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

Ya. V. Fominov; A. A. Mazanik; M. V. Razumovskiy

doi:10.1103/PhysRevB.100.224513

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

Ya. V. Fominov, A. A. Mazanik, M. V. Razumovskiy

DOI 10.1103/PhysRevB.100.224513 · Physical Review B

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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 Δ0, 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=Δ0 with square-root behavior as E deviates from Δ0. The coefficients of this dependence are different at E<Δ0 and E>Δ0, so the peculiarity is asymmetric.