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Peculiarities of the density of states in SN bilayers

A. A. MazanikYa. V. Fominov
May 2022
摘要
We study the density of states (DoS) $\nu(E)$ in a normal-metallic (N) filmcontacted by a bulk superconductor (S). We assume that the system is diffusiveand the SN interface is transparent. In the limit of thin N layer (compared tothe coherence length), we analytically find three different types of the DoSpeculiarity at energy equal to the bulk superconducting order parameter$\Delta_0$. (i) In the absence of the inverse proximity effect, the peculiarityhas the check-mark form with $\nu(\Delta_0)=0$ as long as the thickness of theN layer is smaller than a critical value. (ii) When the inverse proximityeffect comes into play, the check-mark is immediately elevated so that$\nu(\Delta_0)>0$. (iii) Upon further increasing of the inverse proximityeffect, $\nu(E)$ gradually evolves to the vertical peculiarity (with aninfinite-derivative inflection point at $E=\Delta_0$). This crossover iscontrolled by a materials-matching parameter which depends on the relativedegree of disorder in the S and N materials.
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