arXiv subjects

Yasuhiro Hatsugai

Publications and source records attributed to Yasuhiro Hatsugai.

At least 109 records · Page 6Linked to original sources

arXiv2013

Spin-resoloved chiral condensate as a spin-unpolarized ν=0 quantum Hall state in graphene

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 projected onto the n=0 Landau level. For an effective model with the on-site Coulomb repulsion and antiferromagnetic exchange couplings, we show that the ground state is a doubly-degenerate spin-resolved chiral condensate in which all the zero-energy states with up spin are condensed into one chirality, while those with down spin to the other. This can be exactly shown for an Ising-type exchange interaction. The charge gap due to the on-site repulsion in the ground state is shown to grow linearly with the magnetic field, in qualitative agreement with the experiments.

cond-mat.mes-hall↗

arXiv2013

Symmetry Protected Quantization and Bulk-Edge Correspondence of Massless Dirac Fermions: Application to Fermionic Shastry-Sutherland Model

The fermionic Shastry-Sutherland model has a rich phase diagram, including phases with massless Dirac fermions, a quadratic band crossing point, and a pseudospin-1 Weyl fermion. Berry phases defined by the one-dimensional momentum as a parameter are quantized into 0 or pi due to the inversion symmetry combined with the time reversal, or existence of the glide plane, which also protects the massless Dirac cones with continuous parameters. This is the symmetry protected Z2 quantization. We have further demonstrated the Z2 Berry phases generically determine the existence of edge states in various phases and with different types of the boundaries as the bulk-edge correspondence of the massless Dirac fermion systems.

cond-mat.str-el↗

arXiv2013

Interacting Electron Wave Packet Dynamics in a Two-dimensional Nanochannel

Classical and quantum dynamics are important limits for the understanding of the transport characteristics of interacting electrons in nanodevices. Here we apply an intermediate semiclassical approach to investigate the dynamics of two interacting electrons in a planar nanochannel as a function of Coulomb repulsion and electric field. We find that charge is mostly redistributed to the channel edges and that an electric field enhances the particle-like character of electrons. These results may have significant implications for the design and study of future nanodevices.

cond-mat.mes-hall↗

arXiv2012

Chiral Symmetry and Many-Body Effect in Multilayer Graphene

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-body ground state is shown to be a doubly-degenerate chiral condensate irrespective of the number of layers. The energy spectrum calculated numerically with the exact diagonalization method reveals for ABC-stacked multilayer graphenes that the many-body gap decreases monotonically with the number of layers.

cond-mat.mes-hall↗

arXiv2012

Chiral condensate with topological degeneracy in graphene and its manifestation in edge states

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 leading electron-electron interaction is the nearest-neighbor repulsion, a chiral condensate is shown to be, within the subspace of n = 0 Landau level, an exact many-body ground state with a finite gap, for which calculation of Chern numbers reveals that the ground state is a Hall insulator with a topological degeneracy of two. The topological nature of the ground state is shown to manifest itself as a Kekuléan bond order along armchair edges, while the pattern melts in the bulk due to quantum fluctuations. The whole story can be regarded as a realization of the bulk-edge correspondence peculiar to the chiral symmetry.

cond-mat.mes-hall↗

arXiv2012

Generalization of Chiral Symmetry for Tilted Dirac Cones

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. It is shown that the generalized chiral symmetry generically protects the zero modes (n=0 Landau level) of the Dirac cone even when tilted. The present generalized symmetry is equivalent to the condition that the Dirac Hamiltonian is elliptic as a differential operator, which provides an explicit relevance to the index theorem.

cond-mat.mes-hall↗

arXiv2011

Topologically protected Landau levels in bilayer graphene in finite electric fields

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 lattice constants.The robustness of the zero-mode anomaly can be attributed to the preserved chiral symmetry. Unexpectedly, even when we apply a finite potential difference (i.e., an electric field) between the top and the bottom layers, the valley-split $n=0$ Landau levels remain anomalously sharp although they are now shifted away from the zero energy, while the $n=1$ Landau levels exhibit the usual behavior.

cond-mat.mes-hall↗

arXiv2011

Z$_2$ topological number of local quantum clusters in the orthogonal dimer model

We have studied the $Z_2$ topological number defined by the Berry phase for the gapped frustrated systems including the orthogonal dimer model which has a direct product state of local quantum clusters as the exact ground state. The $Z_2$ topological number can clarify what kind of the local quantum clusters is formed to lift the macroscopic degeneracy due to frustration, even when the exact ground state is unknown. As a demonstration, the dimer-singlet and plaquette-singlet phase are identified by two kinds of Z$_2$ topological numbers in the Shastry-Sutherland model and its generalization realized experimentally as SrCu$_2$(BO$_3$)$_2$ and CaV$_4$O$_9$.

cond-mat.mtrl-sci↗

arXiv2011

Generalized Chiral Symmetry and Stability of Zero Modes for Tilted Dirac Cones

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 whether this notion can be extended to tilted Dirac cones as encountered in organic metals. We have found that there exists a "generalized chiral symmetry" that encompasses the tilted Dirac cones, where a generalized chiral operator $γ$, satisfying $γ^{\dagger} H + Hγ=0$ for the Hamiltonian $H$, protects the zero mode. We can use this to show that the $n=0$ Landau level is delta-function-like (with no broadening) by extending the Aharonov-Casher argument. We have numerically confirmed that a lattice model that possesses the generalized chirality has an anomalously sharp Landau level for spatially correlated randomness.

