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Y. Hatsugai

Publications and source records attributed to Y. Hatsugai.

At least 37 records · Page 2Linked to original sources
arXiv2008

Quantum Hall effects of graphene with multi orbitals: Topological numbers, Boltzmann conductance and Semi-classical quantization

Hall conductance $σ_{xy}$ as the Chern numbers of the Berry connection in the magnetic Brillouin zone is calculated for a realistic multi band tight-band model of graphene with non-orthogonal basis. It is confirmed that the envelope of $σ_{xy}$ coincides with a semi-classical result when magnetic field is sufficiently small. The Hall resistivity $ρ_{xy}$ from the weak-field Boltzmann theory also explains the overall behaviour of the $σ_{xy}$ if the Fermi surface is composed of a single energy band. The plateaux of $σ_{xy}$ are explained from semi-classical quantization and necessary modification is proposed for the Dirac fermion regimes.

cond-mat.mes-hall↗
arXiv2008

Quantized Berry Phases of a Spin-1/2 Frustrated Two-Leg Ladder with Four-Spin Exchange

A spin-1/2 frustrated two-leg ladder with four-spin exchange interaction is studied by quantized Berry phases. We found that the Berry phase successfully characterizes the Haldane phase in addition to the rung-singlet phase, and the dominant vector-chirality phase. The Hamiltonian of the Haldane phase is topologically identical to the S=1 antiferromagnetic Heisenberg chain. Decoupled models connected to the dominant vector-chirality phase revealed that the local object identified by the non-trivial ($π$) Berry phase is the direct product of two diagonal singlets.

cond-mat.str-el↗
arXiv2008

Non-adiabatic effect on Laughlin's argument of the quantum Hall effect

We have numerically studied a non-adiabatic charge transport in the quantum Hall system pumped by a magnetic flux, as one of the simplest theoretical realizations of non-adiabatic Thouless pumping. In the adiabatic limit, a pumped charge is quantized, known as Laughlin's argument in a cylindrical lattice. In a uniform electric field, we obtained a formula connecting quantized pumping in the adiabatic limit and no-pumping in the sudden limit. The intermediate region between the two limits is determined by the Landau gap. A randomness or impurity effect is also discussed.

cond-mat.mes-hall↗
arXiv2008

Topological Identification of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange

A spin-1/2 two-leg ladder with four-spin ring exchange is studied by quantized Berry phases, used as local order parameters. Reflecting local objects, non-trivial ($π$) Berry phase is founded on a rung for the rung-singlet phase and on a plaquette for the vector-chiral phase. Since the quantized Berry phase is topological invariant for gapped systems with the time reversal symmetry, topologically identical models can be obtained by the adiabatic modification. The rung-singlet phase is adiabatically connected to a decoupled rung-singlet model and the vector-chiral phase is connected to a decoupled vector-chiral model. Decoupled models reveals that the local objects are a local singlet and a plaquette singlet respectively.

cond-mat.str-el↗
arXiv2007

Charge and spin stripe in La$_{2-x}$Sr$_{x}$NiO$_{4}$ (x=1/3,1/2)

Electronic structure of stripe ordered La$_{2-x}$Sr$_{x}$NiO$_{4}$ is investigated. The system with x=1/3 is insulator, in LSDA+U calculations, and shows charge and spin stripe, consistent with the experimental results. Highly correlated system of x=1/2 is studied by using exact diagonalization of multi-orbital many body Hamiltonian derived from LDA calculations and including on-site and inter-site Coulomb interactions. The fluctuation of the residual spin on Ni$^{3+}$ (hole) site couples with the charge fluctuation between Ni$^{3+}$ and Ni$^{2+}$ states and this correlation lowers the total energy. The resultant ground state is insulator with charge and spin stripe of the energy gap 0.9eV, consistent with observed one. The on-site Coulomb interaction stabilizes integral valency of each Ni ion (Ni$^{3+}$ and Ni$^{2+}$), but does not induce the charge order. Two quantities, inter-site Coulomb interaction and anisotropy of hopping integrals, play an important role to form the charge and spin stripe order in a system of x=1/2.

