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 midgap Majorana modes (either chiral or nonchiral) 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 copropagating chiral edge modes is observed. We also consider ways to distinguish experimentally between the different phases in tunneling experiments.