Zero modes in the random hopping model

P. W. Brouwer; E. Racine; A. Furusaki; Y. Hatsugai; Y. Morita; C. Mudry

doi:10.1103/PhysRevB.66.014204

Zero modes in the random hopping model

P. W. Brouwer, E. Racine, A. Furusaki, Y. Hatsugai, Y. Morita, and C. Mudry

Phys. Rev. B 66, 014204 – Published 9 July 2002

Abstract

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.

Received 31 January 2002

DOI:https://doi.org/10.1103/PhysRevB.66.014204

Authors & Affiliations

P. W. Brouwer and E. Racine

Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501

A. Furusaki

Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

Y. Hatsugai

Department of Applied Physics, University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo 113-8656, Japan
PRESTO, Japan Science and Technology Corporation, Kawaguchi-shi, Saitama, 332-0012, Japan

Y. Morita