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Direct Fabrication of a Superconducting Two-Dimensional Electron Gas on KTaO3(111) via Mg-Induced Surface Reduction
Authors:
Chun Sum Brian Pang,
Bruce A. Davidson,
Fengmiao Li,
Mohamed Oudah,
Peter C. Moen,
Steef Smit,
Cissy T. Suen,
Simon Godin,
Sergey A. Gorovikov,
Marta Zonno,
Sergey Zhdanovich,
Giorgio Levy,
Matteo Michiardi,
Alannah M. Hallas,
George A. Sawatzky,
Robert J. Green,
Andrea Damascelli,
Ke Zou
Abstract:
Two-dimensional electron gases (2DEGs) at the surfaces of KTaO3 have become an exciting platform for exploring strong spin-orbit coupling, Rashba physics, and low-carrier-density superconductivity. Yet, a large fraction of reported KTaO3-based 2DEGs has been realized through chemically complex overlayers that both generate carriers and can obscure the native electronic structure, making spectrosco…
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Two-dimensional electron gases (2DEGs) at the surfaces of KTaO3 have become an exciting platform for exploring strong spin-orbit coupling, Rashba physics, and low-carrier-density superconductivity. Yet, a large fraction of reported KTaO3-based 2DEGs has been realized through chemically complex overlayers that both generate carriers and can obscure the native electronic structure, making spectroscopic access to the underlying 2DEG challenging. Here, we demonstrate a simple and direct method to generate a superconducting 2DEG on KTaO3(111) using Mg-induced surface reduction in molecular-beam epitaxy (MBE). Mg has an extremely low sticking coefficient at elevated temperatures, enabling the formation of an ultrathin (less than 1-2 monolayers) MgO layer that is transparent to soft x-ray photoemission spectroscopy (XPS) and angle-resolved photoemission spectroscopy (ARPES). This allows direct measurement of the surface chemistry and low-energy electronic structure of the pristine reduced surface without the need for a several-nanometer-thick capping layer. XPS shows clear reduction of Ta5+ to lower oxidation states, while ARPES reveals a parabolic Ta 5d conduction band with an approximately 150 meV bandwidth and additional subband features arising from quantum confinement. Transport measurements confirm a superconducting transition below 0.6 K. Together, these results demonstrate a chemically straightforward and controllable pathway for fabricating spectroscopically accessible superconducting 2DEGs on KTaO3(111), and provide a powerful new platform for investigating the mechanisms underlying orientation-dependent superconductivity in KTaO3-based oxide interfaces.
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Submitted 21 December, 2025;
originally announced December 2025.
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Enhanced coherence and layer-selective charge order in a trilayer cuprate superconductor
Authors:
S. Smit,
M. Bluschke,
P. Moen,
N. Heinsdorf,
E. Zavatti,
G. Bellomia,
S. Giuli,
S. K. Y. Dufresne,
C. T. Suen,
V. Zimmermann,
C. Au-Yeung,
S. Zhdanovich,
J. I. Dadap,
M. Zonno,
S. Gorovikov,
H. Lee,
C-T. Kuo,
J-S. Lee,
D. Song,
S. Ishida,
H. Eisaki,
B. Keimer,
M. Michiardi,
I. S. Elfimov,
G. Levy
, et al. (3 additional authors not shown)
Abstract:
Trilayer cuprates hold the record for the highest superconducting critical temperatures ($T_{\text{c}}$), yet the underlying mechanism remains elusive. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES), we uncover a striking interplay between charge order, superconducting gap magnitude, and quasiparticle coherence in Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$ (Bi2223). This constitutes…
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Trilayer cuprates hold the record for the highest superconducting critical temperatures ($T_{\text{c}}$), yet the underlying mechanism remains elusive. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES), we uncover a striking interplay between charge order, superconducting gap magnitude, and quasiparticle coherence in Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$ (Bi2223). This constitutes ARPES-based evidence of charge order on the inner CuO$_2$ plane, as confirmed via resonant x-ray scattering (RXS); in addition, the same inner plane hosts a superconducting gap significantly larger than that of the overdoped outer planes, firmly establishing it as underdoped. Unexpectedly, despite its underdoped nature, the inner plane also exhibits an exceptional degree of quasiparticle coherence; suppressing charge-order fluctuations further enhances this, making it comparable to that of the overdoped outer planes at elevated electronic temperatures. These findings, supported by complementary three-layer single-band Hubbard calculations, reveal a unique interlayer mechanism in which both pairing strength and phase coherence are optimized when interfacing planes with distinct hole concentrations, providing new microscopic insight into the record $T_{\text{c}}$ of Bi2223.
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Submitted 2 June, 2025;
originally announced June 2025.
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Universal electronic structure of multi-layered nickelates via oxygen-centered planar orbitals
Authors:
Christine C. Au-Yeung,
X. Chen,
S. Smit,
M. Bluschke,
V. Zimmermann,
M. Michiardi,
P. C. Moen,
J. Kraan,
C. S. B. Pang,
C. T. Suen,
S. Zhdanovich,
M. Zonno,
S. Gorovikov,
Y. Liu,
G. Levy,
I. S. Elfimov,
M. Berciu,
G. A. Sawatzky,
J. F. Mitchell,
A. Damascelli
Abstract:
Superconductivity has been demonstrated in the family of multi-layered nickelates La$_3$Ni$_2$O$_7$ and La$_4$Ni$_3$O$_{10}$. Key questions remain open regarding the low-energy electronic states that support superconductivity in these compounds. Here we take advantage of the natural polymorphism between bilayer (2222) and alternating monolayer-trilayer (1313) stacking sequences that arises in bulk…
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Superconductivity has been demonstrated in the family of multi-layered nickelates La$_3$Ni$_2$O$_7$ and La$_4$Ni$_3$O$_{10}$. Key questions remain open regarding the low-energy electronic states that support superconductivity in these compounds. Here we take advantage of the natural polymorphism between bilayer (2222) and alternating monolayer-trilayer (1313) stacking sequences that arises in bulk La$_3$Ni$_2$O$_7$ crystals, and by employing angle-resolved photoemission spectroscopy (ARPES) we identify a universal low-energy electronic structure in this family of materials. We observe the fingerprint of a doping-dependent spin-density wave (SDW) instability -- strong and coherent enough to reconstruct the Fermi surface, both by gapping out regions of the low-energy electronic structure as well as translating the $β$ pocket by a vector $Q_{tβ}$ consistent with the results of previous neutron and x-ray scattering experiments. Using an effective tight-binding model, we simulate the spectral weight distribution observed in our ARPES dichroism experiments and establish that the low-energy electronic phenomenology is dominated by oxygen-centered planar orbitals, which evolve from the $d_{3x^2-r^2}$ and $d_{3y^2-r^2}$ symmetry characteristic of 3-spin polarons (3SP) to the familiar $d_{x^2-y^2}$ Zhang-Rice singlets (ZRS) that support high-temperature superconductivity in cuprates. By inclusion of magnetic moments on plaquettes of oxygen orbitals in our model, we show that ZRS-like states mediate the SDW. Combined with the observation that oxygen annealing is required to induce superconductivity in both thin films and bulk La$_3$Ni$_2$O$_7$, this demonstrates that the ZRS population dictates whether the ground state favors density-wave order or superconductivity -- with hole doping suppressing the former and stabilizing the latter, as in the cuprates.
