Surface density of states in superconductors with inhomogeneous pairing constant: Analytical results

Abstract

We consider a superconductor with surface suppression of the BCS pairing constant λ(x). We analytically find the gap in the surface density of states (DOS), behavior of the DOS ν(E) above the gap, a "vertical" peculiarity of the DOS around an energy equal to the bulk order parameter ∆0, and a perturbative correction to the DOS at higher energies. The surface gap in the DOS is parametrically different from the surface value of the order parameter due to a difference between the spatial scale rc, at which λ(x) is suppressed, and the coherence length. The vertical peculiarity implies an infinite-derivative inflection point of the DOS curve at E = ∆0 with square-root behavior as E deviates from ∆0. The coefficients of this dependence are different at E < ∆0 and E > ∆0, so the peculiarity is asymmetric. :1910.11275v2 [cond-mat.supr-con] CONTENTS arXiv