Title: Superconductivity in quantum wires: A symmetry analysis,
Abstract: We study properties of quantim wires with spin-orbit coupling and time
reversal symmetry breaking, in normal and superconducting states. Electronic
band structures are classified according to quasi-one-dimensional magnetic
point groups, or magnetic classes. The latter belong to one of three distinct
types, depending on the way the time reversal operation appears in the group
elements. The superconducting gap functions are constructed using antiunitary
operations and have different symmetry properties depending on the type of the
magnetic point group. We obtain the spectrum of the Andreev boundary modes near
the end of the wire in a model-independent way, using the semiclassical
approach with the boundary conditions described by a phenomenological
scattering matrix. Explicit expressions for the bulk topological invariants
controlling the number of the boundary zero modes are presented in the general
multiband case for two types of the magnetic point groups, corresponding to
DIII and BDI symmetry classes.