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We present a simplified way to access and manipulate the topology of massiveDirac fermions by means of scalar potential. We show systematically how adistribution of scalar potential can manipulate the signature of the gap or themass term as well as the dispersion leading to a band inversion via inverseKlein tunnelling. In one dimension it can lead to the formation of edgelocalisation. In two dimensions this can give rise to an emergent mechanism,which we refer to as the Scalar Hall Effect. This can facilitate a directmanipulation of topological invariants, e.g. the Chern number, as well asallows to manipulate the edge states locally and thus opens new possibilitiesfor tuning physical observables which originate from the nontrivial topology.

Infusing nontrivial topology in massive Dirac fermions with scalar potential: Emergence of Scalar Hall Effect