# Revisiting (higher order and crystalline) topology in old models of lead telluride

## TL;DR

This paper reexamines a classic PbTe model, revealing it as a higher-order topological crystalline insulator with symmetry-protected boundary modes, and discusses its relevance to real PbTe materials.

## Contribution

It demonstrates that the old PbTe model is a higher-order topological crystalline insulator diagnosable by symmetry indicators, linking it to recent predictions for real PbTe.

## Key findings

- The low energy theory corresponds to a higher-order topological crystalline insulator.
- Gapless fermions on domain walls are topological boundary modes.
- Any symmetric completion of the model shares the same topological phase.

## Abstract

In this work, we revisit the model of PbTe presented in [E. Fradkin, E. Dagotto, and D. Boyanovsky, Phys. Rev. Lett. 57, 2967 (1986)]. We show that the low energy theory of this model corresponds to a (higher-order) topological crystalline insulator in space group $Fm\bar{3}m1'$, diagnosable by symmetry indicators. We show that the gapless fermions found on antiphase domain walls are the topological boundary modes of the system, due to a nonvanishing mirror Chern number. Furthermore, we show that any symmetric completion of the model must be in this same topological phase. Finally, we comment on the relationship of this model to realistic PbTe, which has recently been predicted to have a phase which realizes same bulk symmetry indicators.