We present the theory describing the various surface electronic states arisen from the mixing of conduction and valence bands in a strained mercury telluride (HgTe) bulk material. We demonstrate that the strain-induced band gap in the Brillouin zone center of HgTe results in the surface states of two different kinds. Surface states of the first kind exist in the small region of electron wave vectors near the center of the Brillouin zone and have the Dirac linear electron dispersion characteristic for topological states. The surface states of the second kind exist only far from the center of the Brillouin zone and have the parabolic dispersion for large wave vectors. The structure of these surface electronic states is studied both analytically and numerically in the broad range of their parameters, aiming to develop its systematic understanding for the relevant model Hamiltonian. The results bring attention to the rich surface physics relevant for topological systems.
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