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 (dI/dV) 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 dI/dV 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 eV=2Δ bias voltage remaining well-distinguished in the dI/dV-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.