Effects of electron-hole asymmetry on electronic structure of helical edge states in HgTe/HgCdTe quantum wells

We study the effects of electron-hole asymmetry on the electronic structure of helical edge states in HgTe/HgCdTe quantum wells. In the framework of the four-band $\mathbf{kp}$-model, which takes into account the absence of a spatial inversion centre, we obtain analytical expressions for the energy spectrum and wave functions of edge states, as well as the effective $q$-factor tensor and matrix elements of electro-dipole optical transitions between the spin branches of the edge electrons. We show that when two conditions are simultaneously satisfied–electron-hole asymmetry and the absence of an inversion centre–the spectrum of edge electrons deviates from the linear one, in that case we obtain corrections to the linear spectrum.