cond-mat.str-el↗
arXiv2007

Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields

We discuss topological aspects of electronic properties of graphene, including edge effects, with the tight-binding model on a honeycomb lattice and its extensions to show the following: (i) Appearance of the pairn of massless Dirac dispersions, which is the origin of anomalous properties including a peculiar quantum Hall effect (QHE), is not accidental to honeycomb, but is rather generic for a class of two-dimensional lattices that interpolate between square and $π$-flux lattices. Persistence of the peculiar QHE is interpreted as a topological stability. (ii) While we have the massless Dirac dispersion only around E=0, the anomalous QHE associated with the Dirac cone unexpectedly persists for a wide range of the chemical potential. The range is bounded by van Hove singularities, at which we predict a transition to the ordinary fermion behavior acompanied by huge jumps in the QHE with a sign change. (iii) For edges we establish a coincidence between the quantum Hall effect in the bulk and the quantum Hall effect for the edge states, which is a manifestation of the topological bulk-edge correspondence. We have also explicitly shown that the E=0 edge states in honeycomb in zero magnetic field persist in magnetic field.

cond-mat.mes-hall↗
arXiv2006

Quantum spin Hall effect in three dimensional materials: Lattice computation of Z$_2$ topological invariants and its application to Bi and Sb

We derive an efficient formula for Z$_2$ topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three dimensions. Based on this, we study the quantum spin Hall effect in Bi and Sb in quasi-two and three dimensions using a tight-binding model.

cond-mat.mes-hall↗
arXiv2006

Topological analysis of the quantum Hall effect in graphene: Dirac-Fermi transition across van Hove singularities and the edge vs bulk quantum numbers

Inspired by a recent discovery of a peculiar integer quantum Hall effect (QHE) in graphene, we study QHE on a honeycomb lattice in terms of the topological quantum number, with two-fold interests: First, how the zero-mass Dirac QHE around the center of the tight-binding band crosses over to the ordinary finite-mass fermion QHE around the band edges. Second, how the bulk QHE is related with the edge QHE for the entire spectrum including Dirac and ordinary behaviors. We find the following: (i) The zero-mass Dirac QHE persists up to the van Hove singularities, at which the ordinary fermion behavior abruptly takes over. Here a technique developed in the lattice gauge theory enabled us to calculate the behavior of the topological number over the entire spectrum. This result indicates a robustness of the topological quantum number, and should be observable if the chemical potential can be varied over a wide range in graphene. (ii) To see if the honeycomb lattice is singular in producing the anomalous QHE, we have systematically surveyed over square-honeycomb-$π$-flux lattices, which is scanned by introducing a diagonal transfer $t'$. We find that the massless Dirac QHE forms a critical line, that is, the presence of Dirac cones in the Brillouin zone is preserved by the inclusion of $t'$ and the Dirac region sits side by side with ordinary one persists all through the transformation. (iii) We have compared the bulk QHE number obtained by an adiabatic continuity of the Chern number across transformation and numerically obtained edge QHE numbers calculated from the whole energy spectra for sample with edges, which shows that the bulk QHE number coincides, as in ordinary lattices, with the edge QHE number throughout the lattice transformation.

cond-mat.mes-hall↗
arXiv2006

Topological aspects of quantum spin Hall effect in graphene: Z$_2$ topological order and spin Chern number

For generic time-reversal invariant systems with spin-orbit couplings, we clarify a close relationship between the Z$_2$ topological order and the spin Chern number proposed by Kane and Mele and by Sheng {\it et al.}, respectively, in the quantum spin Hall effect. It turns out that a global gauge transformation connects different spin Chern numbers (even integers) modulo 4, which implies that the spin Chern number and the Z$_2$ topological order yield the same classification. We present a method of computing spin Chern numbers and demonstrate it in single and double plane of graphene.

cond-mat.mes-hall↗
arXiv2006

Entanglement entropy and the Berry phase in solid states

The entanglement entropy (von Neumann entropy) has been used to characterize the complexity of many-body ground states in strongly correlated systems. In this paper, we try to establish a connection between the lower bound of the von Neumann entropy and the Berry phase defined for quantum ground states. As an example, a family of translational invariant lattice free fermion systems with two bands separated by a finite gap is investigated. We argue that, for one dimensional (1D) cases, when the Berry phase (Zak's phase) of the occupied band is equal to $π\times ({odd integer})$ and when the ground state respects a discrete unitary particle-hole symmetry (chiral symmetry), the entanglement entropy in the thermodynamic limit is at least larger than $\ln 2$ (per boundary), i.e., the entanglement entropy that corresponds to a maximally entangled pair of two qubits. We also discuss this lower bound is related to vanishing of the expectation value of a certain non-local operator which creates a kink in 1D systems.

cond-mat.mes-hall↗
arXiv2005

Topological Description of (Spin) Hall Conductances on Brillouin Zone Lattices : Quantum Phase Transitions and Topological Changes

