-infrared (MIR) pulse induces a Mott insulator-metal transition in a one-dimensional cuprate, Sr2CuO3, the evolution of which is reflected by the spectral features of HHs. When the electric-field amplitude exceeds 6 MV/cm, carriers are efficiently generated and each harmonic frequency decreases from odd multiples of the MIR frequency. Dynamical mean-field theory indicates that these redshifts originate from a series of electronic-structure reconstructions in each electric-field cycle during the melting of the Mott-insulator state, which modifies the radiation phase from carrier recombination cycle-by-cycle. This phenomenon is negligible in rigid-band systems. This experimental-theoretical study confirms that HH spectroscopy research can potentially unravel the sub-cycle dynamics of nonequilibrium phase transitions in correlated materials. △ Less

Submitted 31 July, 2025; originally announced August 2025.

Stability and Response of Vortex Solid Formed in Second Landau Level

Authors: Yuto Yokota, Dai Nakashima, Ryusuke Ikeda

Abstract: Physical properties of the vortex solid phase formed in the second Landau level (2LL), which may be stabilized by strong paramagnetic pairbreaking (PPB), are examined in type II limit with no magnetic screening. First, it is shown that the spectrum of the low energy mode of this vortex solid has the same form as that of the conventional vortex solid in the first (i.e., the lowest) Landau level. Us… ▽ More Physical properties of the vortex solid phase formed in the second Landau level (2LL), which may be stabilized by strong paramagnetic pairbreaking (PPB), are examined in type II limit with no magnetic screening. First, it is shown that the spectrum of the low energy mode of this vortex solid has the same form as that of the conventional vortex solid in the first (i.e., the lowest) Landau level. Using this result, the melting line of the 2LL vortex solid is examined according to the Lindemann criterion. In contrast to the properties in equlibrium, the electromagnetic response of this vortex solid is quite unusual: Reflecting the presence of antivortices supporting the stability of the lattice structure, the superfluid stiffness measuring the response for a current perpendicular to the magnetic field is found to be nonvanishing, and its sign depends upon the applied current direction. Consequences of this response property are briefly discussed. △ Less

Submitted 24 April, 2025; originally announced April 2025.

Comments: 18 pages, 6 figures

Photo-induced phase transition on black samarium monosulfide

Authors: Hiroshi Watanabe, Yusuke Takeno, Yusuke Negoro, Ryohei Ikeda, Yuria Shibata, Yitong Chen, Takuto Nakamura, Kohei Yamagami, Yasuyuki Hirata, Yujun Zhang, Ryunosuke Takahashi, Hiroki Wadati, Kenji Tamasaku, Keiichiro Imura, Hiroyuki S. Suzuki, Noriaki K. Sato, Shin-ichi Kimura

Abstract: To investigate the role of the excitons for the origin of the pressure-induced phase transition (BGT) from the black-colored insulator (BI) to the golden-yellow-colored metal (GM) of samarium monosulfide (SmS), optical reflectivity, Sm $3d$ X-ray absorption spectroscopy (XAS), and X-ray diffraction (XRD) with the creation of excitons by photoexcitation (PE) are reported. In the pump-probe reflecti… ▽ More To investigate the role of the excitons for the origin of the pressure-induced phase transition (BGT) from the black-colored insulator (BI) to the golden-yellow-colored metal (GM) of samarium monosulfide (SmS), optical reflectivity, Sm $3d$ X-ray absorption spectroscopy (XAS), and X-ray diffraction (XRD) with the creation of excitons by photoexcitation (PE) are reported. In the pump-probe reflectivity measurement, following a huge reflectivity change of about 22 %, three different relaxation times with a vibration component were observed. The fast component with the relaxation time ($τ$) of less than 1 ps is due to the excitation and relaxation of electrons into the conduction band, and the slowest one with $τ> {\rm several} 100$ ps originates from the appearance of the photo-induced (PI) state. The components with $τ\sim 10$ ps and vibration originate from the appearance of the PI state and the interference between the reflection lights at the sample surface and the boundary between the BI and PI states, suggesting that the electronic structure of the PI phase is different from that of the BI state. XAS spectra indicate that the Sm mean valence is shifted from the Sm$^{2+}$ dominant to the intermediate between Sm$^{2+}$ and Sm$^{3+}$ by PE but did not change to that of the GM phase across BGT, consistent with the reflectivity data. The XRD result after PE shows that the PI state has much less lattice contraction than the GM phase. These results suggest that the BGT cannot be achieved solely by creating excitons after PE but requires other effects, such as a lattice contraction. △ Less

Submitted 1 October, 2024; originally announced October 2024.

Comments: 9 pages, 5 figures

Journal ref: Phys. Rev. B. 110, 245133 (2024) [8 pages]

Observation of excitonic Floquet states in a one-dimensional organic Mott insulator using mid-infrared pump near-infrared probe reflection spectroscopy

Authors: R. Ikeda, D. Sakai, T. Yamakawa, T. Miyamoto, T. Hasegawa, H. Okamoto

Abstract: When an electric field of light with a frequency of{\hbar}Ωis applied to a solid, Floquet states, consisting of sidebands with an interval of {\hbar}Ω around an electronic state, are expected to be formed. However, only a few studies have experimentally detected such sidebands. Here, we apply mid-infrared pump near-infrared reflection probe spectroscopy to a one-dimensional Mott insulator, bis(eth… ▽ More When an electric field of light with a frequency of{\hbar}Ωis applied to a solid, Floquet states, consisting of sidebands with an interval of {\hbar}Ω around an electronic state, are expected to be formed. However, only a few studies have experimentally detected such sidebands. Here, we apply mid-infrared pump near-infrared reflection probe spectroscopy to a one-dimensional Mott insulator, bis(ethylendithio)tetrathianfulvalence-difluorotetracyanoquinodimethane (ET-F2TCNQ), to detect the transient change in reflectivity R,ΔR/R, due to the formation of excitonic Floquet states. Analyses, considering both odd- and even-parity excitons, demonstrate that the ΔR/R spectrum reflects the formation of the first-order Floquet sidebands of excitons, and its spectral shape strongly depends on the widths of excitonic states. The experimental and analytical approach reported here is effective in demonstrating excitonic Floquet states in various solids. △ Less

Submitted 25 July, 2024; originally announced July 2024.

Comments: 26pages, 4figures

Vanishing of Resistivity upon Freezing of Vortex Liquid in Clean Superconductors

Authors: Naratip Nunchot, Ryusuke Ikeda

Abstract: Superconducting transition, defined as vanishing of the resistivity, under a magnetic field in a clean bulk type II superconductor with weak sample disorder is believed to be a reflection of freezing of the vortex liquid to a kind of vortex solids. This fundamental issue on superconductivity is examined in detail. Based on the Ginzburg-Landau fluctuation theory for a three-dimensional (3D) system… ▽ More Superconducting transition, defined as vanishing of the resistivity, under a magnetic field in a clean bulk type II superconductor with weak sample disorder is believed to be a reflection of freezing of the vortex liquid to a kind of vortex solids. This fundamental issue on superconductivity is examined in detail. Based on the Ginzburg-Landau fluctuation theory for a three-dimensional (3D) system and through a supplementary study in 2D case, we find that the resistivity in the weakly disordered 3D case vanishes in a nearly discontinuous way, reflecting growth of the Bragg peaks on approaching the vortex lattice melting transition. In contrast, such a sharp decrease of the resistivity does not clearly appear in the corresponding 2D case. The consequences of this difference in the vanishing behavior of the resistivity between the 2D and 3D systems are discussed in relation to available experimental facts. △ Less

Submitted 22 March, 2024; originally announced March 2024.

Comments: 33 pages, 10 figures (to appear in J. Phys. Soc. Jpn.)

Journal ref: J. Phys. Soc. Jpn. 93, 054712 (2024)

Melting of excitonic insulator phase by an intense terahertz pulse in Ta$_2$NiSe$_5$

Authors: Naoki Takamura, Tatsuya Miyamoto, Ryohei Ikeda, Tetsushi Kubo, Masaki Yamamoto, Hiroki Sato, Yang Han, Takayuki Ito, Tetsu Sato, Akitoshi Nakano, Hiroshi Sawa, Hiroshi Okamoto

Abstract: In this study, the optical response to a terahertz pulse was investigated in the transition metal chalcogenide Ta$_2$NiSe$_5$, a candidate excitonic insulator. First, by irradiating a terahertz pulse with a relatively weak electric field (0.3 MV/cm), the spectral changes in reflectivity near the absorption edge due to third-order optical nonlinearity were measured and the absorption peak character… ▽ More In this study, the optical response to a terahertz pulse was investigated in the transition metal chalcogenide Ta$_2$NiSe$_5$, a candidate excitonic insulator. First, by irradiating a terahertz pulse with a relatively weak electric field (0.3 MV/cm), the spectral changes in reflectivity near the absorption edge due to third-order optical nonlinearity were measured and the absorption peak characteristic of the excitonic phase just below the interband transition was identified. Next, by irradiating a strong terahertz pulse with a strong electric field of 1.65 MV/cm, the absorption of the excitonic phase was found to be reduced, and a Drude-like response appeared in the mid-infrared region. These responses can be interpreted as carrier generation by exciton dissociation induced by the electric field, resulting in the partial melting of the excitonic phase and metallization. The presence of a distinct threshold electric field for carrier generation indicates exciton dissociation via quantum-tunnelling processes. The spectral change due to metallization by the electric field is significantly different from that due to the strong optical excitation across the gap, which can be explained by the different melting mechanisms of the excitonic phase in the two types of excitations. △ Less

Submitted 11 September, 2023; originally announced September 2023.

