Duality in the Azbel-Hofstadter problem and the two-dimensional d-wave superconductivity with a magnetic field

Details Duality in the Azbel-Hofstadter problem and the two-dimensional d-wave superconductivity with a magnetic field Duality in the Azbel-Hofstadter problem and the two-dimensional d-wave superconductivity with a magnetic field

2000-07-05

arxiv.org/abs/cond-mat/0007067v1

Physics

Condensed Matter

Superconductivity

3 pages with 5 postscript figures, RevTeX

Scientific paper

10.1103/PhysRevLett.86.151

A single-parameter family of lattice-fermion model is constructed. It is a deformation of the Azbel-Hofstadter problem by a parameter $h={$B%((BDelta}/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 the two-dimensional d-wave superconductivity with a magnetic field. Making use of the duality and a topological argument, we shed light on how the quasiparticles with a magnetic field behave especially in the quantum limit.

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