Properties of Interfaces and Surfaces in Non-centrosymmetric Superconductors

Tunneling spectroscopy at surfaces of unconventional superconductors hasproven an invaluable tool for obtaining information about the pairing symmetry.It is known that mid gap Andreev bound states manifest itself as a zero biasconductance peak in tunneling spectroscopy. The zero bias conductance peak is asignature for a non-trivial pair potential that exhibits different signs ondifferent regions of the Fermi surface. Here, we review recent theoreticalresults on the spectrum of Andreev bound states near interfaces and surfaces innon-centrosymmetric superconductors. We introduce a theoretical scheme tocalculate the energy spectrum of a non-centrosymmetric superconductor. Then, wediscuss the interplay between the spin orbit vector field on the Fermi surfaceand the order parameter symmetry. The Andreev states carry a spin supercurrentand represent a helical edge mode along the interface. We study the topologicalnature of the resulting edge currents. If the triplet component of the orderparameter dominates, then the helical edge mode exists. If, on the other hand,the singlet component dominates, the helical edge mode is absent. A quantumphase transition occurs for equal spin singlet and triplet order parametercomponents. We discuss the tunneling conductance and the Andreev point contactconductance between a normal metal and a non-centrosymmetric superconductor.