Local topological phase transitions in periodic condensed matter systems

TL;DR

This paper establishes a criterion for when topological phase transitions in periodic systems can be localized near a single momentum point, linking gap closings to Dirac-like points and illustrating with real material examples.

Contribution

It introduces a general criterion for localizing topological phase transitions in momentum space, connecting them to Dirac-like gap closings, and demonstrates this with experimental examples.

Findings

Local topological phase transitions occur near Dirac-like points.

Flat band transitions are not localized in momentum space.

The criterion applies to systems like HgTe/CdTe quantum wells and bilayer graphene.

Abstract

Topological properties of a periodic condensed matter system are global features of its Brillouin zone (BZ). In contrast, the validity of effective low energy theories is usually limited to the vicinity of a high symmetry point in the BZ. We derive a general criterion under which the control parameter of a topological phase transition localizes the topological defect in an arbitrarily small neighbourhood of a single point in $k$-space upon approaching its critical value. Such a local phase transition is associated with a Dirac-like gap closing point, whereas a flat band transition is not localized in $k$-space. This mechanism and its limitations are illustrated with the help of experimentally relevant examples such as HgTe/CdTe quantum wells and bilayer graphene nanostructures.