Chiral Nonlinear <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="italic">σ</mi></math></span> Models as Models for Topological Superconductivity

A. G. Abanov; P. B. Wiegmann

doi:10.1103/PhysRevLett.86.1319

Chiral Nonlinear $σ$ Models as Models for Topological Superconductivity

A. G. Abanov and P. B. Wiegmann

Phys. Rev. Lett. 86, 1319 – Published 12 February 2001

Abstract

We study the mechanism of topological superconductivity in a hierarchical chain of chiral nonlinear $σ$ models (models of current algebra) in one, two, and three spatial dimensions. The models illustrate how the 1D Fröhlich's ideal conductivity extends to a genuine superconductivity in dimensions higher than one. The mechanism is based on the fact that a pointlike topological soliton carries an electric charge. We discuss a flux quantization mechanism and show that it is essentially a generalization of the persistent current phenomenon, known in quantum wires. We also discuss why the superconducting state is stable in the presence of a weak disorder.

Received 26 June 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.1319

Authors & Affiliations

A. G. Abanov¹ and P. B. Wiegmann^2,3

¹Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
²James Franck Institute of the University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637
³Landau Institute for Theoretical Physics, Moscow, Russia 117940