Yasuhiro Hatsugai

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A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A "loop" in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological properties, combined with the chiral symmetry, play an essential role. It provides a unified framework to discuss(More)
In this paper we study the spectrum of low-energy edge excitations of a fractional quantum Hall (FQH) droplet. We show how to generate, by conformal field theory (CFT) techniques, the many-electron wave functions for the edge states. And we propose to classify the spectrum of the edge states by the same chiral operator product algebra (OPA) that appears in(More)
Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton's law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we(More)
We reveal from numerical study that the optical Hall conductivity sigma(xy)(omega) has a characteristic feature even in the ac ( approximately THz) regime in that the Hall plateaus are retained both in the ordinary two-dimensional electron gas and in graphene in the quantum Hall regime, although the plateau height is no longer quantized in ac. In graphene(More)
Two-dimensional graphite sheets with a certain type of edges are known to support boundary states localized near the edges. Forming a flat band with a sharp peak in the density of states at the Fermi energy, they can trigger a magnetic instability or a distortion of the lattice in the presence of electron-electron or electron-phonon interactions. We shall(More)
Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving different assumptions on statistical correlations. Thermal activation of quasiparticle pairs and thermodynamic properties of(More)
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(More)
The Hall conductance σxy of two-dimensional lattice electrons with random potential is investigated. The change of σxy due to randomness is focused on. It is a quantum phase transition where the sum rule of σxy plays an important role. By the string (anyon) gauge, numerical study becomes possible in sufficiently weak magnetic field regime. It is essential(More)
Yasuhiro Hatsugai, Mahito Kohmoto, Tohru Koma, and Yong-Shi Wu 1 Department of Applied Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, JAPAN 2 Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106, JAPAN 3 Department of Physics, Gakushuin University, Mejiro, Toshima-ku, Tokyo 171, JAPAN Department of Physics,(More)