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We present a theory of the electron structure and the Zeeman effect for thehelical edge states emerging in two-dimensional topological insulators based onHgTe/HgCdTe quantum wells with strong natural interface inversion asymmetry.The interface inversion asymmetry, reflecting the real atomistic structure ofthe quantum well, drastically modifies both bulk and edge states. For thein-plane magnetic field, this asymmetry leads to a strong anisotropy of theedge-state effective $g$-factor which becomes dependent on the edgeorientation. The interface inversion asymmetry also couples the counterpropagating edge states in the out-of-plane magnetic field leading to theopening of the gap in the edge-state spectrum by arbitrary small fields.

physical review. b./physical review. b

Magnetic field effects on edge and bulk states in topological insulators  based on HgTe/CdHgTe quantum wells with strong natural interface inversion  asymmetry