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

Abstract

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$(quantumparameter).Atopologicalnumberisattachedtoeachenergyband.Adualitybetweentheclassicallimit($h=+0$)andthequantumlimit($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.

3 pages with 5 postscript figures, RevTeX

References in corpus (3)

• Quasiparticle Spectrum of d-wave Superconductors in the Mixed State
• Plateaux Transitions in the Pairing Model:Topology and Selection Rule
• Transitions from the Quantum Hall State to the Anderson Insulator: Fa te of Delocalized States

Cited by in corpus (7)

• Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions
• Index theoretic characterization of d-wave superconductors in the vortex state
• Topologically protected Landau level in the vortex lattice of a Weyl superconductor
• Energy Spectrum of Bloch Electrons Under Checkerboard Field Modulations
• Anisotropy on the Fermi Surface of the Two-Dimensional Hubbard Model
• Landau levels and optical conductivity in the mixed state of a generic Weyl superconductor
• Azbel-Hofstadter model on triangular lattice revisited