Odd-Parity Topological Superconductors: Theory and Application to Cux_xBi2_2Se3_3

Topological superconductors have been theoretically predicted as a new class of time-reversal-invariant superconductors which are fully gapped in the bulk but have protected gapless surface Andreev bound states. In this work, we provide a simple criterion that directly identifies this topological phase in \textit{odd-parity} superconductors. We next propose a two-orbital $U-V$ pairing model for the newly discovered superconductor Cu$_x$Bi$_2$Se$_3$%. Due to its peculiar three-dimensional Dirac band structure, we find that an inter-orbital triplet pairing with odd-parity is favored in a significant part of the phase diagram, and therefore gives rise to a topological superconductor phase. Finally we propose sharp experimental tests of such a pairing symmetry.Comment: 4.1 pages, 2 figure

Topological Superconducting Phases of Weakly Coupled Quantum Wires

An array of quantum wires is a natural starting point in realizing two-dimensional topological phases. We study a system of weakly coupled quantum wires with Rashba spin-orbit coupling, proximity coupled to a conventional s-wave superconductor. A variety of topological phases are found in this model. These phases are characterized by "Strong" and "Weak" topological invariants, that capture the appearance of mid-gap Majorana modes (either chiral or non-chiral) on edges along and perpendicular to the wires. In particular, a phase with a single chiral Majorana edge mode (analogous to a $p+ip$ superconductor) can be realized. At special values of the magnetic field and chemical potential, this edge mode is almost completely localized at the outmost wires. In addition, a phase with two co-propagating chiral edge modes is observed. We also consider ways to distinguish experimentally between the different phases in tunneling experiments