Topological massive Dirac edge modes and long-range superconducting Hamiltonians

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We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower-band eigenvector and the winding number of the Hamiltonians. For exponentially decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive nonlocal Dirac fermion localized at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.
©2016 American Physical Society. M.A.M-D. and O.V. thank the Spanish MINECO Grant FIS2012-33152, the CAM research consortium QUITEMAD+ S2013/ICE-2801, the U.S. Army Research Office through Grant W911NF-14-1-0103, FPU MECD Grant and Residencia de Estudiantes. G.P. and D.V. acknowledge support by the ERC-St Grant ColdSIM (No. 307688), EOARD, UdS via Labex NIE, ANR via BLUSHIELD and IdEX, RYSQ.
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