Comments: 66 pages, 11 figures, 2 tables

Resistivity in Quantum Vortex Liquid of Clean Two-Dimensional Superconductor

Authors: Naratip Nunchot, Ryusuke Ikeda

Abstract: Motivated by a recent controversy on a possible quantum phase in thin films of relatively clean superconductors under an out-of-plane magnetic field, the quantum fluctuation effects on the phase diagram and the resistivity are reexamined. It is argued that most of features seen in the corresponding resistivity data in relatively clean systems reported recently are explained within the present theo… ▽ More Motivated by a recent controversy on a possible quantum phase in thin films of relatively clean superconductors under an out-of-plane magnetic field, the quantum fluctuation effects on the phase diagram and the resistivity are reexamined. It is argued that most of features seen in the corresponding resistivity data in relatively clean systems reported recently are explained within the present theory, and that the fan-shaped resistivity curves, suggestive of the presence of a superconductor to insulator transition at zero temperature, in the vortex liquid regime is a consequence of the insulating behavior of the Aslamasov-Larkin fluctuation conductivity in the quantum regime. △ Less

Submitted 10 July, 2023; originally announced July 2023.

Comments: To appear in JPSJ

Journal ref: J.Phys.Soc.Jpn. 92, 084707 (2023)

Light-field-driven non-Ohmic current and Keldysh crossover in a Weyl semimetal

Authors: R. Ikeda, H. Watanabe, J. H. Moon, M. H. Jung, K. Takasan, S. Kimura

Abstract: In recent years, coherent electrons driven by light fields have attracted significant interest in exploring novel material phases and functionalities. However, observing coherent light-field-driven electron dynamics in solids is challenging because the electrons are scattered within several ten femtoseconds in ordinary materials, and the coherence between light and electrons is disturbed. However,… ▽ More In recent years, coherent electrons driven by light fields have attracted significant interest in exploring novel material phases and functionalities. However, observing coherent light-field-driven electron dynamics in solids is challenging because the electrons are scattered within several ten femtoseconds in ordinary materials, and the coherence between light and electrons is disturbed. However, when we use Weyl semimetals, the electron scattering becomes relatively long (several hundred femtoseconds - several picoseconds), owing to the suppression of the back-scattering process. This study presents the light-field-driven dynamics by the THz pulse to Weyl semimetal Co3Sn2S2, where the intense THz pulse of a monocycle electric field nonlinearly generates direct current (DC) via coherent acceleration without scattering and non-adiabatic excitation (Landau-Zener Transition). In other words, the non-Ohmic current appears in the Weyl semimetal with a combination of the long relaxation time and an intense THz pulse. This nonlinear DC generation also demonstrates a Keldysh crossover from a photon picture to a light-field picture by increasing the electric field strength. △ Less

Submitted 15 June, 2023; originally announced June 2023.

Comments: 14 pages, 5 figures

Magnetoelectrocaloric effect of multiferroic GdFeO3

Authors: Rintaro Ikeda, Takashi Kurumaji, Yusuke Tokunaga, Taka-hisa Arima

Abstract: We report an experimental demonstration of the magnetoelectrocaloric effect (MECE) in multiferroic $\mathrm{GdFeO_3}$. The temperature of the magnetic material changes when an external electric field is suddenly changed. MECE is the largest below the ordering temperature of Gd moments and modifiable by a magnetic field, suggesting that the ferroelectric transition affects MECE. The observed MECE s… ▽ More We report an experimental demonstration of the magnetoelectrocaloric effect (MECE) in multiferroic $\mathrm{GdFeO_3}$. The temperature of the magnetic material changes when an external electric field is suddenly changed. MECE is the largest below the ordering temperature of Gd moments and modifiable by a magnetic field, suggesting that the ferroelectric transition affects MECE. The observed MECE shows a higher energy efficiency than typical magnetocaloric effects and adiabatic nuclear demagnetization. The present findings provide a proof of concept of MECE in multiferroics. △ Less

Submitted 2 March, 2023; originally announced March 2023.

Journal ref: Journal of the Physical Society of Japan, 93, 094709 (2024)

Vortex Lattice Melting Line in Superconductors with Paramagnetic Pair-Breaking

Authors: Dai Nakashima, Ryusuke Ikeda

Abstract: Recent experiments on the Iron-based superconductor FeSe in a high magnetic field have suggested the presence of both the fluctuation-induced vortex liquid regime and a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice. To get a general picture on the magnetic phase diagram in type II superconductors with strong superconducting (SC) fluctuation and strong paramagnetic pair-breaking (PPB) such… ▽ More Recent experiments on the Iron-based superconductor FeSe in a high magnetic field have suggested the presence of both the fluctuation-induced vortex liquid regime and a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice. To get a general picture on the magnetic phase diagram in type II superconductors with strong superconducting (SC) fluctuation and strong paramagnetic pair-breaking (PPB) such as FeSe, the vortex lattice melting curve Hm(T) is theoretically investigated in the situations where a FFLO state is expected to occur. In general, the PPB tends to narrow the vortex liquid regime intervening between Hc2(T) and Hm(T). In particular, the vortex liquid regime is found to rapidly shrink upon entering, by cooling, the temperature range in which the FFLO state with a periodic modulation parallel to the magnetic field is stable in the mean field theory. Based on the present results, the high field SC phase diagrams of FeSe in the parallel and perpendicular field configurations are discussed. △ Less

Submitted 12 July, 2022; v1 submitted 28 April, 2022; originally announced April 2022.

Comments: Submitted version

Journal ref: Phys. Rev. B106,024508 (2022)

Fluctuation Conductivity and Vortex State in Superconductor with Strong Paramagnetic Pair Breaking

Authors: Naratip Nunchot, Dai Nakashima, Ryusuke Ikeda

Abstract: The fluctuation conductivity of a moderately clean type II superconductor with strong Pauli paramagnetic pair-breaking (PPB) is studied by focusing on the quantum regime at low temperatures and in high magnetic fields. First, it is pointed out that, as the PPB effect becomes stronger, the quantum superconducting fluctuation is generally enhanced so that the Aslamasov-Larkin (AL) fluctuation conduc… ▽ More The fluctuation conductivity of a moderately clean type II superconductor with strong Pauli paramagnetic pair-breaking (PPB) is studied by focusing on the quantum regime at low temperatures and in high magnetic fields. First, it is pointed out that, as the PPB effect becomes stronger, the quantum superconducting fluctuation is generally enhanced so that the Aslamasov-Larkin (AL) fluctuation conductivity tends to vanish upon cooling. Further, by examining other (the DOS and the Maki-Thompson (MT)) terms of the fluctuation conductivity, the field dependence of the resulting total conductivity is found to depend significantly on the type of the vortex lattice (or, glass) ordered state at low temperatures where the strong PPB plays important roles. By comparing the present theoretical results with the fluctuation-induced negative magnetoresistance behavior upon entering a PPB-induced novel SC phase of Iron selenide (FeSe), it is argued that the vortex matter states of the superconducting order parameter in the second lowest ($n=1$) Landau level are realized in FeSe in the parallel field configuration in high fields and at low temperatures △ Less

Submitted 9 May, 2022; v1 submitted 22 March, 2022; originally announced March 2022.

Comments: 9 figures, Some figures and some references were added. resubmitted version

Journal ref: Phys.Rev.B 105, 174510 (2022)

Effect of Dipole Energy on Half-Quantum Vortex in Superfluid Polar Phase

Authors: Tomohiro Hisamitsu, Ryusuke Ikeda

Abstract: NMR experiments on superfluid 3He in a nematic aerogel have shown that the stability of the half-quantum vortex (HQV) realized in the polar phase depends on the relative direction between the magnetic field and the anisotropy axis brought by the aerogel. The vortex energy in the polar phase is examined in terms of the Ginzburg-Landau free energy incorporating the dipole energy, and the reason why… ▽ More NMR experiments on superfluid 3He in a nematic aerogel have shown that the stability of the half-quantum vortex (HQV) realized in the polar phase depends on the relative direction between the magnetic field and the anisotropy axis brought by the aerogel. The vortex energy in the polar phase is examined in terms of the Ginzburg-Landau free energy incorporating the dipole energy, and the reason why the HQV in the polar phase in nematic aerogels became unstable in a transverse magnetic field upon a field-cooling is explained. △ Less

Submitted 23 March, 2021; originally announced March 2021.

