Bimodal distribution of delay times and splitting of the zero-bias conductance peak in a double-barrier normal-superconductor junction

Abstract

We formulate a scattering theory of the proximity effect in a weakly disordered SININ junction (S = superconductor, I = insulating barrier, N = normal metal). This allows to relate the conductance and density of states of the junction to the scattering times $\tau$ (eigenvalues of the Wigner-Smith time-delay matrix). The probability density $P(\tau )$ has two peaks, at a short time ${\tau }_{\min }$ and a late time ${\tau }_{\max }$. The density of states at the Fermi level is the geometric mean of the two times. The splitting of the zero-bias conductance peak is given by $\hslash /{\tau }_{\max }$.

arXiv comment7 pages, 5 figures

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