Chiral non-linear sigma-models as models for topological superconductivity

TL;DR

This paper explores how chiral non-linear sigma-models can serve as effective models for topological superconductivity across different dimensions, highlighting the role of topological solitons and flux quantization.

Contribution

It introduces a hierarchical chain of chiral non-linear sigma-models as a novel framework for understanding topological superconductivity in various dimensions.

Findings

Topological solitons carry electric charge.

Flux quantization generalizes persistent current phenomena.

Superconducting states remain stable under weak disorder.

Abstract

We study the mechanism of topological superconductivity in a hierarchical chain of chiral non-linear sigma-models (models of current algebra) in one, two, and three spatial dimensions. The models have roots in the 1D Peierls-Frohlich model and illustrate how the 1D Frohlich's ideal conductivity extends to a genuine superconductivity in dimensions higher than one. The mechanism is based on the fact that a point-like 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.