Resonant states of a double-barrier junction

We study resonant properties of an SIS′ IS junction with quantized Andreev bound states (ABSs); here S, S′ and I denote a superconductor, a superconductor with a smaller energy gap, and an insulating barrier, respectively. Using the quasiclassical approach we compute the local electron density of states, spatial extent of the quantized states and inelastic electron-phonon recombination rate versus junction transparency, nonmagnetic impurity concentration, and the thickness of the middle layer. We find that the local electron density of states in a low-transparency limit has sharp peaks at the ABS level positions while the inelastic electron-phonon recombination time, τe-p (ε), associated with an ABS level E0 is a sharp function of energy variable ε and diverges at ε= E0.