Comments: 6 pages, 5 figures

Journal ref: Phys. Rev. B 103, 224511 (2021)

Superfluid Quantum Criticality in Liquid 3He in Anisotropic Aerogel

Authors: Dai Nakashima, Ryusuke Ikeda

Abstract: In the novel superfluid polar phase realized in liquid 3He in highly anisotropic aerogels, a quantum transition to the polar-distorted A (PdA) phase may occur at a low but finite pressure Pc(0). It is shown that a nontrivial quantum dynamics of the critical fluctuation of the PdA order is induced by the presence of both the columnar-like impurity scattering leading to the Anderson's Theorem for th… ▽ More In the novel superfluid polar phase realized in liquid 3He in highly anisotropic aerogels, a quantum transition to the polar-distorted A (PdA) phase may occur at a low but finite pressure Pc(0). It is shown that a nontrivial quantum dynamics of the critical fluctuation of the PdA order is induced by the presence of both the columnar-like impurity scattering leading to the Anderson's Theorem for the polar phase and the line node of the quasiparticle gap in the state, and that, in contrast to the situation of the normal to the B phase transition in isotropic aerogels, a weakly divergent behavior of the compressibility appears in the quantum critical region close to Pc(0). △ Less

Submitted 26 January, 2021; originally announced January 2021.

Comments: 9 pages, 4 figures. To appear in Phys.Rev.B

Journal ref: Phys.Rev.B103, 064502 (2021)

Half-Quantum Vortex Pair in Polar-distorted B Phase of Superfluid 3He in Aerogels

Authors: Masaki Tange, Ryusuke Ikeda

Abstract: Motivated by the recent observation and argument on a large half-quantum vortex (HQV) pair connencted by a Kibble wall in superfluid 3He in nematic aerogels, we numerically study to what extent a huge HQV pair can intrinsically occur with no pinning effect due to the aerogel structure in the polar-distorted B (PdB) phase of superfluid 3He. By fully examining the impurity-scattering induced pairing… ▽ More Motivated by the recent observation and argument on a large half-quantum vortex (HQV) pair connencted by a Kibble wall in superfluid 3He in nematic aerogels, we numerically study to what extent a huge HQV pair can intrinsically occur with no pinning effect due to the aerogel structure in the polar-distorted B (PdB) phase of superfluid 3He. By fully examining the impurity-scattering induced pairing vertex, the emergence of Anderson's Theorem in the p-wave superfluid is verified in the two opposite limits, the isotropic and strongly anisotropic limits. Solving numerically the resulting Ginzburg-Landau (GL) free energy in the weak-coupling approximation and by taking account of the Fermi-liquid (FL) corrected gradient terms, the anisotropy dependence of the vortex structure minimizing the free energy is examined. It is found that, close to the transition between the polar and PdB phases, an interplay of the strong anisotropy and the FL correction makes emergence of a large HQV pair in the PdB phase possible, and that, nevertheless, such a large pair easily shrinks deep in the PdB phase, indicating that a pinning effect due to the aerogel structure is necessary in order to keep a large pair size there. The obtained result indicates the validity of the London limit for describing the vortex structure, and a consistency with the picture based on the NMR measurement is discussed. △ Less

Submitted 5 December, 2019; v1 submitted 2 December, 2019; originally announced December 2019.

Comments: 15 pages, 10 figures. Color maps have been added, and several parts have been corrected

Journal ref: Phys. Rev. B 101, 094512 (2020)

Impact of Strong Anisotropy on Phase Diagram of Superfluid $^3$He in Aerogels

Authors: Tomohiro Hisamitsu, Masaki Tange, Ryusuke Ikeda

Abstract: Recently, one analog of the Anderson's Theorem for the $s$-wave superconductor has attracted much interest in the context of the $p$-wave polar pairing state of superfluid $^3$He in a model aerogel in the limit of strong uniaxial anisotropy. We discuss to what extent the theorem is satisfied in the polar phase in real aerogels by examining the normal to polar transition temperature $T_c$ and the l… ▽ More Recently, one analog of the Anderson's Theorem for the $s$-wave superconductor has attracted much interest in the context of the $p$-wave polar pairing state of superfluid $^3$He in a model aerogel in the limit of strong uniaxial anisotropy. We discuss to what extent the theorem is satisfied in the polar phase in real aerogels by examining the normal to polar transition temperature $T_c$ and the low temperature behavior of the superfluid energy gap under an anisotropy of a moderate strength and comparing the obtained results with experimental data. The situation in which the Anderson's theorem clearly breaks down is also discussed. △ Less

Submitted 31 January, 2020; v1 submitted 28 August, 2019; originally announced August 2019.

Comments: Minor changes were done, and one reference was added

Journal ref: Phys. Rev. B 101, 100502 (2020)

Double-Core Vortex Stabilized by Disorder in Superfluid $^3$He B Phase in Globally Isotropic Aerogel

Authors: Natsuo Nagamura, Ryusuke Ikeda

Abstract: In a p-wave Fermi superfluid suffering from the nonmagnetic impurity scatterings, a coefficient of a gradient term becomes divergent upon cooling. Consequences of this divergent rigidity in the stable vortices in the B phase in globally isotropic aerogel are considered where the "impurity scattering" events are brought by the aerogel structure. For a moderately strong "impurity scatterings", the s… ▽ More In a p-wave Fermi superfluid suffering from the nonmagnetic impurity scatterings, a coefficient of a gradient term becomes divergent upon cooling. Consequences of this divergent rigidity in the stable vortices in the B phase in globally isotropic aerogel are considered where the "impurity scattering" events are brought by the aerogel structure. For a moderately strong "impurity scatterings", the superfluid transition line T_c(P) has a quantum critical point at a low but finite pressure. We find that, with decreasing T_c via the lowering of the pressure, the distance between the half cores composing the core of the nonaxisymmetric double-core vortex which is stable at lower pressures grows as a result of the rigidity diverging at lowering temperature. The obtained result is compared with the elongation of the half core pair arising from the Fermi-liquid correction. △ Less

Submitted 7 May, 2019; originally announced May 2019.

Comments: 6 pages

Stabilization of vortex-liquid state by strong pairing interaction

Authors: Kyosuke Adachi, Ryusuke Ikeda

Abstract: We theoretically investigate qualitative features of the field-temperature ($H$-$T$) phase diagram of superconductors with strong attractive interaction lying in the BCS-BEC crossover regime. Starting with a simple attractive Hubbard model, we estimate three kinds of characteristic fields, i.e., the pair-formation field $H^*$, the vortex-liquid-formation field $H_\mathrm{c2}$, and the vortex-latti… ▽ More We theoretically investigate qualitative features of the field-temperature ($H$-$T$) phase diagram of superconductors with strong attractive interaction lying in the BCS-BEC crossover regime. Starting with a simple attractive Hubbard model, we estimate three kinds of characteristic fields, i.e., the pair-formation field $H^*$, the vortex-liquid-formation field $H_\mathrm{c2}$, and the vortex-lattice-formation field $H_\mathrm{melt}$. The region between $H_\mathrm{c2}$ and $H_\mathrm{melt}$, as well as that between $H_\mathrm{c2}$ and $H^*$, is found to be enlarged as the interaction is stronger. In other words, a strong attractive interaction can stabilize both the vortex-liquid and preformed-pair regions. We also point out the expected particle-density dependence of the $H$-$T$ phase diagram. △ Less

Submitted 15 February, 2019; v1 submitted 18 November, 2018; originally announced November 2018.

Comments: 14 pages, 7 figures

Journal ref: Phys. Rev. B 99, 064508 (2019)

Dimensionality-induced BCS-BEC crossover in layered superconductors

Authors: Kyosuke Adachi, Ryusuke Ikeda

Abstract: Based on a simple model of a layered superconductor with strong attractive interaction, we find that the separation of the pair-condensation temperature from the pair-formation temperature becomes more remarkable as the interlayer hopping gets smaller. We propose from this result the BCS-BEC crossover induced by the change in dimensionality, for instance, due to insertion of additional insulating… ▽ More Based on a simple model of a layered superconductor with strong attractive interaction, we find that the separation of the pair-condensation temperature from the pair-formation temperature becomes more remarkable as the interlayer hopping gets smaller. We propose from this result the BCS-BEC crossover induced by the change in dimensionality, for instance, due to insertion of additional insulating layers or application of uniaxial pressure. The emergence of a pseudogap in the electronic density of states, which supports the idea of the dimensionality-induced BCS-BEC crossover, is also verified. △ Less

Submitted 17 November, 2018; v1 submitted 6 September, 2018; originally announced September 2018.

