  We consider time-reversal-symmetric two-channel semiconducting quantum wires
proximity coupled to an s-wave superconductor. We analyze the requirements for
a nontrivial topological phase and find that necessary conditions are 1) the
determinant of the pairing matrix in channel space must be negative, 2)
inversion symmetry must be broken, and 3) the two channels must have different
spin-orbit couplings. The first condition can be implemented in semiconducting
nanowire systems where interactions suppress intra-channel pairing, while the
inversion symmetry can be broken by tuning the chemical potentials of the
channels. For the case of collinear spin-orbit directions, we find a general
expression for the topological invariant by block diagonalization into two
blocks with chiral symmetry only. By projection to the low-energy sector, we
solve for the zero modes explicitly and study the details of the gap closing,
which in the general case happens at finite momenta.
