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

A. G. Abanov·P. B. Wiegmann
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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.

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A. G. Abanov, P. B. Wiegmann. 2000-06-20. Chiral non-linear sigma-models as models for topological superconductivity. https://doi.org/10.1103/physrevlett.86.1319

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