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Submitted 29 September, 2025; v1 submitted 27 February, 2025;
originally announced February 2025.
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Hund flat band in a frustrated spinel oxide
Authors:
Dongjin Oh,
Alexander Hampel,
Joshua P. Wakefield,
Peter Moen,
Steef Smit,
Xiangyu Luo,
Marta Zonno,
Sergey Gorovikov,
Mats Leandersson,
Craig Polley,
Asish K. Kundu,
Anil Rajapitamahuni,
Elio Vescovo,
Chris Jozwiak,
Aaron Bostwick,
Eli Rotenberg,
Masahiko Isobe,
Manish Verma,
Matteo Crispino,
Martin Grundner,
Fabian B. Kugler,
Olivier Parcollet,
Ulrich Schollwöck,
Hidenori Takagi,
Andrea Damascelli
, et al. (4 additional authors not shown)
Abstract:
Electronic flat bands associated with quenched kinetic energy and heavy electron mass have attracted great interest for promoting strong electronic correlations and emergent phenomena such as high-temperature charge fractionalization and superconductivity. Intense experimental and theoretical research has been devoted to establishing the rich non-trivial metallic and heavy fermion phases intertwin…
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Electronic flat bands associated with quenched kinetic energy and heavy electron mass have attracted great interest for promoting strong electronic correlations and emergent phenomena such as high-temperature charge fractionalization and superconductivity. Intense experimental and theoretical research has been devoted to establishing the rich non-trivial metallic and heavy fermion phases intertwined with such localized electronic states. Here, we investigate the transition metal oxide spinel LiV2O4, an enigmatic heavy fermion compound lacking localized f orbital states. We use angle-resolved photoemission spectroscopy and dynamical mean field theory to reveal a new kind of correlation-induced flat band with suppressed inter-atomic electron hopping arising from intra-atomic Hund coupling. The appearance of heavy quasiparticles is ascribed to a proximate orbital-selective Mott state characterized by fluctuating local moments as evidenced by complementary magnetotransport measurements. The spectroscopic fingerprints of long-lived quasiparticles and their disappearance with increasing temperature further support the emergence of a high-temperature bad metal state observed in transport data. This work resolves a long-standing puzzle on the origin of heavy fermion behavior and unconventional transport in LiV2O4. Simultaneously, it opens a new path to achieving flat bands through electronic interactions in d-orbital systems with geometrical frustration, potentially enabling the realization of exotic phases of matter such as the fractionalized Fermi liquids.
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Submitted 16 February, 2025; v1 submitted 10 February, 2025;
originally announced February 2025.
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Strongly hybridized phonons in one-dimensional van der Waals crystals
Authors:
Shaoqi Sun,
Qingyun Lin,
Yihuan Li,
Daichi Kozawa,
Huizhen Wu,
Shigeo Maruyama,
Pilkyung Moon,
Toshikaze Kariyado,
Ryo Kitaura,
Sihan Zhao
Abstract:
The phenomena of pronounced electron-electron and electron-phonon interactions in one-dimensional (1D) systems are ubiquitous, which are well described by frameworks of Luttinger liquid, Peierls instability and concomitant charge density wave. However, the experimental observation of strongly hybridized phonons in 1D was not demonstrated. Herein we report the first observation of strongly hybridiz…
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The phenomena of pronounced electron-electron and electron-phonon interactions in one-dimensional (1D) systems are ubiquitous, which are well described by frameworks of Luttinger liquid, Peierls instability and concomitant charge density wave. However, the experimental observation of strongly hybridized phonons in 1D was not demonstrated. Herein we report the first observation of strongly hybridized phonons in 1D condensed matters by using double-walled carbon nanotubes (DWNTs), representative 1D van der Waals crystals, with combining the spectroscopic and microscopic tools as well as the ab initio density functional theory (DFT) calculations. We observe uncharted phonon modes in one commensurate and three incommensurate DWNT crystals, three of which concurrently exhibit strongly-reconstructed electronic band structures. Our DFT calculations for the experimentally observed commensurate DWNT (7,7) @ (12,12) reveal that this new phonon mode originates from a (nearly) degenerate coupling between two transverse acoustic modes (ZA modes) of constituent inner and outer nanotubes having approximately trigonal and pentagonal rotational symmetry along the nanotube circumferences. Such coupling strongly hybridizes the two phonon modes in different shells and leads to the formation of a unique lattice motion featuring evenly distributed vibrational amplitudes over inner and outer nanotubes, distinct from any known phonon modes in 1D systems. All four DWNTs that exhibit the pronounced new phonon modes show small chiral angle twists, closely matched diameter ratios of 3/5 and decreased frequencies of new phonon modes with increased diameters, all supporting the uncovered coupling mechanism. Our discovery of strongly hybridized phonons in DWNTs open new opportunities for engineering phonons and exploring novel phonon-related phenomena in 1D condensed matters.
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Submitted 31 March, 2025; v1 submitted 16 August, 2024;
originally announced August 2024.
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Non-linear Landau fan diagram for graphene electrons exposed to a moiré potential
Authors:
Pilkyung Moon,
Youngwook Kim,
Mikito Koshino,
Takashi Taniguchi,
Kenji Watanabe,
Jurgen H. Smet
Abstract:
Due to Landau quantization, the conductance of two-dimensional electrons exposed to a perpendicular magnetic field exhibits oscillations that generate a fan of linear trajectories when plotted in the parameter space spanned by density and magnetic field. This fan looks identical irrespective of the electron dispersion details that determines the field dependence of the Landau level energy. This is…
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Due to Landau quantization, the conductance of two-dimensional electrons exposed to a perpendicular magnetic field exhibits oscillations that generate a fan of linear trajectories when plotted in the parameter space spanned by density and magnetic field. This fan looks identical irrespective of the electron dispersion details that determines the field dependence of the Landau level energy. This is no surprise, since the position of conductance minima solely depends on the level degeneracy which is linear in flux. The fractal energy spectrum that emerges within each Landau band when electrons are also exposed to a two-dimensional superlattice potential produces numerous additional oscillations, but they too create just linear fans for the same reason. Here, we report on conductance oscillations of graphene electrons exposed to a moiré potential that defy this general rule of flux linearity and attribute the anomalous behavior to the simultaneous occupation of multiple minibands and magnetic breakdown.