Comments: 5 pages, 4 figures (main text); 3 pages, 1 figure (Supplemental Material)

Journal ref: Phys. Rev. B 98, 184502 (2018)

Stability of Half-Quantum Vortices in Equal-Spin Pairing States of $^3$He

Authors: Natsuo Nagamura, Ryusuke Ikeda

Abstract: Recent experiments on superfluid $^3$He in globally anisotropic aerogels have shown realization of the polar superfluid phase and of the half-quantum vortices (HQVs) in this phase upon rotation. To clarify why the HQVs, which had not been detected clearly in the A phase of the bulk liquid, have been realized in the polar phase, we theoretically examine the relative stability of a HQV-pair against… ▽ More Recent experiments on superfluid $^3$He in globally anisotropic aerogels have shown realization of the polar superfluid phase and of the half-quantum vortices (HQVs) in this phase upon rotation. To clarify why the HQVs, which had not been detected clearly in the A phase of the bulk liquid, have been realized in the polar phase, we theoretically examine the relative stability of a HQV-pair against a single phase vortex in both the bulk A-phase and the polar phase in an aerogel. By taking care of important roles of a higher order gradient term, which assists the stability of HQVs but has never been incorporated so far in the Ginzburg-Landau (GL) approach, we find that several consequences, including the extension of the polar phase at lower pressures in the phase diagram, facilitate realization of the HQVs there in contrast to the case of the A phase in a slab geometry. △ Less

Submitted 29 September, 2018; v1 submitted 27 April, 2018; originally announced April 2018.

Comments: 18 pages, 14 figures. Submitted version

Journal ref: Phys. Rev. B 98, 094524 (2018)

Enhanced superconducting-fluctuation effects on thermodynamic properties in BCS-BEC-crossover regime

Authors: Kyosuke Adachi, Ryusuke Ikeda

Abstract: Effects of superconducting fluctuation (SCF) on thermodynamic properties of electron systems in the so-called BCS-BEC-crossover regime are studied. As the attractive interaction between electrons becomes stronger upon approaching the BCS-BEC-crossover regime, importance of the mode coupling between SCF drastically increases. The enhanced mode coupling leads to lowering of both the zero-field super… ▽ More Effects of superconducting fluctuation (SCF) on thermodynamic properties of electron systems in the so-called BCS-BEC-crossover regime are studied. As the attractive interaction between electrons becomes stronger upon approaching the BCS-BEC-crossover regime, importance of the mode coupling between SCF drastically increases. The enhanced mode coupling leads to lowering of both the zero-field superconducting critical temperature and the depairing field $B_\text{c2} (T)$. Consequently, SCF-induced contributions to the specific heat and the diamagnetic susceptibility can seemingly exceed the corresponding values in the Gaussian approximation. We discuss relevance of the present results to the anomalous SCF-induced diamagnetic response observed in the iron selenide (FeSe). △ Less

Submitted 8 September, 2017; originally announced September 2017.

Comments: 12 pages, 14 figures

Journal ref: Phys. Rev. B 96, 184507 (2017)

Possible Triplet Superconducting Order in Magnetic Superconducting Phase induced by Paramagnetic Pair-Breaking

Authors: Ken-ichi Hosoya, Ryusuke Ikeda

Abstract: Motivated by recent thermal conductivity measurements in the superconductor CeCoIn5, we theoretically examine a possible staggered spin-triplet superconducting order to be induced by the coupled spin-density-wave (SDW) and d-wave superconducting (SC) orders in the high field and low temperature (HFLT) SC phase peculiar to this material with strong paramagnetic pair-breaking (PPB). It is shown that… ▽ More Motivated by recent thermal conductivity measurements in the superconductor CeCoIn5, we theoretically examine a possible staggered spin-triplet superconducting order to be induced by the coupled spin-density-wave (SDW) and d-wave superconducting (SC) orders in the high field and low temperature (HFLT) SC phase peculiar to this material with strong paramagnetic pair-breaking (PPB). It is shown that one type of the $π$-triplet order is consistent with the thermal conductivity data and can naturally be incorporated in the picture that the Q-phase is a consequence of the strong PPB effect inducing the SDW order and the FFLO spatial modulation parallel to the applied magnetic field. △ Less

Submitted 15 May, 2017; v1 submitted 17 April, 2017; originally announced April 2017.

Comments: 22 pages, 11 figures. Figs.1, 8. 1nd 9 were added together with comments on NMR data

Journal ref: Phys. Rev. B 95, 224513 (2017)

Fluctuation Diamagnetism in Two-Band Superconductors

Authors: Kyosuke Adachi, Ryusuke Ikeda

Abstract: Anomalously large fluctuation diamagnetism around the superconducting critical temperature has been recently observed on iron selenide (FeSe) [S. Kasahara et al., unpublished]. This indicates that superconducting fluctuations (SCFs) play a more significant role in FeSe, which supposedly has two-band structure, than in the familiar single-band superconductors. Motivated by the data in FeSe, SCF-ind… ▽ More Anomalously large fluctuation diamagnetism around the superconducting critical temperature has been recently observed on iron selenide (FeSe) [S. Kasahara et al., unpublished]. This indicates that superconducting fluctuations (SCFs) play a more significant role in FeSe, which supposedly has two-band structure, than in the familiar single-band superconductors. Motivated by the data in FeSe, SCF-induced diamagnetism is examined in a two-band system, on the basis of a phenomenological approach with a Ginzburg-Landau functional. The obtained results indicate that the SCF-induced diamagnetism may be more enhanced than that in a single-band system due to the existence of two distinct fluctuation modes. Such enhancement of diamagnetism unique to a two-band system seems consistent with the large diamagnetism observed on FeSe, though still far from a quantitative agreement. △ Less

Submitted 7 April, 2016; originally announced April 2016.

Comments: 17 pages, 6 figures

Journal ref: Physical Review B 93, 134503 (2016)

Coupled k-space structure of $d$-wave superconducting and magnetic orders induced by paramagnetic pair-breaking effect

Authors: Yuhki Hatakeyama, Ryusuke Ikeda

Abstract: We theoretically investigate k-space structures of $d_{x^2-y^2}$-wave superconducting (SC) and spin-density-wave (SDW) orders in their coexistent phase induced by a paramagnetic pair-breaking (PPB) effect in relation to the high field and low temperature (HFLT) SC phase in CeCoIn$_5$. It is shown that, in k-space, the SDW order develops near the gap nodes where the SC order is suppressed by PPB, a… ▽ More We theoretically investigate k-space structures of $d_{x^2-y^2}$-wave superconducting (SC) and spin-density-wave (SDW) orders in their coexistent phase induced by a paramagnetic pair-breaking (PPB) effect in relation to the high field and low temperature (HFLT) SC phase in CeCoIn$_5$. It is shown that, in k-space, the SDW order develops near the gap nodes where the SC order is suppressed by PPB, and the nesting condition for the SDW ordering is satisfied. By comparing the results in the $d_{x^2-y^2}$-wave SC model and those in an artificial model with no sign change of the gap function in k-space with each other, it is shown that the $d_{x^2-y^2}$-wave SC and SDW orders are enhanced altogether in k-space due to the sign change of the $d_{x^2-y^2}$-wave gap function there, and that this mutual enhancement largely stabilizes the coexistence of these orders in real space. It is also discussed that the field dependence of a SDW moment can be affected by the k-space structure of these orders, which is dependent on the curvature of the Fermi surface. △ Less

Submitted 9 March, 2016; v1 submitted 18 February, 2016; originally announced February 2016.

Comments: 9 pages, 4 figures

Journal ref: Phys.Rev.B 93, 104503 (2016)

Quasiclassical analysis of vortex lattice states in Rashba noncentrosymmetric superconductors

Authors: Yuichiro Dan, Ryusuke Ikeda

Abstract: Vortex lattice states occurring in noncentrosymmetric superconductors with the spin-orbit coupling of Rashba type under a magnetic field parallel to the symmetry plane are examined by assuming the $s$-wave pairing case and in an approach combining the quasiclassical theory with the Landau level expansion of the superconducting order parameter. The resulting field-temperature phase diagrams include… ▽ More Vortex lattice states occurring in noncentrosymmetric superconductors with the spin-orbit coupling of Rashba type under a magnetic field parallel to the symmetry plane are examined by assuming the $s$-wave pairing case and in an approach combining the quasiclassical theory with the Landau level expansion of the superconducting order parameter. The resulting field-temperature phase diagrams include not only a discontinuous transition but a continuous crossover between different vortex lattice structures, and, further, a critical end point of a structural transition line is found in an intermediate field and at a low temperature in the present approach. It is pointed out that the strange field dependence of the vortex lattice structure is a consequence of that of an anisotropy stemming from the Rashba spin-orbit coupling, and that the critical end point is related to the helical phase modulation peculiar to these materials in the ideal Pauli-limited case. Further, calculation results on the local density of states detectable in STM experiments are also presented. △ Less

Submitted 13 October, 2015; v1 submitted 18 May, 2015; originally announced May 2015.

