Duality in the Azbel-Hofstadter Problem and Two-Dimensional d-Wave Superconductivity with a Magnetic Field
Y. Morita, Y. Hatsugai
DOI 10.1103/PhysRevLett.86.151 · Physical Review Letters
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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.
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