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Influence of bulk inversion asymmetry on the magneto-optical spectrum of a HgTe topological insulator

The influence of bulk inversion asymmetry in [001] and [013] grown HgTe quantum wells is investigated theoretically. The bulk inversion asymmetry leads to an anti-crossing gap between two zero-mode Landau levels in a HgTe topological insulator, i.e., the quantum well with inverted band structure. It is found that this is the main contribution to the anti-crossing splitting observed in recent experimental magneto spectroscopic measurements. The relevant optical transitions involve different subbands, but the electron-electron interaction induced depolarization shift is found to be negligibly small. It is also found that the splitting of this anti-crossing only depends weakly on the tilting angle when the magnetic field is tilted away from the perpendicular direction to the quantum well. Thus, the strength of bulk inversion asymmetry can be determined via a direct comparison between the theoretical calculated one-electron energy levels and experimentally observed anti-crossing energy gap.