Exact result on the supercurrent through a superconductor/quantum-dot/superconductor junction

We present an analytical result for the supercurrent across a superconductor/quantum-dot/superconductor junction. By converting the current integration into a special contour integral, we can express the current as a sum of the residues of poles. These poles are real and give a natural definition of the Andreev bound states. We also use the exact result to explain some features of the supercurrent transport behavior. PACS numbers: 74.50.+r, 73.40.Gk, 73.20.-b, 73.63.Kv. Introduction. The mesoscopic superconductor/quantum-dot/superconductor (S-QD-S) junction is a typical structure to study the phase coherent current transport in mesoscopic hybrid systems [1]. When using Keldysh Green function technique [2] to evaluate the current across the S-QD-S junction, the usual method demands a numerical integration and faces the problem of explaining some features of the current transport behavior [3]. In this paper, we employ a new method to analytically compute the current across the S-QD-S junction in the absence of voltage bias, and use the analytical results to explain some features of current transport properties. Model and Hamiltonian. In the system under consideration, a quantum dot defined in a 2-dimensional electron gas (2DEG) is coupled to two BCS superconducting leads. We model this system by the Hamiltonian Ĥ = ĤL + Ĥd + ĤR + ĤT , (1) 1