title: Duality in the Azbel-Hofstadter Problem and Two-Dimensional d-Wave Superconductivity with a Magnetic Field.
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 = Delta/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.
authors.affiliation: Department of Applied Physics, University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo 113-8656, Japan.
authors.initials: Y
authors.lastname: Morita
authors.initials: Y
authors.lastname: Hatsugai