General response theory of topologically stable Fermi points and its implications for disordered cases

TL;DR

This paper develops a response theory for topologically stable Fermi points, linking their topological charges to effective field theories, and explores implications for disordered systems and symmetry classes.

Contribution

It introduces a general response framework for topological Fermi points and derives associated topological terms in non-linear sigma models, including new examples with quadratic Fermi points.

Findings

Derived Wess-Zumino terms with topological charges as levels.

Presented examples of quadratic Fermi points with charge 2.

Connected topological charges to non-linear sigma model terms.

Abstract

We develop a general response theory of gapless Fermi points with nontrivial topological charges for gauge and nonlinear sigma fields, which asserts that the topological character of the Fermi points is embodied as the terms with discrete coefficients proportional to the corresponding topological charges. Applying the theory to the effective non-linear sigma models for topological Fermi points with disorders in the framework of replica approach, we derive rigorously the Wess-Zumino terms with the topological charges being their levels in the two complex symmetry classes of A and AIII. Intriguingly, two nontrivial examples of quadratic Fermi points with the topological charge `2' are respectively illustrated for the classes A and AIII. We also address a qualitative connection of topological charges of Fermi points in the real symmetry classes to the topological terms in the non-linear sigma models, based on the one-to-one classification correspondence.