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Integer quantum Hall effect
Hideo Aoki
Integer quantum Hall effect, which is the Hall effect quantized into integer times (: elementary charge, : Planck's constant) observed first in two-dimensional electr…
Exact continuum theory of anti-Klein tunneling in bilayer graphene
P. A. Maksym, H. Aoki
Exact conditions for anti-Klein transmission zeros are found analytically with a 4-component continuum approach which includes trigonal warping. Anti-Klein tunneling occurs at obli…
Optical imprinting of superlattices in two-dimensional materials
Hwanmun Kim, Hossein Dehghani, Hideo Aoki +2
We propose an optical method of shining circularly polarized and spatially periodic laser fields to imprint superlattice structures in two-dimensional electronic systems. By changi…
Complete Spin and Valley Polarization by Total External Reflection from Potential Barriers in Bilayer Graphene and Monolayer Transition Metal Dichalcogenides
P. A. Maksym, H. Aoki
It is shown that potential barriers in bilayer graphene (BLG) and monolayer transition metal dichalcogenides (TMDs) can split a valley unpolarized incident current into reflected a…
Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions
Tohru Kawarabayashi, Hideo Aoki, Yasuhiro Hatsugai
The doubling of massless Dirac fermions on two-dimensional lattices is theoretically studied. It has been shown that the doubling of massless Dirac fermions on a lattice with broke…
Lattice realization of the generalized chiral symmetry in two dimensions
T. Kawarabayashi, H. Aoki, Y. Hatsugai
While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, suc…
Dirac electrons on three-dimensional graphitic zeolites --- a scalable mass gap
Mikito Koshino, Hideo Aoki
A class of graphene wound into three-dimensional periodic curved surfaces ("graphitic zeolites") is proposed and their electronic structures are obtained to explore how the massles…
Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators
Takahiro Mikami, Sota Kitamura, Kenji Yasuda +3
We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hami…
Electronic structure of helicoidal graphene: massless Dirac particles on a curved surface with a screw symmetry
Masataka Watanabe, Hisato Komatsu, Naoto Tsuji +1
Massless Dirac particles on the helicoid are theoretically investigated. With its possible application being helical graphene, we explore how the peculiarities of Dirac particles a…
Flat bands in Weaire-Thorpe model and silicene
Y. Hatsugai, K. Shiraishi, H. Aoki
In order to analytically capture and identify peculiarities in the electronic structure of silicene, Weaire-Thorpe(WT) model, a standard model for treating three-dimensional (3D) s…
Survival of sharp Landau levels in massive tilted Dirac fermions: Protection by generalized chiral operator
Yasuhiro Hatsugai, Tohru Kawarabayashi, Hideo Aoki
Anomalously sharp (delta-function-like) Landau level in the presence of disorder is usually considered to be a manifestation of the massless Dirac fermions in magnetic fields…
Polarization as a topological quantum number in graphene
Hideo Aoki, Yasuhiro Hatsugai
Graphene, with its quantum Hall topological (Chern) number reflecting the massless Dirac particle, is shown to harbor yet another topological quantum number. This is obtained by co…
Spin-resoloved chiral condensate as a spin-unpolarized ν=0 quantum Hall state in graphene
Yuji Hamamoto, Tohru Kawarabayashi, Hideo Aoki +1
Motivated by the recent experiments indicating a spin-unpolarized ν=0 quantum Hall state in graphene, we theoretically investigate the ground state based on the many-body problem p…
Chiral Symmetry and Many-Body Effect in Multilayer Graphene
Yuji Hamamoto, Tohru Kawarabayashi, Hideo Aoki +1
Influence of the chiral symmetry on the many-body problem in multilayer graphene in magnetic fields is investigated. For a spinless electron model on the honeycomb lattice the many…
Stability of zero-mode Landau levels in bilayer graphene against disorder in the presence of the trigonal warping
Tohru Kawarabayashi, Yasuhiro Hatsugai, Hideo Aoki
The stability of the zero-energy Landau levels in bilayer graphene against the chiral symmetric disorder is examined in the presence of the trigonal warping. Based on the tight-bin…
Chiral symmetry and fermion doubling in the zero-mode Landau levels of massless Dirac fermions with disorder
T. Kawarabayashi, T. Honda, H. Aoki +1
The effect of disorder on the Landau levels of massless Dirac fermions is examined for the cases with and without the fermion doubling. To tune the doubling a tight-binding model h…
Chiral condensate with topological degeneracy in graphene and its manifestation in edge states
Yuji Hamamoto, Hideo Aoki, Yasuhiro Hatsugai
Role of chiral symmetry in many-body states of graphene in strong magnetic fields is theoretically studied with the honeycomb lattice model. For a spin-split Landau level where the…
Faraday rotation in bilayer and trilayer graphene in the quantum Hall regime
Takahiro Morimoto, Mikito Koshino, Hideo Aoki
Optical Hall conductivity, as directly related to Faraday rotation, is theoretically studied for bilayer and trilayer graphene. In bilayer graphene, the trigonal warping of the ban…
Generalization of Chiral Symmetry for Tilted Dirac Cones
Tohru Kawarabayashi, Yasuhiro Hatsugai, Takahiro Morimoto +1
The notion of chiral symmetry for the conventional Dirac cone is generalized to include the tilted Dirac cones, where the generalized chiral operator turns out to be non-hermitian.…
Topologically protected Landau levels in bilayer graphene in finite electric fields
Tohru Kawarabayashi, Yasuhiro Hatsugai, Hideo Aoki
The zero-energy Landau level of bilayer graphene is shown to be anomalously sharp (delta-function like) against bond disorder as long as the disorder is correlated over a few latti…
Two parameter flow of σ_{xx}(ω) - σ_{xy}(ω) for the graphene quantum Hall system in ac regime
Takahiro Morimoto, Hideo Aoki
Flow diagram of in finite-frequency () regime is numerically studied for graphene quantum Hall effect (QHE) system. The ac flow diagrams turn out to show qual…
Generalized Chiral Symmetry and Stability of Zero Modes for Tilted Dirac Cones
Tohru Kawarabayashi, Yasuhiro Hatsugai, Takahiro Morimoto +1
While it has been well-known that the chirality is an important symmetry for Dirac-fermion systems that gives rise to the zero-mode Landau level in graphene, here we explore whethe…
Anomalous criticality in the quantum Hall transition at Landau level of graphene with chiral-symmetric disorders
Tohru Kawarabayashi, Takahiro Morimoto, Yasuhiro Hatsugai +1
We investigate numerically whether the chiral symmetry is the sole factor dominating the criticality of the quantum Hall transitions in disordered graphene. When the disorder respe…
Half-integer contributions to the quantum Hall conductivity from single Dirac cones
Haruki Watanabe, Yasuhiro Hatsugai, Hideo Aoki
While the quantum Hall effect in graphene has been regarded as a realization of the anomaly associated with the massless Dirac particle carrying half the usual topological integer,…