Effective field theories of topological crystalline insulators and topological crystals

TL;DR

This paper develops a general method to derive effective field theories for topological crystalline insulators using massive Dirac fermions and mass interfaces, revealing quantized topological responses and enabling classification of these phases.

Contribution

It introduces a unified approach to obtain effective field theories for crystalline topological phases via dimensional reduction and mass interface analysis.

Findings

Identification of quantized topological terms in effective theories

Framework for classifying crystalline topological insulators

Generalization to other symmetry-protected phases

Abstract

We present a general approach to obtain effective field theories for topological crystalline insulators whose low-energy theories are described by massive Dirac fermions. We show that these phases are characterized by the responses to spatially dependent mass parameters with interfaces. These mass interfaces implement the dimensional reduction procedure such that the state of interest is smoothly deformed into a topological crystal, which serves as a representative state of a phase in the general classification. Effective field theories are obtained by integrating out the massive Dirac fermions, and various quantized topological terms are uncovered. Our approach can be generalized to other crystalline symmetry protected topological phases and provides a general strategy to derive effective field theories for such crystalline topological phases.