Theory of Microwave-Assisted Supercurrent in Diffusive SNS Junctions

The observation of very large microwave-enhanced critical currents in superconductor–normal-metal–superconductor (SNS) junctions at temperatures well below the critical temperature of the electrodes has remained without a satisfactory theoretical explanation for more than three decades. Here we present a theory of the supercurrent in diffusive SNS junctions under microwave irradiation based on the quasiclassical Green’s function formalism. We show that the enhancement of the critical current is due to the energy redistribution of the quasiparticles in the normal wire induced by the electromagnetic field. The theory provides predictions across a wide range of temperatures, frequencies, and radiation powers, both for the critical current and the current-phase relationship.

Figure 1

(a) Local density of states (DOS) in the middle of the normal wire for $\Delta =100E_T$ and different values of the phase difference $\phi /\pi$, in the absence of microwaves. (b) Absorption rate ${\eta }_{+}$ for a high frequency $\hslash {\omega }_0/E_T=8$ and $\phi =\pi /2$, $s=0.125$. Thin line shows the approximation from Eq. (4). Inset: Schematic representation of the SNS junction. (c) Correction $\delta \overline{f}=\overline{f}-f_0$ to the electron distribution function vs energy at two different temperatures for $\phi =\pi /2$, $\hslash {\omega }_0/E_T=4$, and $s=0.125$. Solid lines correspond to the exact numerical results and the dashed lines to the approximation in Eq. (4). The thin black line shows the spectral supercurrent $j_S(E)$ in the absence of microwaves. (d) The same as in (c) for $k_{B}T/E_T=15$ and $\phi =0.8\pi$.

Figure 2

Correction to the critical current, normalized by the critical current in the absence of the field, as a function of temperature and inelastic rate for $\Delta =100E_T$ and several frequencies. The field strength is $s=0.125$ in all cases. The lines separate the region of parameters for which the critical current is enhanced from that in which it is reduced.

Figure 3

Critical current (normalized by the current without ac field at the corresponding temperature) versus radiation amplitude $s$ for a wire with $\Delta /E_T=100$. (a) For different temperatures at $\hslash {\omega }_0/E_T=4$ and $\Gamma /E_T=0.05$. (b) For different frequencies and $k_{B}T/E_T=15$.

Figure 4

(a) Distribution function (solid black) and density of states (green) for large amplitude $s=2$, and $\hslash {\omega }_0/E_T=4$, $\Delta /E_T=100$, $k_{B}T/E_T=10$, $\Gamma /E_T=0.05$, and $\phi =\pi /2$. Microwaves cause heating from $k_{B}T/E_T=10$ (dotted) to $k_{B}T\approx \hslash {\omega }_0\sqrt{E_A/4\Gamma }$ (blue). (b) Current-phase relation normalized to equilibrium critical current at $k_{B}T/E_T=15$, 1 (top to bottom) and $s=0.125$ (solid) and 0.25 (dashed), for $\hslash {\omega }_0/E_T=4$, $\Delta /E_T=100$, $\Gamma /E_T=0.05$. (c) Current-phase relation for different amplitudes $s=0$, 0.2, 0.3, 0.5, 0.75 (solid, top to bottom) at $k_{B}T/E_T=10$ and $\hslash {\omega }_0/E_T=1.2$. Relaxation rate is chosen as $\Gamma /E_T=0.2(k_{B}T/10E_T{)}^3$, and $\Delta /E_T=58$. Experimental data from Ref. 9 are shown as dots. (d) As in (c), for $s=0.3$, $\hslash {\omega }_0/E_T=2$, and temperatures $k_{B}T/E_T=8$, 9.5, 10, 11, 12.5 (top to bottom).