Amplitudes of minima in dynamic conductance spectra of the SNS Andreev contact

Abstract

Although several theoretical approaches describing multiple Andreev reflection (MAR) effects in the superconductor-normal metal-superconductor (SNS) junction are elaborated, the problem of the comprehensive and adequate description of MAR is highly actual. In particular, a broadening parameter Γ is still unaccounted at all, whereas a ballistic condition (the mean free path for inelastic scattering l to the barrier width d ratio) is considered only in the framework of Kümmel, Gunsenheimer, and Nikolsky (KGN), as well as Gunsenheimer-Zaikin approaches, for an isotropic case and fully transparent constriction. Nonetheless, the influence of the l / d ratio on the dynamic conductance spectrum (d I / d V) features remains disregarded, thus being one of the aims of the current work. Our numerical calculations in the framework of an extended KGN approach develop the l / d variation to determine both the number of the Andreev features and their amplitudes in the d I / d V spectrum. We show, in the spectrum of a diffusive SNS junction (l / d → 1), a suppression of the Andreev excess current and a dramatic change in the current voltage I (V)-curve slope at low bias, with only the main harmonic at e V = 2 Δ bias voltage remaining well-distinguished in the d I / d V-spectrum. Additionally, we attempt to make a first-ever comparison between experimental data for the high-transparency SNS junctions (more than 85 %) and theoretical predictions. As a result, we calculate the temperature dependences of amplitudes and areas of Andreev features within the extended KGN approach, which qualitatively agree with our experimental data obtained using a "break-junction"technique.