Asymmetric versus symmetric $\mathrm{H}\mathrm{g}\mathrm{T}\mathrm{e}\mathrm{/}\mathrm{C}{\mathrm{d}}_{\mathrm{x}}\mathrm{H}{\mathrm{g}}_{1-\mathrm{x}}\mathrm{T}\mathrm{e}$ double quantum wells: Band gap tuning without electric field

We investigate the electron states in double asymmetric $\mathrm{H}\mathrm{g}\mathrm{T}\mathrm{e}\mathrm{/}\mathrm{C}{\mathrm{d}}_{\mathrm{x}}\mathrm{H}{\mathrm{g}}_{1-\mathrm{x}}\mathrm{T}\mathrm{e}$ quantum wells grown along the $[001]$ direction. The subbands are computed by means of the envelope function approximation applied to the 8-band Kane $\mathbf{k}\cdot \mathbf{p}$ model. The asymmetry of the confining potential of the double quantum wells results in a gap opening which is absent in the symmetric system where it can only be induced by an applied electric field. The band gap and the subbands are affected by spin-orbit coupling which is a consequence of the asymmetry of the confining potential. The electron-like and hole-like states are mainly confined in different quantum wells, and the enhanced hybridization between them opens a spin-dependent hybridization gap at a finite in-plane wavevector. We show that both the ratio of the widths of the two quantum wells and the mole fraction of the $\mathrm{C}{\mathrm{d}}_{\mathrm{x}}\mathrm{H}{\mathrm{g}}_{1-\mathrm{x}}\mathrm{T}\mathrm{e}$ barrier control both the energy gap between the hole-like states and the hybridization gap. The energy subbands are shown to exhibit inverted ordering, and therefore a nontrivial topological phase could emerge in the system.