Theory of Microwave-Assisted Supercurrent in Quantum Point Contacts

We present a microscopic theory of the effect of a microwave field on the supercurrent through a quantum point contact of arbitrary transmission. Our theory predicts that (i) for low temperatures and weak fields, the supercurrent is suppressed at certain values of the superconducting phase, (ii) at strong fields, the current-phase relation is strongly modified and the current can even reverse its sign, and (iii) at finite temperatures, the microwave field can enhance the critical current of the junction. Apart from their fundamental interest, our findings are also important for the description of experiments that aim at the manipulation of the quantum state of atomic point contacts.

Figure 1

Dispersion relation of the ABSs in a single-channel QPC with transmission $\tau =0.95$. The vertical dashed lines indicate one- and two-photon transitions between the ABSs (a),(b), and transitions between the continuum and ABSs (c),(d). We have chosen $E=0$ at the Fermi energy.

Figure 2

Zero-temperature supercurrent, in units of $I_0=e{\Delta }_0/\hslash$, as a function of the phase. (a) The solid line shows the exact result for $\tau =0.95$, $\hslash \omega =0.6\Delta$, and $\alpha =0.1$, the dashed line corresponds to the approximation of Eq. (5), and the dotted line to the TLM. The rest of the panels show the exact result for (b) $\tau =0.95$, $\alpha =0.1$, and different frequencies; (c) $\tau =0.95$, $\hslash \omega =0.3\Delta$, and different $\alpha$’s; (d) $\hslash \omega =0.3\Delta$, $\alpha =0.1$, and different $\tau$’s.

Figure 3

Panels (a) and (b) show the critical current as a function of $\alpha$ for (a) $\hslash \omega =0.3\Delta$, $\tau =0.95$ and different values of $T$, and (b) $\hslash \omega =0.3\Delta$, $k_{B}T=0.5\Delta$, and different values of $\tau$. In both panels the solid lines correspond to exact results and the dashed lines to Eq. (5). (c) Current as a function of the frequency for $\phi =2.0$, $k_{B}T=0.5\Delta$, $\tau =0.95$, and $\alpha =0.1$.