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Submitted 27 November, 2023;
originally announced November 2023.
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Orbital-selective time-domain signature of nematicity dynamics in the charge-density-wave phase of La$_{1.65}$Eu$_{0.2}$Sr$_{0.15}$CuO$_4$
Authors:
Martin Bluschke,
Naman K. Gupta,
Hoyoung Jang,
Ali A. Husain,
Byungjune Lee,
MengXing Na,
Brandon Dos Remedios,
Steef Smit,
Peter Moen,
Sang-Youn Park,
Minseok Kim,
Dogeun Jang,
Hyeongi Choi,
Ronny Sutarto,
Alexander H. Reid,
Georgi L. Dakovski,
Giacomo Coslovich,
Quynh L. Nguyen,
Nicolas G. Burdet,
Ming-Fu Lin,
Alexandre Revcolevschi,
Jae-Hoon Park,
Jochen Geck,
Joshua J. Turner,
Andrea Damascelli
, et al. (1 additional authors not shown)
Abstract:
Understanding the interplay between charge, nematic, and structural ordering tendencies in cuprate superconductors is critical to unraveling their complex phase diagram. Using pump-probe time-resolved resonant x-ray scattering on the (0 0 1) Bragg peak at the Cu $L_3$ and O $K$ resonances, we investigate non-equilibrium dynamics of $Q_a = Q_b = 0$ nematic order and its association with both charge…
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Understanding the interplay between charge, nematic, and structural ordering tendencies in cuprate superconductors is critical to unraveling their complex phase diagram. Using pump-probe time-resolved resonant x-ray scattering on the (0 0 1) Bragg peak at the Cu $L_3$ and O $K$ resonances, we investigate non-equilibrium dynamics of $Q_a = Q_b = 0$ nematic order and its association with both charge density wave (CDW) order and lattice dynamics in La$_{1.65}$Eu$_{0.2}$Sr$_{0.15}$CuO$_4$. The orbital selectivity of the resonant x-ray scattering cross-section allows nematicity dynamics associated with the planar O 2$p$ and Cu 3$d$ states to be distinguished from the response of anisotropic lattice distortions. A direct time-domain comparison of CDW translational-symmetry breaking and nematic rotational-symmetry breaking reveals that these broken symmetries remain closely linked in the photoexcited state, consistent with the stability of CDW topological defects in the investigated pump fluence regime.
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Submitted 9 September, 2023; v1 submitted 23 September, 2022;
originally announced September 2022.
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Interlayer interactions in one-dimensional van der Waals moiré superlattices
Authors:
Sihan Zhao,
Ryo Kitaura,
Pilkyung Moon,
Mikito Koshino,
Feng Wang
Abstract:
Different atomistic registry between the layers forming the inner and outer nanotubes can form one-dimensional (1D) van der Waals (vdW) moiré superlattices. Unlike the two-dimensional (2D) vdW moiré superlattices, effects of 1D vdW moiré superlattices on electronic and optical properties in 1D moiré superlattices are not well understood, and they are often neglected. In this Perspective, we summar…
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Different atomistic registry between the layers forming the inner and outer nanotubes can form one-dimensional (1D) van der Waals (vdW) moiré superlattices. Unlike the two-dimensional (2D) vdW moiré superlattices, effects of 1D vdW moiré superlattices on electronic and optical properties in 1D moiré superlattices are not well understood, and they are often neglected. In this Perspective, we summarize new experimental observations and theoretical perspectives related to interlayer interactions in double-walled carbon nanotubes (DWNTs), a representative 1D vdW moiré system. Our discussion will focus on new optical features emerging from the interlayer electronic interactions in DWNTs. Exciting correlated physics and exotic phases of matter are anticipated to exist in 1D vdW moiré superlattices, analogous with those discovered in the 2D vdW moiré superlattices. We further discuss the future directions in probing and uncovering interesting physical phenomena in 1D moiré superlattices.
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Submitted 29 July, 2021;
originally announced July 2021.
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Resonant interaction in chiral, Eshelby-twisted van der Waals atomic layers
Authors:
Pilkyung Moon
Abstract:
We study the electronic structures of chiral, Eshelby-twisted van der Waals atomic layers with a particular focus on a chiral twisted graphite (CTG), a graphene stack with a constant twist angle $θ$ between successive layers. We show that each CTG can host infinitely many resonant states which arise from the interaction between the degenerate monolayer states of the constituent layers. Each resona…
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We study the electronic structures of chiral, Eshelby-twisted van der Waals atomic layers with a particular focus on a chiral twisted graphite (CTG), a graphene stack with a constant twist angle $θ$ between successive layers. We show that each CTG can host infinitely many resonant states which arise from the interaction between the degenerate monolayer states of the constituent layers. Each resonant state has a screw rotational symmetry, and may have a smaller reduced Brillouin zone than other non-resonant states in the same structure. And each CTG can have the resonant states with up to four different screw symmetries. We derive the energies and wave functions of the resonant states in a universal form of a one-dimensional chain regardless of $θ$, and show that these states exhibit a clear optical selection rule for circularly polarized light. Finally, we discuss the uniqueness and existence of the exact center of the lattice and the self-similarity of the wave amplitudes of the resonant states.
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Submitted 27 August, 2021; v1 submitted 10 May, 2021;
originally announced May 2021.
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Odd integer quantum Hall states with interlayer coherence in twisted bilayer graphene
Authors:
Youngwook Kim,
Pilkyung Moon,
Kenji Watanabe,
Takashi Taniguchi,
Jurgen H. Smet
Abstract:
We report on the quantum Hall effect in two stacked graphene layers rotated by 2 degree. The tunneling strength among the layers can be varied from very weak to strong via the mechanism of magnetic breakdown when tuning the density. Odd-integer quantum Hall physics is not anticipated in the regime of suppressed tunneling for balanced layer densities, yet it is observed. We interpret this as a sign…
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We report on the quantum Hall effect in two stacked graphene layers rotated by 2 degree. The tunneling strength among the layers can be varied from very weak to strong via the mechanism of magnetic breakdown when tuning the density. Odd-integer quantum Hall physics is not anticipated in the regime of suppressed tunneling for balanced layer densities, yet it is observed. We interpret this as a signature of Coulomb interaction induced interlayer coherence and Bose Einstein condensation of excitons that form at half filling of each layer. A density imbalance gives rise to reentrant behavior due to a phase transition from the interlayer coherent state to incompressible behavior caused by simultaneous condensation of both layers in different quantum Hall states. With increasing overall density, magnetic breakdown gains the upper hand. As a consequence of the enhanced interlayer tunneling, the interlayer coherent state and the phase transition vanish.
