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

Abstract

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 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, 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 → 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∆ 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.

Induced Superconductivity in Hybrid Au/YBa2Cu3O7-x Electrodes on Vicinal Substrates

“…A representative conductance curve of the 100-nm-wide nanoconstriction measured at T = 4.2 K shows a nonmonotonic step-like behavior with a number of conductance steps with corresponding dips (Figure 4a). Here, we follow the numerical simulations of Popovich et al 44 for the SNS junctions with transparent normal metal-superconductor interfaces to assign the position of the conductance dips with the n th MAR harmonic at V = 2Δ/ne. The position of a smeared dip at V= 41.2 mV indicated by the green arrow is close to the expected values of Δ/e corresponding to the energy gap in the b-axis direction of YBCO Δ b = 44 meV.…”

Quantum size effects in ultra-thin YBa2Cu3O7-x films

“…At higher voltages V Δ/2e, the number of AR becomes energy limited, decreasing with increasing energy that the quasiparticle received per AR and only a few isolated dips occur in the conductance curve 25 . In this high-voltage region, each current enhancement due to AR leads to the corresponding step-wise increase of the SNS junction conductance.…”

“…Here n is an integer and e is an electron charge. As consequences of MAR, the IV curves and especially the conductance curves show many nonlinear structures [23][24][25] .…”

“…In this high-voltage region, each current enhancement due to AR leads to the corresponding step-wise increase of the SNS junction conductance. According to these theoretical predictions, the measurements of the AR spectrum provide information on the magnitude of the superconducting energy gaps in the nanoconstriction electrodes [22][23][24][25][26] .…”

“…The estimated width of this constriction is 3-6 nm which is comparable to the a-b plane coherence length of YBCO ξ ab = 1.3 nm 27 . The dI/dV curve has a well-de ned ladder-like structure due to AR in the normal-state region of the nanoconstriction 22,25,26 . Our numerical simulations show that for the given barrier properties, the sharpness of the conductance step is an indicator of the energy gap anisotropy in the electrodes.…”