Comments: 17 pages and 13 figures

Journal ref: Phys. Rev. B 92, 144504 (2015)

Possible Field-Temperature Phase Diagrams of Two-Band Superconductors with Paramagnetic Pair-Breaking

Authors: Kyosuke Adachi, Ryusuke Ikeda

Abstract: Possible field-temperature superconducting (SC) phase diagrams in two-band quasi-two-dimensional materials with a strong paramagnetic pair-breaking (PPB) are considered theoretically. Attention is paid to the case under a magnetic field $perpendicular$ to the SC layers and to essential differences from the counterpart in the ordinary single-band material. It is found by examining the $H_{c2}(T)$ c… ▽ More Possible field-temperature superconducting (SC) phase diagrams in two-band quasi-two-dimensional materials with a strong paramagnetic pair-breaking (PPB) are considered theoretically. Attention is paid to the case under a magnetic field $perpendicular$ to the SC layers and to essential differences from the counterpart in the ordinary single-band material. It is found by examining the $H_{c2}(T)$ curve and the vortex lattices to be realized close to $H_{c2}$ that a PPB-induced SC phase with a spatial modulation parallel to the field tends to occur more easily than in the single-band case, and that a crisscrossing vortex lattice proposed previously can occur in place of the conventional Fulde-Ferrell-Larkin-Ovchinnikov state within a parameter range. The relevance of the obtained results to FeSe and other iron-based superconductors is discussed. △ Less

Submitted 26 May, 2015; v1 submitted 1 April, 2015; originally announced April 2015.

Comments: 21 pages, 3 figures

Journal ref: Journal of the Physical Society of Japan 84, 064712 (2015)

Anisotropic Strong Coupling Effects on Superfluid 3He in Aerogels - Conventional Spin-Fluctuation Approach -

Authors: Ryusuke Ikeda

Abstract: Motivated by recent experiments on liquid $^3$He reporting emergence of novel superfluid phases in globally anisotropic aerogels, our previous theory on superfluid $^3$He in globally anisotropic aerogels is extended to incorporate effects of an anisotropy of the quasiparticle scattering cross section on the strong coupling (SC) contributions to the Ginzburg-Landau (GL) free energy on the basis of… ▽ More Motivated by recent experiments on liquid $^3$He reporting emergence of novel superfluid phases in globally anisotropic aerogels, our previous theory on superfluid $^3$He in globally anisotropic aerogels is extended to incorporate effects of an anisotropy of the quasiparticle scattering cross section on the strong coupling (SC) contributions to the Ginzburg-Landau (GL) free energy on the basis of the spin-fluctuation (paramagnon) approach to the SC contributions developed by Brinkman et al. [Phys. Rev. A {\bf 10}, 2386 (1974)]. In the globally isotropic case, impurity effects on the SC correction destabilize the A-phase even at higher pressures of about 30 (bar) and make the B-phase the only state in equilibrium, while SC contributions accompanied by a global stretched anisotropy to the GL quartic terms generally tend to broaden the stability region of the A-phase compared with that of the B-phase. In particular, in contrast to the cases in bulk and in the isotropic aerogel, the SC corrections to the GL {\it quadratic} terms are not negligible in the globally anisotropic case but may change the sign of the apparent anisotropy depending on the magnitude of the frequency cutoff of the normal paramagnon propagator. Based on this sign change of the apparent anisotropy, we discuss different strange observations on superfluid $^3$He in porous media such as disappearance of the polar superfluid phase at higher pressures seen in nematically-ordered aerogels and absence of the B-phase and of the A-phase with planar ${\hat {\bf l}}$-vector in a stretched aerogel. △ Less

Submitted 5 January, 2015; originally announced January 2015.

Comments: 18 pages, 9 figures

Journal ref: Phys. Rev. B 91, 174515 (2015)

Antiferromagnetic Order oriented by Fulde-Ferrell-Larkin-Ovchinnikov Superconducting Order

Authors: Yuhki Hatakeyama, Ryusuke Ikeda

Abstract: Resolving the high-field superconducting phase (HFSP), often called as the Q-phase, and the antiferromagnetic or spin-density-wave (SDW) order appearing in the phase remains a crucial issue on the superconductor CeCoIn$_5$. It is shown that a switching of the SDW domain due to a tiny change of the magnetic field direction in HFSP, reported and interpreted as an evidence of the presence of a $π$-tr… ▽ More Resolving the high-field superconducting phase (HFSP), often called as the Q-phase, and the antiferromagnetic or spin-density-wave (SDW) order appearing in the phase remains a crucial issue on the superconductor CeCoIn$_5$. It is shown that a switching of the SDW domain due to a tiny change of the magnetic field direction in HFSP, reported and interpreted as an evidence of the presence of a $π$-triplet pairing inducing the SDW order [S. Gerber et al., Nature Physics 10, 126 (2014)], can be explained with no triplet pairing component if the $d$-wave superconducting order in HFSP includes the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulation parallel to the field. This result corroborates the picture that HFSP of CeCoIn$_5$ and the SDW order found only in the phase are consequences of the strong paramagnetic pair-breaking in this $d$-wave superconductor. △ Less

Submitted 9 March, 2015; v1 submitted 9 December, 2014; originally announced December 2014.

Comments: 8 pages, 4 figures. figure 1 was divided, appendix was added, and some revisions were made. the version accepted for publication in Phys. Rev. B

Journal ref: Phys. Rev. B 91, 094504 (2015)

Strong-coupling approach to antiferromagnetic ordering driven by paramagnetic pair-breaking in d-wave superconducting phase

Authors: Yuhki Hatakeyama, Ryusuke Ikeda

Abstract: The field-induced antiferromagnetic (AFM) ordering in the $d_{x^2-y^2}$-paired superconducting phase, which has been recently found in the weak-coupling approach as a basic mechanism due to the Pauli paramagnetic pair-breaking (PPB) in relation to the high-field behaviors in CeCoIn_5, is studied in the strong-coupling approach taking account of the electron correlation. Applying the fluctuation-ex… ▽ More The field-induced antiferromagnetic (AFM) ordering in the $d_{x^2-y^2}$-paired superconducting phase, which has been recently found in the weak-coupling approach as a basic mechanism due to the Pauli paramagnetic pair-breaking (PPB) in relation to the high-field behaviors in CeCoIn_5, is studied in the strong-coupling approach taking account of the electron correlation. Applying the fluctuation-exchange (FLEX) approximation to the two-dimensional Hubbard model including the Zeeman term, it is shown that the PPB-induced AFM ordering in the superconducting (SC) phase and the first order SC transition on H_{c2}(T) are realized in the strong-coupling approach as well as those in the weak-coupling model, and that the AFM ordering is affected by the quasiparticle renormalization and the amplitude of the SC order parameter. This AFM ordering may appear in a wide range of materials close to an AFM quantum critical point (QCP). △ Less

Submitted 4 October, 2013; v1 submitted 18 September, 2013; originally announced September 2013.

Comments: 24 pages, 9 figures, revisions are made mainly in section 6, title is changed slightly

Journal ref: J. Phys. Soc. Jpn. 83, 024713 (2014)

Field-induced reentrant superconductivity in thin films of nodal superconductor

Authors: M. Hachiya, K. Aoyama, R. Ikeda

Abstract: Previous works on nodal d-wave superconductors have shown that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like modulated superconducting (SC) state can be realized with no magnetic field when quasiparticles acquire an additional linear term in the wavevector in their dispersion. In the present work, stability of such a novel modulated SC state in an artificial film against an applied magnetic field… ▽ More Previous works on nodal d-wave superconductors have shown that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like modulated superconducting (SC) state can be realized with no magnetic field when quasiparticles acquire an additional linear term in the wavevector in their dispersion. In the present work, stability of such a novel modulated SC state in an artificial film against an applied magnetic field is studied. As a reflection of the presence of the two different FFLO states, one close to zero field and the other at the high field end, in a single field v.s. temperature phase diagram of thin films, the conventional uniform SC state generally tends to appear as a reentrant ordered phase bounded by the normal phase in {\it lower} fields. △ Less

Submitted 7 June, 2013; originally announced June 2013.

Comments: 6 figures, 9 pages

Angular dependence of antiferromagnetic order induced by paramagnetism in d-wave superconductor

Authors: Ken-ichi Hosoya, Ryusuke Ikeda

Abstract: Antiferromagnetic (AFM) order and a spatial order peculiar to Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, previously indicated in the quasi two-dimensional d-wave superconductors CeCoIn_5 with strong paramagnetic pair breaking (PPB) in a magnetic-field parallel to the basal plane, are considered in the field configurations tilted from the basal plane within an approach assuming that the wavele… ▽ More Antiferromagnetic (AFM) order and a spatial order peculiar to Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, previously indicated in the quasi two-dimensional d-wave superconductors CeCoIn_5 with strong paramagnetic pair breaking (PPB) in a magnetic-field parallel to the basal plane, are considered in the field configurations tilted from the basal plane within an approach assuming that the wavelength of the FFLO modulation is relatively long. It is demonstrated that, with increasing the tilt angle, both the AFM and FFLO orders are gradually suppressed, and that disappearance of the AFM order in zero temperature limit occurs at a lower angle than that of the FFLO state. Consequently, a nonmagnetic FFLO-ordered high field SC phase is realized in an intermediate range of the tilt angle even at low enough temperatures. As the perpendicular field configuration (${\bf H} \parallel c$) is approached by the field-tilt, the AFM order in real space is found close to the FFLO nodal planes in contrast to the high field behavior in ${\bf H} \perp c$ case. Further, in the field v.s. temperature (H-T) phase diagram, the AFM order reduces, at a higher angle, to an AFM quantum critical point (QCP) lying at a lower field than H_{c2}(0) as a consequence of competition between the field dependences of the nesting condition and of PPB. These features of the AFM order and the resulting H-T phase diagram strikingly coincide with those seen in a recent NMR measurement on CeCoIn_5 in tilted field configurations. △ Less

Submitted 5 June, 2013; originally announced June 2013.

