Microscopic origin of scalar potential induced topological transition in massive Dirac fermions and scalar Hall effect

TL;DR

This paper investigates how scalar potentials can induce topological phase transitions in massive Dirac fermions, leading to a novel scalar Hall effect that allows local manipulation of topological properties and edge states.

Contribution

It introduces the concept of scalar Hall effect driven by scalar potentials, distinct from traditional mechanisms, and explores its implications for topological phase control.

Findings

Scalar potentials can invert bands and manipulate topological invariants.

The scalar Hall effect is intrinsically different from topological Anderson insulators.

Potential for local control of edge states and topological properties.

Abstract

We present a systematic study of scalar potential induced topological transition in massive Dirac fermions. We show how a distribution of scalar potential can manipulate the signature of the gap or the mass, as well as the dispersion leading to a band inversion. This is mediated by the Klein tunnelling as well as inverse Klein tunnelling which makes it inherently different from the mechanism leading to topological Anderson insulator. In one dimension it can lead to the formation of edge localisation. In two dimensions this can give rise to the quantised Hall effect. Unlike conventional Hall effects, this is induced by a scalar interaction and intrinsic in nature. Therefore we call it a scalar Hall effect. This can facilitate a direct manipulation of topological invariants, e.g. the Chern number, as well as the manipulation of the edge states locally in a trivial insulator and thus opens new possibilities for tuning physical observables which originate from the nontrivial topology.