Proximity effects and a topological invariant in a Chern insulator connected to leads

TL;DR

This paper reveals that in Chern insulators connected to leads, edge current leakage affects the quantization of Hall conductance, which can be linked to a topological invariant involving reflection phase winding.

Contribution

It demonstrates that proximity effects in Chern insulators connected to leads influence conductance quantization and introduces a topological invariant based on reflection phase winding.

Findings

Edge current leaks into leads near the Chern insulator.

Quantized Hall conductance depends on proximity effects.

A topological invariant is identified via reflection phase winding.

Abstract

The observed robustly quantized Hall conductance in quantum Hall systems and Chern insulators (CI) have so far been understood in terms of the topology of isolated systems, which are not coupled to leads. It is assumed that the leads act as inert reservoirs that simply supply/absorb electrons to/from the sample. Within a model of a CI coupled to leads with a cylindrical geometry, we show that this is not true. In the proximity of the CI, the edge current leaks into the leads, with the Hall conductance quantized only if this novel proximity effect is taken into account. For a special choice of leads, we identify the conductance with a topological invariant of the system, in terms of the winding number of the phase of the reflection coefficients of the scattering states.