Comments: 18 pages, 4 figures

Fluctuation and Order of Antiferromagnetism induced by Paramagnetic Pair-Breaking in Superconducting Vortex Lattice

Authors: Kazushi Aoyama, Ryusuke Ikeda

Abstract: Effects of the strong Pauli-paramagnetic pair-breaking (PPB) on the vortex lattice in d-wave superconductors are theoretically studied by putting emphasis on consequences of the PPB-induced antiferromagnetic (AFM) ordering in the spatial modulation in the vortex lattice. It is shown that the PPB-induced AFM fluctuation in the superconducting state leads to an enhancement of the vortex lattice form… ▽ More Effects of the strong Pauli-paramagnetic pair-breaking (PPB) on the vortex lattice in d-wave superconductors are theoretically studied by putting emphasis on consequences of the PPB-induced antiferromagnetic (AFM) ordering in the spatial modulation in the vortex lattice. It is shown that the PPB-induced AFM fluctuation in the superconducting state leads to an enhancement of the vortex lattice form factor which is a measure of spatial variations of the internal magnetic field and that the enhancement becomes more remarkable as an AFM instability is approached. It is also demonstrated that the PPB-induced AFM ordering is assisted by the vortex-lattice modulation, and thus, that the resulting AFM order is spatially modulated, while it is not localized in the vortex cores but coexistent with the nonvanishing superconducting order parameter. These results are discussed in connection with two phenomena observed in CeCoIn5, the anomalous field dependence of the vortex lattice form factor and the AFM order appearing inside the high-field and low-temperature superconducting phase. △ Less

Submitted 27 July, 2011; originally announced July 2011.

Comments: 26 pages, 13 figures

Journal ref: Phys. Rev. B 84, 184516 (2011)

Vortex-lattice melting in two-dimensional superconductors in intermediate fields

Authors: Taro Saiki, Ryusuke Ikeda

Abstract: To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level (LL) approximation to include several {\it higher} LL modes of the superconducting order parameter with LL indices up to six. It is found that a nearly vertical… ▽ More To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level (LL) approximation to include several {\it higher} LL modes of the superconducting order parameter with LL indices up to six. It is found that a nearly vertical melting line in lower fields, which is familiar within the elastic theory, is reached just by including higher LL modes with LL indices less than five, and that the first order character of the melting transition in higher fields is significantly weakened with decreasing the field. Nevertheless, a genuine crossover to the consecutive continuous melting picture intervened by a hexatic liquid is not found within the use of the GL model. △ Less

Submitted 2 April, 2011; originally announced April 2011.

Comments: 6 pages, 7 figures. To appear in Phys. Rev. B

Emergent Antiferromagnetism in D-wave Superconductor with Strong Paramagnetic Pair-Breaking

Authors: Yuhki Hatakeyama, Ryusuke Ikeda

Abstract: It is theoretically shown that, in the four-fold symmetric d-wave superconducting phase, a paramagnetic pair-breaking (PPB) enhanced sufficiently by increasing the applied magnetic field induces not only the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state but also an incommensurate antiferromagnetic (AFM) order with Q-vector parallel to a gap node. This AFM ordering tends to occur on… ▽ More It is theoretically shown that, in the four-fold symmetric d-wave superconducting phase, a paramagnetic pair-breaking (PPB) enhanced sufficiently by increasing the applied magnetic field induces not only the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state but also an incommensurate antiferromagnetic (AFM) order with Q-vector parallel to a gap node. This AFM ordering tends to occur only below H_{c2} at low temperatures, i.e., in the presence of a nonvanishing superconducting energy gap $Δ$ rather than in the normal phase. Through a detailed study on the resulting AFM order and its interplay with the FFLO spatial modulation of $Δ$, it is argued that the strange high field and low temperature (HFLT) superconducting phase of CeCoIn_5 is a coexisting phase of the FFLO and incommensurate AFM orders, and that this PPB mechanism of an AFM ordering is also the origin of the AFM quantum critical fluctuation which has occurred close to H_{c2}(0) in several unconventional superconductors including CeCoIn_5. △ Less

Submitted 16 May, 2011; v1 submitted 9 March, 2011; originally announced March 2011.

Comments: 22 pages, 12 figures.2 references and related comnments are added.Accepted for publication in Phys. Rev. B

Journal ref: Phys. Rev. B 83, 224518 (2011)

Diamagnetism above Tc in underdoped Bi2.2Sr1.8Ca2Cu3O10+d

Authors: Tetsuya Iye, Takenori Nagatochi, Ryusuke Ikeda, Azusa Matsuda

Abstract: Single crystals of ${\rm Bi}_{2+x}{\rm Sr}_{2-x}{\rm Ca}_{2}{\rm Cu}_{3}{\rm O}_{10+δ}$(Bi2223) with $x=0.2$ were grown by a traveling solvent floating zone method in order to investigate the superconducting properties of highly underdoped Bi2223.Grown crystals were characterized by X-ray diffraction, DC susceptibility and resistivity measurements, confirming Bi2223 to be the main phase.The crysta… ▽ More Single crystals of ${\rm Bi}_{2+x}{\rm Sr}_{2-x}{\rm Ca}_{2}{\rm Cu}_{3}{\rm O}_{10+δ}$(Bi2223) with $x=0.2$ were grown by a traveling solvent floating zone method in order to investigate the superconducting properties of highly underdoped Bi2223.Grown crystals were characterized by X-ray diffraction, DC susceptibility and resistivity measurements, confirming Bi2223 to be the main phase.The crystals were annealed under various oxygen partial pressures to adjust their carrier densities from optimally doped to highly underdoped.The fluctuation diamagnetic component above the superconducting transition temperature $T_{\rm c}$ extracted from the anisotropic normal state susceptibilities $χ_{ab}(T)$ ($H\perp c$) and $χ_{c}(T)$ ($H\parallel c$) was found to increase with underdoping, suggesting a decrease in the superconducting dimensionality and/or increase in the fluctuating vortex liquid region. △ Less

Submitted 25 October, 2010; v1 submitted 25 August, 2010; originally announced August 2010.

Comments: 6 pages, 7 figures, corrected fig.4 and references, published in J. Phys. Soc. Jpn. 79, 114711 (2010)

Journal ref: J. Phys. Soc. Jpn. 79, 114711 (2010)

Vortex core transitions in superfluid 3He in globally anisotropic aerogels

Authors: Kazushi Aoyama, Ryusuke Ikeda

Abstract: Core structures of a single vortex in A-like and B-like phases of superfluid 3He in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although any uniaxial deformation leads to a wider A-like phase with the axial pairing in the pressure-temperature phase diagram, the vortex core states in the two pha… ▽ More Core structures of a single vortex in A-like and B-like phases of superfluid 3He in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although any uniaxial deformation leads to a wider A-like phase with the axial pairing in the pressure-temperature phase diagram, the vortex core states in the two phases in aerogel depend highly on the type of deformation. In a compressed aerogel, the first-order vortex core transition (VCT) previously seen in the bulk B phase appears at any pressure in the B-like phase while no strange vortex core is expected in the corresponding A-like phase. By contrast, in a stretched aerogel, the VCT in the B-like phase is lost while another VCT is expected to occur between a nonunitary core and a polar one in the A-like phase. Experimental search for these results is hoped to understand correlation between superfluid 3He and aerogel structure. △ Less

Submitted 13 October, 2010; v1 submitted 23 July, 2010; originally announced July 2010.

Comments: 7 pages, 6 figures Text was changed. Resubmitted version

Journal ref: Phys. Rev. B 82, 144514 (2010)

Coexistence of d-wave superconductivity and antiferromagnetism induced by paramagnetic depairing

Authors: Yuhki Hatakeyama, Ryusuke Ikeda

Abstract: It is shown theoretically that, in the superconducting state with $d_{x^2-y^2}$-pairing, a strong Pauli paramagnetic depairing (PD) induces not only the modulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state but also an incommensurate antiferromagnetic (AFM) (or spin-density wave) ordering with ${\bf Q}$-vector nearly paralle to a gap node. This intrinsic mechanism of field-induce… ▽ More It is shown theoretically that, in the superconducting state with $d_{x^2-y^2}$-pairing, a strong Pauli paramagnetic depairing (PD) induces not only the modulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state but also an incommensurate antiferromagnetic (AFM) (or spin-density wave) ordering with ${\bf Q}$-vector nearly paralle to a gap node. This intrinsic mechanism of field-induced coexistence of the $d$-wave superconducting and AFM orders does not need to assume a pair-density wave but is enhanced by the FFLO ordering. It is argued that this is the common origin of {\it both} the coexistent FFLO and AFM phases of CeCoIn$_5$ {\it and} the AFM quantum critical behavior around the superconducting $H_{c2}(0)$ seen in several heavy fermion superconductors and overdoped cuprates. △ Less

Submitted 21 July, 2010; v1 submitted 12 June, 2010; originally announced June 2010.

