Symmetry and topology of noncentrosymmetric superconductors

We present a detailed analysis of the pairing symmetry and the order parameter topology in superconductors without centre of inversion. Strong spin-orbit coupling of electrons with the crystal lattice leads to a large splitting of the Bloch bands, which makes it necessary to use a multiband description of superconductivity. We identify stable superconducting states and derive the Bogoliubov-de Gennes Hamiltonian, which determines the spectrum of fermionic quasiparticles. To develop a topological classification of the superconducting states we introduce two different types of topological invariants, the Chern numbers and the Maurer-Cartan invariants, and apply them to three-dimensional noncentrosymmetric superconductors, both with and without time reversal symmetry breaking.