It is widely accepted that topological quantities are useful to describe quantum liquids in low dimensions. The (spin) Hall conductances are typical examples. They are expressed by the Chern numbers, which are topological invariants given by the Berry connections of the ground states. We present a topological description for the (spin) Hall conductances on a discretized Brillouin Zone. At the same time, it is quite efficient in practical numerical calculations for concrete models. We demonstrate its validity in a model with quantum phase transitions. Topological changes supplemented with the transition is also described in the present lattice formulation.

cond-mat.mes-hall↗
arXiv2003

Dirac Monopole and Spin Hall Conductance for Anisotropic Superconductivities

Concept of the topological order is useful to characterize anisotropic superconductivities. The spin Hall conductance distinguishes superconductivities with the same symmetry. The Chern number for the spin Hall conductance is given by the covering degree of a closed surface around the Dirac monopole. It gives a clear illustration for the on-critical condition for the $d_{x^2-y^2}$ supreconductivitiy with non zero chemical potential. Non trivial topological orders on the triangular lattice are also presented and demonstrated by the topological objects.

cond-mat.supr-con↗
arXiv2003

Superconductivity and Abelian Chiral Anomalies

Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are given by the Chern numbers of degenerate condensate bands for unitary order, which are realizations of Abelian chiral anomalies for non-Abelian connections. The three types of Chern numbers for the $x,y$ and $z$-directions are given by covering degrees of some doubled surfaces around the Dirac monopoles. For nonunitary states, several topological invariants are defined by analyzing the so-called $q$-helicity. Topological origins of the nodal structures of superconducting gaps are also discussed.

cond-mat.supr-con↗
arXiv2002

Anderson Localization and Polarization

Effects of randomness have supplied fundamental problems in condensed matter physics and localization due to interference of quantum mechanical electrons are well studied as the Anderson localization. Although we have well established understanding of the localization of non-interacting electrons, information of the correlated electrons with randomness is still missing. It was mainly due to lack of reliable numerical techniques for the correlated electrons. For the one dimensional correlated systems without randomness, lots of numerical results are collected by the Density Matrix Renormalization Group (DMRG) method and consistent understanding with analytical predictions has been achieved. In this paper, we plan to apply DMRG for the random electron systems by calculating direct responses of the system with electric field. At first, random systems without interaction are carefully investigated. Then we try to treat both of interaction and randomness in one dimensional systems.

cond-mat.dis-nn↗
arXiv2002

Correlation effects on the Fermi surface of the two-dimensional Hubbard model

Effects of electron correlation on the Fermi surface is investigated for the two-dimensional Hubbard model by the quantum Monte Carlo method. At first, an infinitesimal doping from the half filling is focused on and the momentum dependent charge susceptibility $κ(k)=\frac {dn(k)}{dμ}$ is calculated at a finite temperature. At the temperature $T \sim \frac {t^2} U$, it shows peak structure at $(\pm π/2,\pm π/2)$ on the Fermi surface (line). It is consistent with the mean-field prediction of the d-wave pairing state or the staggerd flux state. This momentum dependent structure disappears at the high temperature $T \approx U$. After summarizing the results of the half filling case, we also discuss the effects of the doping on the momentum dependent charge susceptibility. The anisotropic structure at half filling fades out with sufficient doping.

cond-mat.str-el↗
arXiv2002

Anisotropy on the Fermi Surface of the Two-Dimensional Hubbard Model

We investigate anisotropic charge fluctuations in the two-dimensional Hubbard model at half filling. By the quantum Monte Carlo method, we calculate a momentum-resolved charge compressibility $κ(\bm{k}) = {d < n(\bm{k}) >}/{d μ}$, which shows effects of an infinitesimal doping. At the temperature $T \sim {t^2}/{U}$, $κ(\bm{k})$ shows peak structure at the $(\pm π/2,\pm π/2)$ points along the $|k_x| + |k_y| = π$ line. A similar peak structure is reproduced in the mean-filed calculation for the d-wave pairing state or the staggered flux state.

cond-mat.str-el↗
arXiv2002

Zero-modes in the random hopping model

If the number of lattice sites is odd, a quantum particle hopping on a bipartite lattice with random hopping between the two sublattices only is guaranteed to have an eigenstate at zero energy. We show that the localization length of this eigenstate depends strongly on the boundaries of the lattice, and can take values anywhere between the mean free path and infinity. The same dependence on boundary conditions is seen in the conductance of such a lattice if it is connected to electron reservoirs via narrow leads. For any nonzero energy, the dependence on boundary conditions is removed for sufficiently large system sizes.

cond-mat.dis-nn↗