Peculiarities of the density of states in SN junctions

Abstract

We study the density of states (DoS) $ν(E)$ in a normal-metallic (N) film contacted by a bulk superconductor (S). We assume that the system is diffusive and the SN interface is transparent. In the limit of thin N layer (compared to the coherence length), we analytically find three different types of the DoS peculiarity at energy equal to the bulk superconducting order parameter $Δ_0$. (i) In the absence of the inverse proximity effect, the peculiarity has the check-mark form with $ν(Δ_0)=0$ as long as the thickness of the N layer is smaller than a critical value. (ii) When the inverse proximity effect comes into play, the check-mark is immediately elevated so that $ν(Δ_0)>0$. (iii) Upon further increasing of the inverse proximity effect, $ν(E)$ gradually evolves to the vertical peculiarity (with an infinite-derivative inflection point at $E=Δ_0$). This crossover is controlled by a materials-matching parameter which depends on the relative degree of disorder in the S and N materials.