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Submitted 5 May, 2021; v1 submitted 4 May, 2021;
originally announced May 2021.
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Trigonal Quasicrystalline States in $30^\circ$ Rotated Double Moiré Superlattices
Authors:
J. A. Crosse,
Pilkyung Moon
Abstract:
We study the lattice configuration and electronic structure of a double moiré superlattice, which is composed of a graphene layer encapsulated by two other layers in a way such that the two hexagonal moiré patterns are arranged in a dodecagonal quasicrystalline configuration. We show that there are between 0 and 4 such configurations depending on the lattice mismatch between graphene and the encap…
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We study the lattice configuration and electronic structure of a double moiré superlattice, which is composed of a graphene layer encapsulated by two other layers in a way such that the two hexagonal moiré patterns are arranged in a dodecagonal quasicrystalline configuration. We show that there are between 0 and 4 such configurations depending on the lattice mismatch between graphene and the encapsulating layer. We then reveal the resonant interaction, which is distinct from the conventional 2-, 3-, 4-wave mixing of moiré superlattices, that brings together and hybridizes twelve degenerate Bloch states of monolayer graphene. These states do not fully satisfy the dodecagonal quasicrystalline rotational symmetry due to the symmetry of the wave vectors involved. Instead, their wave functions exhibit trigonal quasicrystalline order, which lacks inversion symmetry, at the energies much closer to the charge neutrality point of graphene.
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Submitted 25 February, 2021;
originally announced February 2021.
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Faraday rotations, ellipticity and circular dichroism in the magneto-optical spectrum of moiré superlattices
Authors:
J. A. Crosse,
Pilkyung Moon
Abstract:
We study the magneto-optical conductivity of a number of Van der Waals heterostructures, namely, twisted bilayer graphene, AB-AB and AB-BA stacked twisted double bilayer graphene and monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride. As magnetic field increases, the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy…
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We study the magneto-optical conductivity of a number of Van der Waals heterostructures, namely, twisted bilayer graphene, AB-AB and AB-BA stacked twisted double bilayer graphene and monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride. As magnetic field increases, the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum. Whilst twisted bilayer graphene displays only weak circular dichroism, monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride show specifically strong circular dichroism, owing to strong inversion symmetry breaking properties of the hexagonal boron nitride layer. As, the left and right circularly polarized light interact with these structures differently, plane polarized incident light undergoes a Faraday rotation and gains an ellipticity when transmitted. The size of the respective angles is on the order of a degree.
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Submitted 19 February, 2021;
originally announced February 2021.
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Rectification by hydrodynamic flow in an encapsulated graphene Tesla valve
Authors:
Johannes Geurs,
Youngwook Kim,
Kenji Watanabe,
Takashi Taniguchi,
Pilkyung Moon,
Jurgen H. Smet
Abstract:
Systems in which interparticle interactions prevail can be described by hydrodynamics. This regime is typically difficult to access in the solid state for electrons. However, the high purity of encapsulated graphene combined with its advantageous phonon properties make it possible, and hydrodynamic corrections to the conductivity of graphene have been observed. Examples include electron whirlpools…
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Systems in which interparticle interactions prevail can be described by hydrodynamics. This regime is typically difficult to access in the solid state for electrons. However, the high purity of encapsulated graphene combined with its advantageous phonon properties make it possible, and hydrodynamic corrections to the conductivity of graphene have been observed. Examples include electron whirlpools, enhanced flow through constrictions as well as a Poiseuille flow profile. An electronic device relying specifically on viscous behaviour and acting as a viscometer has however been lacking. Here, we implement the analogue of the Tesla valve. It exhibits nonreciprocal transport and can be regarded as an electronic viscous diode. Rectification occurs at carrier densities and temperatures consistent with the hydrodynamic regime, and disappears both in the ballistic and diffusive transport regimes. In a device in which the electrons are exposed to a Moiré superlattice, the Lifshitz transition when crossing the Van Hove singularity is observed in the rectifying behaviour.
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Submitted 11 August, 2020;
originally announced August 2020.
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Anisotropic band flattening in graphene with 1D superlattices
Authors:
Yutao Li,
Scott Dietrich,
Carlos Forsythe,
Takashi Taniguchi,
Kenji Watanabe,
Pilkyung Moon,
Cory R. Dean
Abstract:
Patterning graphene with a spatially-periodic potential provides a powerful means to modify its electronic properties. Dramatic effects have been demonstrated in twisted bilayers where coupling to the resulting moiré-superlattice yields an isolated flat band that hosts correlated many-body phases. However, both the symmetry and strength of the effective moiré potential are constrained by the const…
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Patterning graphene with a spatially-periodic potential provides a powerful means to modify its electronic properties. Dramatic effects have been demonstrated in twisted bilayers where coupling to the resulting moiré-superlattice yields an isolated flat band that hosts correlated many-body phases. However, both the symmetry and strength of the effective moiré potential are constrained by the constituent crystals, limiting its tunability. Here we exploit the technique of dielectric patterning to subject graphene to a one-dimensional electrostatic superlattice (SL). We observe the emergence of multiple Dirac cones and find evidence that with increasing SL potential the main and satellite Dirac cones are sequentially flattened in the direction parallel to the SL basis vector. Our results demonstrate the ability to induce tunable transport anisotropy in high mobility two-dimensional materials, a long-desired property for novel electronic and optical applications, as well as a new approach to engineering flat energy bands where electron-electron interactions can lead to emergent properties.
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Submitted 17 June, 2020; v1 submitted 15 June, 2020;
originally announced June 2020.
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Quasicrystalline electronic states in twisted bilayers and the effects of interlayer and sublattice symmetries
Authors:
J. A. Crosse,
Pilkyung Moon
Abstract:
We study the electronic structure of quasicrystals composed of incommensurate stacks of atomic layers. We consider two systems: a pair of square lattices with a relative twist angle of $θ=45^\circ$ and a pair of hexagonal lattices with a relative twist angle of $θ=30^\circ$, with various interlayer interaction strengths. This constitutes every two-dimensional bilayer quasicrystal system. We invest…
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We study the electronic structure of quasicrystals composed of incommensurate stacks of atomic layers. We consider two systems: a pair of square lattices with a relative twist angle of $θ=45^\circ$ and a pair of hexagonal lattices with a relative twist angle of $θ=30^\circ$, with various interlayer interaction strengths. This constitutes every two-dimensional bilayer quasicrystal system. We investigate the resonant coupling governing the quasicrystalline order in each quasicrystal symmetry, and calculate the quasi-band dispersion. The resonant interaction emerges in bilayer quasicrystals if all the dominant interlayer interactions occur between the atomic orbitals that have the same magnetic quantum number. Thus, not only the quasicrystal composed of the widely studied graphene, but also those composed of transition metal dichalcogenides will exhibit the quasicrystalline states. We find that some quasicrystalline states, which are usually obscured by decoupled monolayer states, are more prominent, i.e., "exposed", in the systems with strong interlayer interaction. We also show that we can switch the states between quasicrystalline configuration and its layer components, by turning on and off the interlayer symmetry.
