Duality in the Azbel-Hofstadter Problem and Two-Dimensional <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="italic">d</mi></math></span>-Wave Superconductivity with a Magnetic Field

Y. Morita; Y. Hatsugai

doi:10.1103/PhysRevLett.86.151

Duality in the Azbel-Hofstadter Problem and Two-Dimensional $d$ -Wave Superconductivity with a Magnetic Field

Y. Morita and Y. Hatsugai

Phys. Rev. Lett. 86, 151 – Published 1 January 2001

Abstract

A single-parameter family of the lattice-fermion model is constructed. It is a deformation of the Azbel-Hofstadter problem by a parameter $h = Δ / t$ (quantum parameter). A topological number is attached to each energy band. A duality between the classical limit ( $h = + 0$ ) and the quantum limit ( $h = 1$ ) is revealed in the energy spectrum and the topological number. The model has a close relation to two-dimensional $d$ -wave superconductivity with a magnetic field. Making use of the duality and a topological argument, we shed light on how quasiparticles with a magnetic field behave, especially in the quantum limit.

Received 5 July 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.151

Authors & Affiliations

Y. Morita¹ and Y. Hatsugai^1,2

¹Department of Applied Physics, University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo 113-8656, Japan
²PRESTO, Japan Science and Technology Corporation, Kawaguchi-shi, Saitama, 332-0012, Japan