Effect of external fields in high Chern number quantum anomalous Hall insulators

A quantum anomalous Hall state with a high Chern number has so far been realized in multilayer structures consisting of alternating magnetic and undoped topological insulator (TI) layers. However, in previous proposals, the Chern number can only be tuned by varying the doping concentration or the width of the magnetic TI layers. This drawback largely restricts the applications of dissipationless chiral edge currents in electronics since the number of conducting channels remains fixed. In this paper, we propose a way of varying the Chern number at will in these multilayered structures by means of an external electric field applied along the stacking direction. In the presence of an electric field in the stacking direction, the inverted bands of the unbiased structure coalesce and hybridize, generating new inverted bands and collapsing the previously inverted ones. In this way, the number of Chern states can be tuned externally in the sample, without the need for modifying the number and width of the layers or the doping level. We showed that this effect can be uncovered by the variation of the transverse conductance as a function of the electric field at constant injection energy at the Fermi level.