Crossover from Josephson to Multiple Andreev Reflection Currents in Atomic Contacts

The basic current-carrying mechanism through a superconducting weak link embedded in a resistive environment undergoes a continuous crossover, as the voltage increases, from Josephson Cooper pair transfer exciting electromagnetic modes in the environment to multiple Andreev reflections leading to the creation of quasiparticles. We corroborate these ideas through measurements of the dc current-voltage characteristics of superconducting atomic contacts containing channels of arbitrary and adjustable transmission. We present a simple model, in the spirit of the classical resistively shunted junction model, that accounts well for the observed characteristics.

Figure 1

(a) Resistively shunted junction model. Weak-link connected to a current source in parallel with a shunt resistor generating Johnson noise $\delta v$. (b) Schematics of actual circuit: atomic contact (orange double triangle symbol) integrated into microfabricated environment (light box) consisting of four resistors $r\sim 40\Omega$ and four capacitors $C\sim 90\mathrm{pF}$. Resistor $R\sim 50\Omega$ is a commercial discrete element, a few centimeters away from the chip. Dark box shows elements placed at base temperature $T_0$ of the refrigerator. The current through the atomic contact is measured by monitoring the voltage drop across the resistor $r$.

Figure 2

Upper right panel: energy $E_{\pm }(\theta )=\pm \Delta \sqrt{1-\tau {sin}^2\theta /2}$ [5] of the two Andreev levels for a channel of $\tau =0.99$ (full lines) and for a ballistic channel (dashed line). Near the anticrossing at $\theta =\pi$, Landau-Zener transitions become possible at finite voltage with probability $p$. Lower right panel: corresponding current-phase relation $I_{\pm }(\theta )=(2\pi /{\Phi }_0)\partial E_{\pm }/\partial \theta$. Left panel: single channel low bias current-voltage characteristic calculated with self-consistent model, for three transmission values ($T=0.01\Delta /k_B$, $r=6\times {10}^{-4}{R}_K$). Currents are normalized to the maximum supercurrent $I_{\max }(\tau )$ for each transmission. The dashed (dotted) line corresponds to the perfect transmission case at $T=0$ assuming a Landau-Zener probability $p=1$ ($p=0$).

Figure 3

Subgap current-voltage characteristic for Al atomic contact with measured $\{{\tau }_i\}=\{0.677,0.391,0.201,0.2,0.2\}$, $\Delta =178\mu \mathrm{eV}$. Critical current $I_{\max }(\{{\tau }_i\})=41.8\mathrm{nA}$. Symbols: experimental data measured at $T_0=20\mathrm{mK}$. Full line: self-consistent calculation for these transmissions and the independently measured $r=40.5\Omega$. The only adjustable parameter is the effective noise temperature $T_{\mathrm{eff}}=125\mathrm{mK}$ of $r$.

Figure 4

Subgap current-voltage characteristic for Al atomic contact with measured $\{{\tau }_i\}=\{0.995,0.372,0.174,0.022\}$, $\Delta =179.3\mu \mathrm{eV}$. Symbols: experimental data measured at $T_0=20\mathrm{mK}$. Critical current $I_{\max }(\{{\tau }_i\})=49.9\mathrm{nA}$. Full line: self-consistent calculation for these transmissions and the independently measured $r=39.4\Omega$. The only adjustable parameter is the effective noise temperature $T_{\mathrm{eff}}=125\mathrm{mK}$ of $r$. Dashed line: predictions of MAR theory. Dotted line: predictions for the ASC using the equilibrium CPR. Dashed-dotted line: sum of the MAR and the ASC currents.