Comments: 4 pages, 2 figures, the version accepted for publication in J.Phys.Conf.Series (Proc. of SCES2010)

Antiferromagnetic ordering induced by paramagnetic depairing in unconventional superconductors

Authors: Ryusuke Ikeda, Yuhki Hatakeyama, Kazushi Aoyama

Abstract: Antiferromagnetic (AFM) (or spin-density wave) quantum critical fluctuation enhanced just below H_c2(0) have been often observed in d-wave superconductors with a strong Pauli paramagnetic depairing (PD) including CeCoIn_5. It is shown here that such a tendency of field-induced AFM ordering is a consequence of strong PD and should appear particularly in superconductors with a gap node along the AFM… ▽ More Antiferromagnetic (AFM) (or spin-density wave) quantum critical fluctuation enhanced just below H_c2(0) have been often observed in d-wave superconductors with a strong Pauli paramagnetic depairing (PD) including CeCoIn_5. It is shown here that such a tendency of field-induced AFM ordering is a consequence of strong PD and should appear particularly in superconductors with a gap node along the AFM modulation. Two phenomena seen in CeCoIn_5, the anomalous vortex lattice form factor and the AFM order in the Fulde-Ferrell-Larkin-Ovchinnikov state, are explained based on this peculiar PD effect. △ Less

Submitted 15 June, 2010; v1 submitted 1 March, 2010; originally announced March 2010.

Comments: 4 pages, 3 figures Title and text were changed. References are added. Resubmitted version

Journal ref: Phys. Rev. B 82, 060510(R) (2010)

Roles of Antiferromagnetic Fluctuation in High Field Phase Diagram of Superconductors with Strong Paramagnetic Depairing

Authors: Ryusuke Ikeda, Kazushi Aoyama

Abstract: The high field phase diagram and magnetic properties of CeCoIn_5 below H_c2(0) are examined from the picture regarding the high field and low temperature (HFLT) phase as a possible Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice. Crucial roles of antiferromagnetic (AFM) fluctuations enhanced close to H_c2(0) are stressed. The FFLO vortex lattice with a longitudinal modulation parallel to… ▽ More The high field phase diagram and magnetic properties of CeCoIn_5 below H_c2(0) are examined from the picture regarding the high field and low temperature (HFLT) phase as a possible Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice. Crucial roles of antiferromagnetic (AFM) fluctuations enhanced close to H_c2(0) are stressed. The FFLO vortex lattice with a longitudinal modulation parallel to the field is stabilized compared with those with lateral modulations as a consequence of the presence of AFM fluctuations. Further, an unusual field-induced enhancement of the flux distribution is argued to be a consequence of interplay between the paramagnetic depairing and AFM fluctuation, both of which are enhanced with increasing field. △ Less

Submitted 4 February, 2010; originally announced February 2010.

Comments: 2 pages, 2 figures, M2S-IX, Tokyo (2009) conference proceedings, Available online in Physica C

Impurity-induced broadening of the transition to a Fulde-Ferrell-Larkin-Ovchinnikov phase

Authors: Ryusuke Ikeda

Abstract: Recent study on doping effects in the heavy fermion superconductor CeCoIn$_5$ has shown that a small amount of doping induces unexpectedly large broadening of the second order transition into the high field and low temperature (HFLT) phase of this material. Motivated by this observation, effects of quenched disorder on the second order transition into a longitudinal Fulde-Ferrell-Larkin-Ovchinni… ▽ More Recent study on doping effects in the heavy fermion superconductor CeCoIn$_5$ has shown that a small amount of doping induces unexpectedly large broadening of the second order transition into the high field and low temperature (HFLT) phase of this material. Motivated by this observation, effects of quenched disorder on the second order transition into a longitudinal Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are examined. The observed large broadening of the transition is naturally explained as a consequence of softness of each FFLO nodal plane. The present results strongly support the scenario identifying the HFLT phase of CeCoIn$_5$ with a longitudinal FFLO vortex state. △ Less

Submitted 4 March, 2010; v1 submitted 1 December, 2009; originally announced December 2009.

Comments: 4 pages, 2 figures, The title has been slightly changed

Journal ref: Phys. Rev. B 81, 060510(R) (2010)

Anisotropy-induced Vortex Core Transitions in Superfluid 3He in Aerogel

Authors: Kazushi Aoyama, Ryusuke Ikeda

Abstract: Core structures of a single vortex in A-like and B-like phases of superfluid 3He in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although the A-like phase with axial pairing is extended by any uniaxial deformation, the vortex core states in the two phases depend highly on the type of deformati… ▽ More Core structures of a single vortex in A-like and B-like phases of superfluid 3He in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although the A-like phase with axial pairing is extended by any uniaxial deformation, the vortex core states in the two phases depend highly on the type of deformation in aerogel: In a compressed aerogel, the first order vortex core transition (VCT) previously seen in the bulk B phase appears at any pressure in B-like phase, while no strange vortex core is expected in A-like phase. By contrast, in a stretched aerogel, the VCT in B-like phase is lost, while another VCT is expected to occur between a nonunitary core and the polar one in A-like phase. An experimental search for these results is hoped to understand correlation between superfluid $^3$He and aerogel structures. △ Less

Submitted 25 July, 2010; v1 submitted 4 May, 2009; originally announced May 2009.

Comments: This manuscript is withdrawn because the corresponding extended version is available as arXiv:1007.4045

Vortex lattice structure dependent on pairing symmetry in Rashba superconductors

Authors: Norihito Hiasa, Taro Saiki, Ryusuke Ikeda

Abstract: Vortex lattice structures in Rashba noncentrosymmetric superconductors in magnetic fields parallel to the basal plane (${\bf H} \perp c$) are examined based on the BCS-like Hamiltonian and the resulting Ginzburg-Landau functional. Due to the momentum dependent anisotropy of the Zeeman effect induced by the broken inversion symmetry, the vortex lattice in higher fields generally shows some unidir… ▽ More Vortex lattice structures in Rashba noncentrosymmetric superconductors in magnetic fields parallel to the basal plane (${\bf H} \perp c$) are examined based on the BCS-like Hamiltonian and the resulting Ginzburg-Landau functional. Due to the momentum dependent anisotropy of the Zeeman effect induced by the broken inversion symmetry, the vortex lattice in higher fields generally shows some unidirectional modulation of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type orienting in the plane perpendicular to ${\bf H}$. However, the direction of the modulation and the lattice structure depend significantly on the underlying pairing symmetry: When the mixing between spin singlet and triplet pairing components is negligible, the resulting modulated structure tends to have reflection symmetry, while the vortex lattice in systems with a significant singlet-triplet mixing has no reflection symmetry in most cases. The latter result implying the presence in {\it real} materials of two degenerate orientations of the lattice structure separated by domain walls may be relevant to the extremely low magnetic decay rate observed in CePt$_3$Si. △ Less

Submitted 15 June, 2009; v1 submitted 1 May, 2009; originally announced May 2009.

Comments: 11 figures, Minor changes in the text. Accepted for publication in Phys.Rev.B

Superfluid $^3$He in globally isotropic random media

Authors: Ryusuke Ikeda, Kazushi Aoyama

Abstract: Recent theoretical and experimental studies of superfluid $^3$He in aerogels with a global anisotropy, e.g., due to an external stress, have definitely shown that the A-like phase with an equal spin pairing (ESP) in such aerogel samples is in the ABM (or, axial) pairing state. In this paper, the A-like phase of superfluid $^3$He in globally {\it isotropic} aerogel is studied in details by assumi… ▽ More Recent theoretical and experimental studies of superfluid $^3$He in aerogels with a global anisotropy, e.g., due to an external stress, have definitely shown that the A-like phase with an equal spin pairing (ESP) in such aerogel samples is in the ABM (or, axial) pairing state. In this paper, the A-like phase of superfluid $^3$He in globally {\it isotropic} aerogel is studied in details by assuming a weakly disordered system in which singular topological defects are absent. Through calculation of the free energy, a disordered ABM state is found to be the best candidate of the pairing state of the globally isotropic A-like phase. Further, it is found through a one-loop renormalization group calculation that the coreless continuous vortices (or, vortex-skyrmions) are irrelevant to the long-distance behavior of the disorder-induced textures, and that the superfluidity is maintained in spite of lack of the conventional off-diagonal long range order. Therefore, the globally isotropic A-like phase at weak disorder is, like in the case with a global stretched anisotropy, a superfluid glass with the ABM pairing. △ Less

Submitted 25 January, 2009; v1 submitted 14 November, 2008; originally announced November 2008.

