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 $\lambda (x)$. We analytically find the gap in the surface density of states (DOS), behavior of the DOS $\nu (E)$ above the gap, a "vertical" peculiarity of the DOS around an energy equal to the bulk order parameter ${\Delta }_0$, 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 $r_c$, at which $\lambda (x)$ is suppressed, and the coherence length. The vertical peculiarity implies an infinite-derivative inflection point of the DOS curve at $E={\Delta }_0$ with square-root behavior as $E$ deviates from ${\Delta }_0$. The coefficients of this dependence are different at $E<{\Delta }_0$ and $E>{\Delta }_0$, so the peculiarity is asymmetric.

9 pages, 3 figures. Version 2: extended introduction, added references, extended discussion of the results. Final version as published in PRB

References in corpus (4)

• Surface impedance and optimum surface resistance of a superconductor with imperfect surface
• Local modulations of the spin-fluctuation mediated pairing interaction by impurities in d-wave superconductors
• Effect of inhomogeneous coupling on superconductivity
• Impurity-induced subgap states in superconductors with inhomogeneous pairing