Topological Marker Currents in Chern Insulators

TL;DR

This paper explores local topological markers in Chern insulators, demonstrating their use in identifying phase transitions and revealing topological currents out of equilibrium, with implications for experimental measurement.

Contribution

It introduces the concept of topological marker currents in Chern insulators and analyzes their behavior both in equilibrium and out of equilibrium, including their propagation dynamics.

Findings

Topological markers can detect critical behavior at phase transitions.

Out of equilibrium, topological markers flow as currents with bounded speed.

Potential experimental methods for measuring topological currents are discussed.

Abstract

Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However, local topological markers can distinguish between topological phases, and they can vary in space. In equilibrium, we show that the topological marker can be used to extract the critical behavior of topological phase transitions. Out of equilibrium, we show that the topological marker spreads via a flow of currents, with a bounded maximum propagation speed. We discuss the possibilities for measuring the topological marker and its flow in experiment.