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Several IV-VI semiconductor compounds made of heavy atoms, such asPb$_{1-x}$Sn$_{x}$Te, may undergo band-inversion at the $L$ point of theBrillouin zone upon variation of their chemical composition. This inversiongives rise to topologically distinct phases, characterized by a change in atopological invariant. In the framework of the $\mathbf{k}\cdot\mathbf{p}$theory, band-inversion can be viewed as a change of sign of the fundamentalgap. A two-band model within the envelope-function approximation predicts theappearance of midgap interface states with Dirac cone dispersions inband-inverted junctions, namely, when the gap changes sign along the growthdirection. We present a thorough study of these interface electron states inthe presence of crossed electric and magnetic fields, the electric field beingapplied along the growth direction of a band-inverted junction. We show thatthe Dirac cone is robust and persists even if the fields are strong. Inaddition, we point out that Landau levels of electron states lying in thesemiconductor bands can be tailored by the electric field. Tunable devices arethus likely to be realizable exploiting the properties studied herein.

Robust midgap states in band-inverted junctions under electric and magnetic fields