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Submitted 28 November, 2020; v1 submitted 11 June, 2020;
originally announced June 2020.
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Hofstadter butterfly and the quantum Hall effect in twisted double bilayer graphenes
Authors:
J. A. Crosse,
Naoto Nakatsuji,
Mikito Koshino,
Pilkyung Moon
Abstract:
We study the energy spectrum and quantum Hall effects of the twisted double bilayer graphene in uniform magnetic field. We investigate two different arrangements, AB-AB and AB-BA, which differ in the relative orientation but have very similar band structures in the absence of a magnetic field. For each system, we calculate the energy spectrum and quantized Hall conductivities at each spectral gap…
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We study the energy spectrum and quantum Hall effects of the twisted double bilayer graphene in uniform magnetic field. We investigate two different arrangements, AB-AB and AB-BA, which differ in the relative orientation but have very similar band structures in the absence of a magnetic field. For each system, we calculate the energy spectrum and quantized Hall conductivities at each spectral gap by using a continuum Hamiltonian that satisfies the magneto-translation condition. We show that the Hofstadter butterfly spectra of AB-AB and AB-BA stackings differ significantly, even though their zero magnetic field band structures closely resemble; the spectrum of AB-AB has valley degeneracy, which can be lifted by applying interlayer potential asymmetry, while the spectrum of AB-BA has no such degeneracy in any case. We explain the origin of the difference from the perspectives of lattice symmetry and band topology.
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Submitted 13 May, 2020;
originally announced May 2020.
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Gate tunable optical absorption and band structure of twisted bilayer graphene
Authors:
Kwangnam Yu,
Van Luan Nguyen,
Tae Soo Kim,
Jiwon Jeon,
Jiho Kim,
Pilkyung Moon,
Young Hee Lee,
E. J. Choi
Abstract:
We report the infrared transmission measurement on electrically gated twisted bilayer graphene. The optical absorption spectrum clearly manifests the dramatic changes such as the splitting of inter-linear-band absorption step, the shift of inter-van Hove singularity transition peak, and the emergence of very strong intra-valence (intra-conduction) band transition. These anomalous optical behaviors…
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We report the infrared transmission measurement on electrically gated twisted bilayer graphene. The optical absorption spectrum clearly manifests the dramatic changes such as the splitting of inter-linear-band absorption step, the shift of inter-van Hove singularity transition peak, and the emergence of very strong intra-valence (intra-conduction) band transition. These anomalous optical behaviors demonstrate consistently the non-rigid band structure modification created by the ion-gel gating through the layer-dependent Coulomb screening. We propose that this screening-driven band modification is an universal phenomenon that persists to other bilayer crystals in general, establishing the electrical gating as a versatile technique to engineer the band structures and to create new types of optical absorptions that can be exploited in electro-optical device application.
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Submitted 7 November, 2019;
originally announced November 2019.
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Mapping the twist angle and unconventional Landau levels in magic angle graphene
Authors:
Aviram Uri,
Sameer Grover,
Yuan Cao,
J. A. Crosse,
Kousik Bagani,
Daniel Rodan-Legrain,
Yuri Myasoedov,
Kenji Watanabe,
Takashi Taniguchi,
Pilkyung Moon,
Mikito Koshino,
Pablo Jarillo-Herrero,
Eli Zeldov
Abstract:
The emergence of flat electronic bands and of the recently discovered strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle $θ_M \approx 1.1°$. Although advanced fabrication methods allow alignment of graphene layers with global twist angle control of about 0.1$°$, little information is currently…
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The emergence of flat electronic bands and of the recently discovered strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle $θ_M \approx 1.1°$. Although advanced fabrication methods allow alignment of graphene layers with global twist angle control of about 0.1$°$, little information is currently available on the distribution of the local twist angles in actual magic angle twisted bilayer graphene (MATBG) transport devices. Here we map the local $θ$ variations in hBN encapsulated devices with relative precision better than 0.002$°$ and spatial resolution of a few moir$é$ periods. Utilizing a scanning nanoSQUID-on-tip, we attain tomographic imaging of the Landau levels in the quantum Hall state in MATBG, which provides a highly sensitive probe of the charge disorder and of the local band structure determined by the local $θ$. We find that even state-of-the-art devices, exhibiting high-quality global MATBG features including superconductivity, display significant variations in the local $θ$ with a span close to 0.1$°$. Devices may even have substantial areas where no local MATBG behavior is detected, yet still display global MATBG characteristics in transport, highlighting the importance of percolation physics. The derived $θ$ maps reveal substantial gradients and a network of jumps. We show that the twist angle gradients generate large unscreened electric fields that drastically change the quantum Hall state by forming edge states in the bulk of the sample, and may also significantly affect the phase diagram of correlated and superconducting states. The findings call for exploration of band structure engineering utilizing twist-angle gradients and gate-tunable built-in planar electric fields for novel correlated phenomena and applications.
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Submitted 13 August, 2019;
originally announced August 2019.
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Observation of drastic electronic structure change in one-dimensional moiré crystals
Authors:
Sihan Zhao,
Pilkyung Moon,
Yuhei Miyauchi,
Kazunari Matsuda,
Mikito Koshino,
Ryo Kitaura
Abstract:
We report the first experimental observation of strong coupling effect in one-dimensional moiré crystals. We study one-dimensional double-wall carbon nanotubes (DWCNTs) in which van der Waals-coupled two single nanotubes form one-dimensional moiré superlattice. We experimentally combine Rayleigh scattering spectroscopy and electron beam diffraction on the same individual DWCNTs to probe the optica…
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We report the first experimental observation of strong coupling effect in one-dimensional moiré crystals. We study one-dimensional double-wall carbon nanotubes (DWCNTs) in which van der Waals-coupled two single nanotubes form one-dimensional moiré superlattice. We experimentally combine Rayleigh scattering spectroscopy and electron beam diffraction on the same individual DWCNTs to probe the optical transitions of structure-identified DWCNTs in the visible spectral range. Among more than 30 structure-identified DWCNTs examined, we experimentally observed and identified a drastic change of optical transition spectrum in DWCNT with chirality (12,11)@(17,16). The origin of the marked change is attributed to the strong intertube coupling effect in a moiré superlattice formed by two nearly-armchair nanotubes. Our numerical simulation is consistent to these experimental findings.
