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A method for constructing the low energy effective models for pairings in the generalized Bernevig-Hughes-Zhang model for materials like Bi$_{2}$Se$_{3}$ is proposed. Pairings in this two-orbital model are identified with those familiar in one-orbital models, enabling a unified understanding. The theory provides an easy way to understand the topological nature of the superconducting state that is not directly related to the topological order in the normal state but due to subtle coupling among the degrees of freedom. Furthermore this approach shows a simple way to characterize the anisotropic nature of surface Andreev bound states (SABSs). In particular, we have identified the conditions to have a surprising new result of having two pairs of SABSs. It also leads to a conclusion that SABSs always connect with the topological surface states if the latter are well defined at the chemical potential.
We study the effects of electron correlations on the topological phase transition in the Bernevig-Hughes-Zhang model using the variational cluster approach where the short-range spatial correlations are taken into account exactly. We calculate the sp
The energy spectrum of cake shape normal - superconducting systems is calculated by solving the Bogoliubov-de Gennes equation. We take into account the mismatch in the effective masses and Fermi energies of the normal and superconducting regions as w
We report anomalous enhancement of the critical current at low temperatures in gate-tunable Josephson junctions made from topological insulator BiSbTeSe$_2$ nanoribbons with superconducting Nb electrodes. In contrast to conventional junctions, as a f
High resolution measurements of the specific heat of liquid $^{3}$He in the presence of a silver surface have been performed at temperatures near the superfluid transition in the pressure range of 1 to 29 bar. The surface contribution to the heat cap
We calcuate electronic spin susceptibility and spin-lattice relaxation rate in singlet superconductor near a pairbreaking surface, or in a domain wall of the order parameter. We directly link presence of high-density Andreev bound states in the inhom