Symmetry-dependent topological phase transitions in PbTe layers

TL;DR

This study explores how stacking PbTe layers affects their topological phases, revealing that symmetry and layer number induce non-monotonic topological transitions, with external pressure enabling control over these phases.

Contribution

It demonstrates that stacking symmetry and external pressure can tune topological phases in PbTe layers, highlighting the role of symmetry in finite-size topological transitions.

Findings

Odd layers can be tuned to topological phases with pressure.

Even layers maintain a larger band gap due to nonsymmorphic symmetry.

Symmetry differences explain the distinct topological behaviors.

Abstract

By stacking PbTe layers there is a non-monotonic topological phase transition as a function of the number of monolayers. Based on first principles calculations we find that the proper stacked crystal symmetry determines the topological nature of the slab. While a single PbTe monolayer has a nontrivial phase, pressure can induce topological phase transition in bulk PbTe. Between these two limits, where finite size effects are inherent, we verified that, by applying an external pressure, odd stacking layers can be tuned easily to a topological phase, while even stacking keeps a larger band gap, avoiding band inversion. The quite distinct behavior for odd/even layer is due to the symmetry of the finite stacking. Odd layers preserve the bulk symmorphic symmetry with strong surface hybridization, while even layers belong to a nonsymmorphic group symmetry. Nonsymmorphism induces extra degeneracy reducing the hybridization, thus protecting band inversion, postponing topological phase transitions.