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Submitted 27 June, 2019; v1 submitted 22 June, 2019;
originally announced June 2019.
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Quasicrystalline electronic states in 30$^\circ$ rotated twisted bilayer graphene
Authors:
Pilkyung Moon,
Mikito Koshino,
Young-Woo Son
Abstract:
The recently realized bilayer graphene system with a twist angle of $30^\circ$ offers a new type of quasicrystal which unites the dodecagonal quasicrystalline nature and graphene's relativistic properties. Here, we introduce a concise theoretical framework that fully respects both the dodecagonal rotational symmetry and the massless Dirac nature, to describe the electronic states of the system. We…
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The recently realized bilayer graphene system with a twist angle of $30^\circ$ offers a new type of quasicrystal which unites the dodecagonal quasicrystalline nature and graphene's relativistic properties. Here, we introduce a concise theoretical framework that fully respects both the dodecagonal rotational symmetry and the massless Dirac nature, to describe the electronic states of the system. We find that the electronic spectrum consists of resonant states labeled by 12-fold quantized angular momentum, together with the extended relativistic states. The resulting quasi-band structure is composed of the nearly flat bands with spiky peaks in the density of states, where the wave functions exhibit characteristic patterns which fit to the fractal inflations of the quasicrystal tiling. We also demonstrate that the 12-fold resonant states appear as spatially-localized states in a finite-size geometry, which is another hallmark of quasicrystal. The theoretical method introduced here is applicable to a broad class of "extrinsic quasicrystals" composed of a pair of two-dimensional crystals overlaid on top of the other with incommensurate configurations.
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Submitted 9 May, 2019; v1 submitted 15 January, 2019;
originally announced January 2019.
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Dirac Electrons in a Dodecagonal Graphene Quasicrystal
Authors:
Sung Joon Ahn,
Pilkyung Moon,
Tae-Hoon Kim,
Hyun-Woo Kim,
Ha-Chul Shin,
Eun Hye Kim,
Hyun Woo Cha,
Se-Jong Kahng,
Philip Kim,
Mikito Koshino,
Young-Woo Son,
Cheol-Woong Yang,
Joung Real Ahn
Abstract:
Quantum states of quasiparticles in solids are dictated by symmetry. Thus, a discovery of unconventional symmetry can provide a new opportunity to reach a novel quantum state. Recently, Dirac and Weyl electrons have been observed in crystals with discrete translational symmetry. Here we experimentally demonstrate Dirac electrons in a two-dimensional quasicrystal without translational symmetry. A d…
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Quantum states of quasiparticles in solids are dictated by symmetry. Thus, a discovery of unconventional symmetry can provide a new opportunity to reach a novel quantum state. Recently, Dirac and Weyl electrons have been observed in crystals with discrete translational symmetry. Here we experimentally demonstrate Dirac electrons in a two-dimensional quasicrystal without translational symmetry. A dodecagonal quasicrystal was realized by epitaxial growth of twisted bilayer graphene rotated exactly 30 degree. The graphene quasicrystal was grown up to a millimeter scale on SiC(0001) surface while maintaining the single rotation angle over an entire sample and was successfully isolated from a substrate, demonstrating its structural and chemical stability under ambient conditions. Multiple Dirac cone replicated with the 12-fold rotational symmetry were observed in angle resolved photoemission spectra, showing its unique electronic structures with anomalous strong interlayer coupling with quasi-periodicity. Our study provides a new way to explore physical properties of relativistic fermions with controllable quasicrystalline orders.
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Submitted 11 April, 2018;
originally announced April 2018.
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Band Structure Engineering of 2D Materials using Patterned Dielectric Superlattices
Authors:
Carlos Forsythe,
Xiaodong Zhou,
Takashi Taniguchi,
Kenji Watanabe,
Abhay Pasupathy,
Pilkyung Moon,
Mikito Koshino,
Philip Kim,
Cory R. Dean
Abstract:
The ability to manipulate two-dimensional (2D) electrons with external electric fields provides a route to synthetic band engineering. By imposing artificially designed and spatially periodic superlattice (SL) potentials, 2D electronic properties can be further engineered beyond the constraints of naturally occurring atomic crystals. Here we report a new approach to fabricate high mobility SL devi…
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The ability to manipulate two-dimensional (2D) electrons with external electric fields provides a route to synthetic band engineering. By imposing artificially designed and spatially periodic superlattice (SL) potentials, 2D electronic properties can be further engineered beyond the constraints of naturally occurring atomic crystals. Here we report a new approach to fabricate high mobility SL devices by integrating surface dielectric patterning with atomically thin van der Waals materials. By separating the device assembly and SL fabrication processes, we address the intractable tradeoff between device processing and mobility degradation that constrains SL engineering in conventional systems. The improved electrostatics of atomically thin materials moreover allows smaller wavelength SL patterns than previously achieved. Replica Dirac cones in ballistic graphene devices with sub 40nm wavelength SLs are demonstrated, while under large magnetic fields we report the fractal Hofstadter spectra from SLs with designed lattice symmetries vastly different from that of the host crystal. Our results establish a robust and versatile technique for band structure engineering of graphene and related van der Waals materials with dynamic tunability.
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Submitted 5 October, 2017; v1 submitted 3 October, 2017;
originally announced October 2017.
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Emergence of Tertiary Dirac Points in Graphene Moiré Superlattices
Authors:
Guorui Chen,
Mengqiao Sui,
Duoming Wang,
Shuopei Wang,
Jeil Jung,
Pilkyung Moon,
Shaffique Adam,
Kenji Watanabe,
Takashi Taniguchi,
Shuyun Zhou,
Mikito Koshino,
Guangyu Zhang,
Yuanbo Zhang
Abstract:
The electronic structure of a crystalline solid is largely determined by its lattice structure. Recent advances in van der Waals solids, artificial crystals with controlled stacking of two-dimensional (2D) atomic films, have enabled the creation of materials with novel electronic structures. In particular, stacking graphene on hexagonal boron nitride (hBN) introduces moiré superlattice that fundam…
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The electronic structure of a crystalline solid is largely determined by its lattice structure. Recent advances in van der Waals solids, artificial crystals with controlled stacking of two-dimensional (2D) atomic films, have enabled the creation of materials with novel electronic structures. In particular, stacking graphene on hexagonal boron nitride (hBN) introduces moiré superlattice that fundamentally modifies graphene's band structure and gives rise to secondary Dirac points (SDPs). Here we find that the formation of a moiré superlattice in graphene on hBN yields new, unexpected consequences: a set of tertiary Dirac points (TDPs) emerge, which give rise to additional sets of Landau levels when the sample is subjected to an external magnetic field. Our observations hint at the formation of a hidden Kekulé superstructure on top of the moiré superlattice under appropriate carrier doping and magnetic fields.
