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

Despite several theoretical approaches describing multiple Andreev reflections (MAR) effect in superconductor-normal metal-superconductor (SNS) junction are elaborated, the problem of comprehensive and adequate description of MAR is highly actual. In particular, a broadening parameter $\Gamma$ 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 Kummel, Gunsenheimer, and Nikolsky (KGN), as well as Gunsenheimer-Zaikin approaches, for an isotropic case and fully-transparent constriction. Nonetheless, an influence of $l/d$ ratio to 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 ($l/d \rightarrow 1$) a suppression of the Andreev excess current, dramatic change in the current voltage $I(V)$-curve slope at low bias, with only the main harmonic at $eV=2\Delta$ bias voltage remains 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 agrees with our experimental data obtained using a "break-junction" technique.