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

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 tunneling as well as inverse Klein tunneling, which makes it inherently different from the mechanism leading to topological Anderson insulator. In one dimension it can lead to the formation of edge localization. In two dimensions this can give rise to the quantized Hall effect. Unlike conventional Hall effects, this is induced by a scalar interaction and is intrinsic in nature. Therefore, we call it a scalar Hall effect. This can facilitate 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.