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Submitted 10 February, 2017;
originally announced February 2017.
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Charge inversion and topological phase transition at a twist angle induced van Hove singularity of bilayer graphene
Authors:
Youngwook Kim,
Patrick Herlinger,
Pilkyung Moon,
Mikito Koshino,
Takashi Taniguchi,
Kenji Watanabe,
Jurgen. H Smet
Abstract:
Van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With t…
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Van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neigbouring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with conventional gating. Here we have addressed magnetotransport when the chemical potential crosses the twist angle induced VHS in twisted bilayer graphene. A topological phase transition is experimentally disclosed in the abrupt conversion of electrons to holes or vice versa, a loss of a non-zero Berry phase and distinct sequences of integer quantum Hall states above and below the singularity.
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Submitted 12 July, 2016; v1 submitted 18 May, 2016;
originally announced May 2016.
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Incommensurate double-walled carbon nanotubes as one-dimensional moiré crystals
Authors:
Mikito Koshino,
Pilkyung Moon,
Young-Woo Son
Abstract:
Cylindrical multishell structure is one of the prevalent atomic arrangements in nanowires. Being multishell, the well-defined atomic periodicity is hardly realized in it because the periodic units of individual shells therein generally do not match except for very few cases, posing a challenge to understand its physical properties. Here we show that moiré patterns generated by superimposing atomic…
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Cylindrical multishell structure is one of the prevalent atomic arrangements in nanowires. Being multishell, the well-defined atomic periodicity is hardly realized in it because the periodic units of individual shells therein generally do not match except for very few cases, posing a challenge to understand its physical properties. Here we show that moiré patterns generated by superimposing atomic lattices of individual shells are decisive in determining its electronic structures. Double- walled carbon nanotubes, as an example, are shown to have spectacular variations in their electronic properties from metallic to semiconducting and further to insulating states depending on their moiré patterns, even when they are composed of only semiconducting nanotubes with almost similar energy gaps and diameters. Thus, aperiodic multishell nanowires can be classified into new one-dimensional moiré crystals with distinct electronic structures.
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Submitted 9 January, 2015; v1 submitted 28 October, 2014;
originally announced October 2014.
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Optical absorption of twisted bilayer graphene with interlayer potential asymmetry
Authors:
Pilkyung Moon,
Young-Woo Son,
Mikito Koshino
Abstract:
We investigate the band structure and the optical absorption spectrum of twisted bilayer graphenes with changing interlayer bias and Fermi energy simultaneously. We show that the interlayer bias lifts the degeneracy of the superlattice Dirac point, while the amount of the Dirac point shift is significantly suppressed in small rotation angles, and even becomes opposite to the applied bias. We calcu…
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We investigate the band structure and the optical absorption spectrum of twisted bilayer graphenes with changing interlayer bias and Fermi energy simultaneously. We show that the interlayer bias lifts the degeneracy of the superlattice Dirac point, while the amount of the Dirac point shift is significantly suppressed in small rotation angles, and even becomes opposite to the applied bias. We calculate the optical absorption spectrum in various asymmetric potentials and Fermi energies, and associate the characteristic spectral features with the band structure. The spectroscopic features are highly sensitive to the interlayer bias and the Fermi energy, and widely tunable by the external field effect.
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Submitted 16 October, 2014; v1 submitted 19 August, 2014;
originally announced August 2014.
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Electronic properties of graphene hexagonal boron nitride moiré superlattice
Authors:
Pilkyung Moon,
Mikito Koshino
Abstract:
We theoretically investigate the electronic structures of moiré superlattices arising in monolayer / bilayer graphene stacked on hexagonal boron nitride (hBN) in presence and absence of magnetic field. We develop an effective continuum model from a microscopic tight-binding lattice Hamiltonian, and calculate the electronic structures of graphene-hBN systems with different rotation angles. Using th…
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We theoretically investigate the electronic structures of moiré superlattices arising in monolayer / bilayer graphene stacked on hexagonal boron nitride (hBN) in presence and absence of magnetic field. We develop an effective continuum model from a microscopic tight-binding lattice Hamiltonian, and calculate the electronic structures of graphene-hBN systems with different rotation angles. Using the effective model, we explain the characteristic band properties such as the gap opening at the corners of the superlattice Brillouin zone (mini-Dirac point). We also investigate the energy spectrum and quantum Hall effect of graphene-hBN systems in uniform magnetic field and demonstrate the evolution of the fractal spectrum as a function of the magnetic field. The spectrum generally splits in the valley degrees of freedom ($K$ and $K'$) due to the lack of the inversion symmetry, and the valley splitting is more significant in bilayer graphene on hBN than in monolayer graphene on hBN because of the stronger inversion-symmetry breaking in bilayer.
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Submitted 8 October, 2014; v1 submitted 3 June, 2014;
originally announced June 2014.
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Optical properties of the Hofstadter butterfly in the Moiré superlattice
Authors:
Pilkyung Moon,
Mikito Koshino
Abstract:
We investigate the optical absorption spectrum and the selection rule for the Hofstadter butterfly in twisted bilayer graphene under magnetic fields. We demonstrate that the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum. We find that the optical selection rule has a nested self-similar structure as well, and it is governed by the…
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We investigate the optical absorption spectrum and the selection rule for the Hofstadter butterfly in twisted bilayer graphene under magnetic fields. We demonstrate that the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum. We find that the optical selection rule has a nested self-similar structure as well, and it is governed by the conservation of the total angular momentum summed over different hierarchies.
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Submitted 9 January, 2014; v1 submitted 3 August, 2013;
originally announced August 2013.
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Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
Authors:
B. Hunt,
J. D. Sanchez-Yamagishi,
A. F. Young,
K. Watanabe,
T. Taniguchi,
P. Moon,
M. Koshino,
P. Jarillo-Herrero,
R. C. Ashoori
Abstract:
Van der Waals heterostructures comprise a new class of artificial materials formed by stacking atomically-thin planar crystals. Here, we demonstrate band structure engineering of a van der Waals heterostructure composed of a monolayer graphene flake coupled to a rotationally-aligned hexagonal boron nitride substrate. The spatially-varying interlayer atomic registry results both in a local breaking…
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Van der Waals heterostructures comprise a new class of artificial materials formed by stacking atomically-thin planar crystals. Here, we demonstrate band structure engineering of a van der Waals heterostructure composed of a monolayer graphene flake coupled to a rotationally-aligned hexagonal boron nitride substrate. The spatially-varying interlayer atomic registry results both in a local breaking of the carbon sublattice symmetry and a long-range moiré superlattice potential in the graphene. This interplay between short- and long-wavelength effects results in a band structure described by isolated superlattice minibands and an unexpectedly large band gap at charge neutrality, both of which can be tuned by varying the interlayer alignment. Magnetocapacitance measurements reveal previously unobserved fractional quantum Hall states reflecting the massive Dirac dispersion that results from broken sublattice symmetry. At ultra-high fields, integer conductance plateaus are observed at non-integer filling factors due to the emergence of the Hofstadter butterfly in a symmetry-broken Landau level.
