Measurement of the Current-Phase Relation of Superconducting Atomic Contacts

We have probed the current-phase relation of an atomic contact placed with a tunnel junction in a small superconducting loop. The measurements are in quantitative agreement with the predictions of a resistively shunted SQUID model in which the Josephson coupling of the contact is calculated using the independently determined transmissions of its conduction channels.

Figure 1

(a) Schematic experimental setup: dc SQUID formed by an atomic contact (phase $\delta$) and a tunnel junction (phase $\gamma$). The on-chip capacitor $C\approx 21\mathrm{pF}$ is formed between the metallic substrate and a 100 nm-thick gold electrode ($1.3{\mathrm{mm}}^2$), with a $1.6\mu \mathrm{m}$-thick dielectric polyimide layer. The resistor $r\approx 0.6\Omega$, corresponds to the sheet resistance of the capacitor gold electrode. The bias current $I_b$ is governed by voltage source $U$ and discrete macroscopic resistor $R\approx 25\Omega$ mounted close to sample, at base temperature (20 mK) of dilution refrigerator. (b) SEM image of SQUID loop. The tunnel junction is fabricated using double-angle evaporation of aluminum through a suspended mask. This results in a parasitic structure of no practical importance. Bright regions on the left corners correspond to the gold thin films that connect the superconducting loop to the rest of the circuit, and provide the top plate of the capacitor. These normal regions also act as quasiparticle traps.

Figure 2

Upper panel: Experimental current-voltage curves for three atomic contacts (symbols) for $0<eV<2\Delta$, compared to best fits $I_{\{{\tau }_i\}}(V)$ using MAR (full lines). Fits provide gap $\Delta \simeq 180\mu \mathrm{eV}$ and set $\{{\tau }_i\}$ of transmission coefficients for each contact: $\mathrm{AC}1\to \{0.62;0.22;0.07\}$; $\mathrm{AC}2\to \{0.957;0.19\}$; $\mathrm{AC}3\to \{0.993;0.14\}$. Lower panel: $I(V)$ curve for contact AC3, obtained as the difference between $I_{\mathrm{SQUID}}(V)$ and $I_J(V)$. Inset: Large scale characteristic of SQUID, displaying supercurrent branch at $V=0$.

Figure 3

Symbols: measured switching current $[s^{*}(\phi )-s_0]I_0$ as a function of applied flux $\varphi /{\varphi }_0$, for the three SQUIDS corresponding to the contacts of Fig. 2. Curves AC3 and AC1 shifted for clarity. Dashed curves: predicted ground state current-phase relation $I_{\{{\tau }_i\}}^{-}(\delta )$. Full lines: predictions of resistively shunted SQUID theory at $T_{\mathrm{esc}}=130\mathrm{mK}$ on the basis of Eq. (1). The transmission sets indicated in Fig. 2 caption have been used for both theories.

Figure 4

Solid line: washboard potential of a SQUID with a single channel contact for $\tau =0.99$, $s=0.87$ and $\phi =0$, as function of the Josephson junction phase $\gamma$. Thermal activation allows the phase to escape at a rate $\Gamma$ above the barrier of height $\Delta U$. Dashed line: washboard potential of Josephson tunnel junction alone for the same parameters.