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Physical Review B - Condensed Matter and Materials Physics


We further investigate a class of time-reversal-invariant two-band s-wave topological superconductors introduced earlier [Deng, Viola, and Ortiz, Phys. Rev. Lett. 108, 036803 (2012)]. Provided that a sign reversal between the two superconducting pairing gaps is realized, the topological phase diagram can be determined exactly (within mean field) in one and two dimensions as well as in three dimensions upon restricting to the excitation spectrum of time-reversal-invariant momentum modes. We show how, in the presence of time-reversal symmetry, Z2 invariants that distinguish between trivial and nontrivial quantum phases can be constructed by considering only one of the Kramers’ sectors in which the Hamiltonian decouples into. We find that the main features identified in our original two-dimensional setting remain qualitatively unchanged, with nontrivial topological superconducting phases supporting an odd number of Kramers’ pairs of helical Majorana modes on each boundary, as long as the required π-phase difference between gaps is maintained. We also analyze the consequences of time-reversal-symmetry breaking either due to the presence of an applied or impurity magnetic field or to a deviation from the intended phase matching between the superconducting gaps. We demonstrate how the relevant notion of topological invariance must be modified when time-reversal symmetry is broken, and how both the persistence of gapless Majorana modes and their robustness properties depend in general upon the way in which the original Hamiltonian is perturbed. Interestingly, a topological quantum phase transition between helical and chiral superconducting phases can be induced by suitably tuning a Zeeman field in conjunction with a phase mismatch between the gaps. Recent experiments in doped semiconducting crystals, of potential relevance to the proposed model, and possible candidate material realizations in superconductors with s± pairing symmetry are discussed.