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Submitted 27 March, 2013;
originally announced March 2013.
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Optical Absorption in Twisted Bilayer Graphene
Authors:
Pilkyung Moon,
Mikito Koshino
Abstract:
We theoretically study the optical absorption property of twisted bilayer graphenes with various stacking geometries, and demonstrate that the spectroscopic characteristics serve as a fingerprint to identify the rotation angle between two layers. We find that the absorption spectrum almost continuously evolves in changing the rotation angle, regardless of the lattice commensurability. The spectrum…
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We theoretically study the optical absorption property of twisted bilayer graphenes with various stacking geometries, and demonstrate that the spectroscopic characteristics serve as a fingerprint to identify the rotation angle between two layers. We find that the absorption spectrum almost continuously evolves in changing the rotation angle, regardless of the lattice commensurability. The spectrum is characterized by series of peaks associated with the van Hove singularity, and the peak energies systematically shift with the rotation angle. We calculate the optical absorption in two different frameworks; the tight-binding model and the effective continuum model based on the Dirac equation. For small rotation angles less than $10^\circ$, the effective model well reproduces the low-energy band structure and the optical conductivity of the tight-binding model, and also explains the optical selection rule analytically in terms of the symmetry of the effective Hamiltonian.
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Submitted 25 February, 2013; v1 submitted 21 February, 2013;
originally announced February 2013.
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Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
Authors:
C. R. Dean,
L. Wang,
P. Maher,
C. Forsythe,
F. Ghahari,
Y. Gao,
J. Katoch,
M. Ishigami,
P. Moon,
M. Koshino,
T. Taniguchi,
K. Watanabe,
K. L. Shepard,
J. Hone,
P. Kim
Abstract:
Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum, consisting of highly degenerate Landau energy levels. In 1976 Douglas Hofstadter theoretically considered the intersection of these two problems and discovered t…
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Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum, consisting of highly degenerate Landau energy levels. In 1976 Douglas Hofstadter theoretically considered the intersection of these two problems and discovered that 2D electrons subjected to both a magnetic field and a periodic electrostatic potential exhibit a self-similar recursive energy spectrum. Known as Hofstadter's butterfly, this complex spectrum results from a delicate interplay between the characteristic lengths associated with the two quantizing fields, and represents one of the first quantum fractals discovered in physics. In the decades since, experimental attempts to study this effect have been limited by difficulties in reconciling the two length scales. Typical crystalline systems (<1 nm periodicity) require impossibly large magnetic fields to reach the commensurability condition, while in artificially engineered structures (>100 nm), the corresponding fields are too small to completely overcome disorder. Here we demonstrate that moire superlattices arising in bilayer graphene coupled to hexagonal boron nitride provide a nearly ideal-sized periodic modulation, enabling unprecedented experimental access to the fractal spectrum. We confirm that quantum Hall effect features associated with the fractal gaps are described by two integer topological quantum numbers, and report evidence of their recursive structure. Observation of Hofstadter's spectrum in graphene provides the further opportunity to investigate emergent behaviour within a fractal energy landscape in a system with tunable internal degrees of freedom.
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Submitted 19 December, 2012;
originally announced December 2012.
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The Effects of Post-Thermal Annealing on the Emission Spectra of GaAs/AlGaAs Quantum Dots grown by Droplet Epitaxy
Authors:
Pilkyung Moon,
J. D. Lee,
S. K. Ha,
E. H. Lee,
W. J. Choi,
J. D. Song,
J. S. Kim,
L. S. Dang
Abstract:
We fabricated GaAs/AlGaAs quantum dots by droplet epitaxy method, and obtained the geometries of the dots from scanning transmission electron microscopy data. Post-thermal annealing is essential for the optical activation of quantum dots grown by droplet epitaxy. We investigated the emission energy shifts of the dots and underlying superlattice by post-thermal annealing with photoluminescence and…
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We fabricated GaAs/AlGaAs quantum dots by droplet epitaxy method, and obtained the geometries of the dots from scanning transmission electron microscopy data. Post-thermal annealing is essential for the optical activation of quantum dots grown by droplet epitaxy. We investigated the emission energy shifts of the dots and underlying superlattice by post-thermal annealing with photoluminescence and cathodoluminescence measurements, and specified the emissions from the dots by selectively etching the structure down to a lower layer of quantum dots. We studied the influences of the degree of annealing on the optical properties of the dots from the peak shifts of the superlattice, which has the same composition as the dots, since the superlattice has uniform and well-defined geometry. Theoretical analysis provided the diffusion length dependence of the peak shifts of the emission spectra.
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Submitted 21 August, 2012;
originally announced August 2012.
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Energy Spectrum and Quantum Hall Effect in Twisted Bilayer Graphene
Authors:
Pilkyung Moon,
Mikito Koshino
Abstract:
We investigate the electronic spectra and quantum Hall effect in twisted bilayer graphenes with various rotation angles under magnetic fields, using a model rigorously including the interlayer interaction. We describe the spectral evolution from discrete Landau levels in the weak field regime to the fractal band structure in the strong field regime, and estimate the quantized Hall conductivity for…
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We investigate the electronic spectra and quantum Hall effect in twisted bilayer graphenes with various rotation angles under magnetic fields, using a model rigorously including the interlayer interaction. We describe the spectral evolution from discrete Landau levels in the weak field regime to the fractal band structure in the strong field regime, and estimate the quantized Hall conductivity for each single gap. In weak magnetic fields, the low-energy conduction band of the twisted bilayer is quantized into electron-like Landau levels and hole-like Landau levels above and below the van Hove singularity, respectively, reflecting a topological change of the Fermi surface between electron pocket and hole pocket. Accordingly the Hall conductivity exhibits a sharp drop from positive to negative at the transition point. In increasing magnetic field, the spectrum gradually evolves into fractal band structure so-called Hofstadter's butterfly, where the Hall conductivity exhibits a nonmonotonic behavior varying from a minigap to a minigap. The magnetic field strength required to invoke the fractal band structure is more feasible in smaller rotating angle.
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Submitted 29 May, 2012; v1 submitted 20 February, 2012;
originally announced February 2012.