Effective field theories for superconducting systems with multiple Fermi surfaces

TL;DR

This paper develops effective field theories for superconductors with multiple Fermi surfaces, revealing topological states and the role of vortex configurations in their electromagnetic response.

Contribution

It introduces a general procedure to derive low energy actions for multi-Fermi surface superconductors, highlighting non-conservation of supercurrent due to vortex effects.

Findings

Single Fermi surface superconductor is a topological state.

Multiple Fermi surfaces lead to a time reversal symmetric topological superconductor.

Non-conservation of supercurrent is driven by vortex configurations.

Abstract

In this work we investigate the description of superconducting systems with multiple Fermi surfaces. For the case of one Fermi surface we re-obtain the result that the superconductor is more precisely described as a topological state of matter. Studying the case of more than one Fermi surface, we obtain the effective theory describing a time reversal symmetric topological superconductor. These results are obtained by employing a general procedure to construct effective low energy actions describing states of electromagnetic systems interacting with charges and defects. The procedure consists in taking into account the proliferation or dilution of these charges and defects and its consequences for the low energy description of the electromagnetic response of the system. We find that the main ingredient entering the low energy characterization of the system with more the one Fermi surface is a non-conservation of the canonical supercurrent triggered by particular vortex configurations.