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Article

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

Physical Review B: Condensed Matter and Materials Physics. 2019. Vol. 100. No. 22. P. 224513-1-224513-8.
Fominov Ya.V., Mazanik A., Razumovskiy M.

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 energy equal to the bulk order parameter $\Delta_0$, and 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 difference between the spatial scale $r_c$, at which $\lambda(x)$ is suppressed, and coherence length. The vertical peculiarity implies 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.