cond-mat.mes-hall↗

arXiv2010

Half-integer contributions to the quantum Hall conductivity from single Dirac cones

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, this is hidden due to the doubling of the Dirac cones. In order to confirm the half-integer contribution from each Dirac cone, here we theoretically consider a lattice model in which the relative energy between the two Dirac points is systematically shifted. With an explicit calculation of the topological (Chern) number, we have demonstrated that each Dirac cone does indeed contribute to the Hall conductivity as the half odd integer series (... -3/2, -1/2, 1/2, 3/2, ...) when the Fermi energy traverses the (shifted sets of) Landau levels. The picture is also endorsed, via the bulk-edge correspondence, from the edge mode spectrum for the present model.

cond-mat.mes-hall↗

arXiv2010

Topological aspect of graphene physics

Topological aspects of graphene are reviewed focusing on the massless Dirac fermions with/without magnetic field. Doubled Dirac cones of graphene are topologically protected by the chiral symmetry. The quantum Hall effect of the graphene is described by the Berry connection of a manybody state by the filled Landau levels which naturally possesses non-Abelian gauge structures. A generic principle of the topologically non trivial states as the bulk-edge correspondence is applied for graphene with/without magnetic field and explain some of the characteristic boundary phenomena of graphene.

cond-mat.mes-hall↗

arXiv2010

Anomalous criticality in the quantum Hall transition at $n=0$ Landau level of graphene with chiral-symmetric disorders

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 respects the chiral symmetry, the plateau-to-plateau transition at the $n=0$ Landau level is shown to become anomalous (i.e., step-function-like). Surprisingly, however, the anomaly is robust against the inclusion of the uniform next-nearest neighbor hopping, which degrades the chiral symmetry of the lattice models. We have also shown that the ac (optical) Hall conductivity exhibits a robust plateau structure when the disorder respects the chiral symmetry.

cond-mat.mes-hall↗

arXiv2010

Topological quantum phase transition in the BEC-BCS crossover phenomena

A crossover between the Bose Einstein condensation (BEC) and BCS superconducting state is described topologically in the chiral symmetric fermion system with attractive interaction. Using a local Z_2 Berry phase, we found a quantum phase transition between the BEC and BCS phases without accompanying the bulk gap closing.

cond-mat.str-el↗

arXiv2009

Optical Hall conductivity in 2DEG and graphene QHE systems

We have revealed from a numerical study that the Hall plateaus are retained in the optical Hall conductivity $σ_{xy}(ω)$ in the ac ($\sim$ THz) regime in both of the ordinary two-dimensional electron gas and graphene in the quantum Hall regime, although the plateau height in ac deviates from integer multiples of $e^2/h$. The effect remains unexpectedly robust against a significant strength of disorder, which we attribute to an effect of localization. We predict the ac Hall plateaus are observable through the Faraday rotation with the rotation angle characterized by the fine-structure constant $α$. In this paper we clarify the relationship between plateau structures and the disorder strength by performing numerical calculation.

cond-mat.mes-hall↗

arXiv2009

Numerical study of quantum Hall effect in two-dimensional multi-band system: single- and multi-layer graphene

The Chern numbers which correspond to quantized Hall conductance $σ_{xy}$ were calculated for single- and bi-layer honeycomb lattices. The quantization of $σ_{xy}$ occurs in entire energy range. Several large jumps of Chern numbers appear at van-Hove singularities of energy bands without magnetic fields. The plateauxof $σ_{xy}$ are discussed from semi-classical quantization.

cond-mat.mes-hall↗

arXiv2009

Quantum Hall plateau transition in graphene with spatially correlated random hopping

We investigate how the criticality of the quantum Hall plateau transition in disordered graphene differs from those in the ordinary quantum Hall systems, based on the honeycomb lattice with ripples modeled as random hoppings. The criticality of the graphene-specific n=0 Landau level is found to change dramatically to an anomalous, almost exact fixed point as soon as we make the random hopping spatially correlated over a few bond lengths. We attribute this to the preserved chiral symmetry and suppressed scattering between K and K' points in the Brillouin zone. The results suggest that a fixed point for random Dirac fermions with chiral symmetry can be realized in free-standing, clean graphene with ripples.

cond-mat.mes-hall↗

arXiv2009

Optical Hall conductivity in ordinary and graphene QHE systems

We have revealed from a numerical study that the optical Hall conductivity $σ_{xy}(ω)$ has a characteristic feature even in the ac ($\sim$ THz) regime in that the Hall plateaus are retained both in the ordinary two-dimensional electron gas and in graphene in the quantum Hall (QHE) regime, although the plateau height is no longer quantized in ac. In graphene $σ_{xy}(ω)$ reflects the unusual Landau level structure. The effect remains unexpectedly robust against a significant strength of disorder, which we attribute to an effect of localization. We predict the ac quantum Hall measurements are feasible through the Faraday rotation characterized by the fine-structure constant $α$.

cond-mat.mes-hall↗

arXiv2009

Landau level broadening in graphene with long-range disorder -- Robustness of the n=0 level

Broadening of the Landau levels in graphene and the associated quantum Hall plateau-to-plateau transition are investigated numerically. For correlated bond disorder, the graphene-specific n=0 Landau level of the Dirac fermions becomes anomalously sharp accompanied by the Hall transition exhibiting a fixed-point-like criticality. Similarly anomalous behavior for the n=0 Landau level is also shown to occur in correlated random magnetic fields, which suggests that the anomaly is generic to disorders that preserve the chiral symmetry.

cond-mat.mes-hall↗