Comments: Revised version accepted for publication in Phys.Rev.B

Orbital-limiting and modulation induced by missing parity in non-centrosymmetric superconductors

Authors: Norihito Hiasa, Ryusuke Ikeda

Abstract: We examine the depairing field $H_{c2}(T)$ of non-centrosymmetric superconductors with a spin-orbit coupling larger than the Zeeman energy at $H_{c2}(0)$ by taking account of the mixing of spin-singlet and triplet pairing states due to the missing parity. When the singlet and triplet pairing components are mixed with an equal weight in a cubic non-centrosymmetric system, the paramagnetic depairi… ▽ More We examine the depairing field $H_{c2}(T)$ of non-centrosymmetric superconductors with a spin-orbit coupling larger than the Zeeman energy at $H_{c2}(0)$ by taking account of the mixing of spin-singlet and triplet pairing states due to the missing parity. When the singlet and triplet pairing components are mixed with an equal weight in a cubic non-centrosymmetric system, the paramagnetic depairing effect is significantly suppressed so that $H_{c2}(T)$ approaches its orbital-limited value. A similar event also occurs in a quasi two-dimensional Rashba non-centrosymmetric system. The present results are relevant to the $H$-$T$ phase diagrams of CePt$_3$Si and the families of Li$_2$Pd$_{3-x}$Pt$_x$B. △ Less

Submitted 19 November, 2008; v1 submitted 10 October, 2008; originally announced October 2008.

Comments: 4 figures, To appear in Phys. Rev. B

Instability of square vortex lattice in d-wave superconductors is due to paramagnetic depairing

Authors: Norihito Hiasa, Ryusuke Ikeda

Abstract: Effects of the paramagnetic depairing on structural transitions between vortex lattices of a quasi two dimensional d-wave superconductor are examined. It is found that, in systems with Maki parameter $α_{\rm M}$ of order unity, a square lattice induced by a d-wave pairing is destabilized with {\it increasing} fields, and that a reentrant rhombic lattice occurs in higher fields. Further, a weak F… ▽ More Effects of the paramagnetic depairing on structural transitions between vortex lattices of a quasi two dimensional d-wave superconductor are examined. It is found that, in systems with Maki parameter $α_{\rm M}$ of order unity, a square lattice induced by a d-wave pairing is destabilized with {\it increasing} fields, and that a reentrant rhombic lattice occurs in higher fields. Further, a weak Fermi surface anisotropy competitive with the pairing symmetry induces another structural transition near $H_{c2}$. These results are consistent with the structure changes of the vortex lattice in CeCoIn$_5$ in ${\bf H} \parallel c$ determined from recent neutron scattering data. △ Less

Submitted 11 June, 2008; v1 submitted 11 March, 2008; originally announced March 2008.

Comments: Effects of thermal fluctuation were discussed additionally, and the title was slightly changed. Accepted for publication in Physical Review Letters

Modulated vortex states in Rashba non-centrosymmetric superconductors

Authors: Yuichi Matsunaga, Norihito Hiasa, Ryusuke Ikeda

Abstract: Vortex lattice structures to occur in Rashba non-centrosymmetric superconductors under a magnetic field parallel to the basal plane are studied by assuming a singlet Cooper pairing and taking account of both the paramagnetic and orbital depairings. A vortex lattice of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type with modulation perpendicular to the field is expected to occur in the limit of vani… ▽ More Vortex lattice structures to occur in Rashba non-centrosymmetric superconductors under a magnetic field parallel to the basal plane are studied by assuming a singlet Cooper pairing and taking account of both the paramagnetic and orbital depairings. A vortex lattice of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type with modulation perpendicular to the field is expected to occur in the limit of vanishing ${\tilde η}$, where ${\tilde η}$ is the spin-orbit coupling {\it normalized} by Fermi energy. As ${\tilde η}$ increases, however, this state tends to be replaced by another new vortex lattice with a modulation of the gap amplitude parallel to the helical phase modulation induced by the absence of inversion symmetry. Differences of the present results from those in the Pauli limit and a correlation of a structural transition with the $H_{c2}(T)$-curve are discussed in relation to possible experimental realization. △ Less

Submitted 2 December, 2008; v1 submitted 4 January, 2008; originally announced January 2008.

Comments: Final version accepted for publication in Phys.Rev.B (Rapid Commmun.)

Comment on "Spatial line nodes and fractional vortex pairs in the Fulde-Ferrell-Larkin-Ovchinnikov phase"

Authors: Ryusuke Ikeda

Abstract: This is a Comment on Phys.Rev.Lett. 100, 017001 (2008). This is a Comment on Phys.Rev.Lett. 100, 017001 (2008). △ Less

Submitted 27 January, 2009; v1 submitted 20 December, 2007; originally announced December 2007.

Comments: To appear in Phys.Rev.Lett

Josephson vortex lattices with modulation perpendicular to an in-plane magnetic field in layered superconductor

Authors: Ryusuke Ikeda, Hidehumi Nawata

Abstract: In quasi low dimensional superconductors under {\it parallel} magnetic fields applied along a conducting direction, vortex lattices with a modulation of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type {\it perpendicular} to the field may occur due to an enhanced paramagnetic depairing. As the strength of an in-plane field is varied in a Q2D material, the Josephson vortex lattices accompanied by nod… ▽ More In quasi low dimensional superconductors under {\it parallel} magnetic fields applied along a conducting direction, vortex lattices with a modulation of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type {\it perpendicular} to the field may occur due to an enhanced paramagnetic depairing. As the strength of an in-plane field is varied in a Q2D material, the Josephson vortex lattices accompanied by nodal planes are formed in higher Landau level (LL) modes of the superconducting (SC) order parameter and show field-induced structural transitions. A change of orientation of nodal planes induced by these transitions should be observed in transport measurements for an out-of-plane current in real superconductors with point disorder effective on the SC layers. Further, the $H_{c2}$-transition from this higher LL state to the normal phase is of second order for moderately strong paramagnetic effects but, in the case with a strong enough paramagnetic effect, becomes discontinuous as well as the transition between this modulated state and an ordinary Abrikosov vortex lattice in the lowest LL. Relevance of these results to recent observations in organic superconductors suggesting the presence of an FFLO state are discussed. △ Less

Submitted 16 August, 2007; originally announced August 2007.

Comments: 8 figures

Effect of in-plane line defects on field-tuned superconductor-insulator transition behavior in homogeneous thin film

Authors: Kiyokazu Myojin, Ryusuke Ikeda

Abstract: Field-tuned superconductor-insulator transition (FSIT) behavior in 2D isotropic and homogeneous thin films is usually accompanied by a nonvanishing critical resistance at low $T$. It is shown that, in a 2D film including line defects paralle to each other but with random positions perpendicular to them, the (apparent) critical resistance in low $T$ limit vanishes, as in the 1D quantum supercondu… ▽ More Field-tuned superconductor-insulator transition (FSIT) behavior in 2D isotropic and homogeneous thin films is usually accompanied by a nonvanishing critical resistance at low $T$. It is shown that, in a 2D film including line defects paralle to each other but with random positions perpendicular to them, the (apparent) critical resistance in low $T$ limit vanishes, as in the 1D quantum superconducting (SC) transition, under a current parallel to the line defects. This 1D-like critical resistive behavior is more clearly seen in systems with weaker point disorder and may be useful in clarifying whether the true origin of FSIT behavior in the parent superconductor is the glass fluctuation or the quantum SC fluctuation. As a by-product of the present calculation, it is also pointed out that, in 2D films with line-like defects with a long but {\it finite} correlation length parallel to the lines, a quantum metallic behavior intervening the insulating and SC ones appears in the resistivity curves. △ Less

Submitted 19 July, 2007; originally announced July 2007.

Comments: 16 pages, 14 figures

Strong Coupling Correction in Superfluid $^3$He in Aerogel

Authors: Kazushi Aoyama, Ryusuke Ikeda

Abstract: Effects of impurity scatterings on the strong coupling (SC) contribution, stabilizing the ABM (axial) pairing state, to the quartic term of the Ginzburg-Landau (GL) free energy of superfluid $^3$He are theoretically studied to examine recent observations suggestive of an anomalously small SC effect in superfluid $^3$He in aerogels. To study the SC corrections, two approaches are used. One is bas… ▽ More Effects of impurity scatterings on the strong coupling (SC) contribution, stabilizing the ABM (axial) pairing state, to the quartic term of the Ginzburg-Landau (GL) free energy of superfluid $^3$He are theoretically studied to examine recent observations suggestive of an anomalously small SC effect in superfluid $^3$He in aerogels. To study the SC corrections, two approaches are used. One is based on a perturbation in the short-range repulsive interaction, and the other is a phenomenological approach used previously for the bulk liquid by Sauls and Serene [Phys.Rev.B 24, 183 (1981)]. It is found that the impurity scattering favors the BW pairing state and shrinks the region of the ABM pairing state in the T-P phase diagram. In the phenomenological approach, the resulting shrinkage of the ABM region is especially substantial and, if assuming an anisotropy over a large scale in aerogel, leads to justifying the phase diagrams determined experimentally. △ Less

Submitted 20 August, 2007; v1 submitted 6 July, 2007; originally announced July 2007.

Comments: 19 pages, 9 figures, Accepted for publication in Phys. Rev. B