Long-range Topological Superconductors: Majorana & Non-local Dirac fermions

Long-range interactions can dramatically modify the phase diagram of condensed matter systems. Novel topological superconducting phases can be induced in both wire-shaped and planar structures by including long-range effects. In 1D, massless Majorana modes at the edge pair into a new topological quasiparticle: a massive Dirac fermion localized at both edges of the wire. This new topological phase has fractional quantum numbers as a consequence of the long-range couplings. Moreover, we remarkably observe a staircase of higher-order topological phase transitions. In 2D, we show how long-range interactions may greatly enhance the formation of chiral topological superconductivity. The inclusion of long-range effects is potentially applicable to recent experiments with magnetic impurities and islands in superconductors.
[1] Chiral Topological Superconductors Enhanced by Long-range Interactions, O. Viyuela, L. Fu, M.A. Martin-Delgado, arXiv: 1707.02326 (2017).
[2] Staircase to Higher-Order Topological Phase Transitions, P. Cats, A. Quelle, O. Viyuela, M.A. Martin-Delgado, C.Morais Smith, arXiv: 1710.05691 (2017).