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Magnetic Force Between Two Parallel Currents01:13

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

Morita1, Hatsugai

  • 1Department of Applied Physics, University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo 113-8656, Japan.

Physical Review Letters
|January 3, 2001
PubMed
Summary

We introduce a lattice-fermion model, a quantum deformation of the Azbel-Hofstadter problem. A duality reveals how quasiparticles behave in magnetic fields, particularly in the quantum limit.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Topological Materials

Background:

  • The Azbel-Hofstadter problem describes electron behavior in a magnetic field on a lattice.
  • Understanding quasiparticle dynamics in magnetic fields is crucial for novel electronic devices.

Purpose of the Study:

  • To construct and analyze a single-parameter family of the lattice-fermion model.
  • To explore the duality between classical and quantum limits of this model.
  • To investigate quasiparticle behavior in magnetic fields within the quantum limit.

Main Methods:

  • Deformation of the Azbel-Hofstadter model using a quantum parameter h = Delta/t.
  • Attaching a topological number to each energy band.
  • Analyzing the energy spectrum and topological number across different limits.
  • Employing duality and topological arguments.

Main Results:

  • Construction of a single-parameter lattice-fermion model.
  • Revealed duality between the classical (h=0) and quantum (h=1) limits in energy spectrum and topological number.
  • Established a connection to 2D d-wave superconductivity in a magnetic field.

Conclusions:

  • The constructed model exhibits a significant duality, offering insights into quantum phenomena.
  • The findings illuminate quasiparticle behavior under magnetic fields, especially in the quantum regime.
  • This work provides a theoretical framework for understanding topological properties in superconducting systems.