Microwave-induced pi-junction transition in a superconductor / quantum-dot / superconductor structure

Using the nonequilibrium Green function, we show that microwave irradiation can reverse the supercurrent flowing through a superconductor / quantum-dot / superconductor structure. In contrast with the conventional sideband effect in normal-metal / quantum-dot / normal-metal junctions, the photon-assisted structures appear near $E_0=\frac{n}{2}\mathrm{\hslash }\omega (n=\pm 1,\pm \mathrm{2...})$, where $E_0$ is the resonant energy level of the quantum dot and $\omega$ is the frequency of microwave field. Each photon-assisted structure is composed of a negative and a positive peak, with an abrupt jump from the negative peak to the positive peak around $E_0=\frac{n}{2}\mathrm{\hslash }\omega$. The microwave-induced $\pi$-junction transition is interpreted in the picture of photon-assisted Andreev bound states, which are formed due to multiple photon-assisted Andreev reflection between the two superconductors. Moreover, the main resonance located at $E_0=0$ can also be reversed with proper microwave strength and frequency.