Microscopic Model of a Transition Edge Sensor as a Weak Link

We have developed a microscopic model of the transition edge sensor (TES). In order to describe the TES as a laterally proximized S-S'-S weak link we used the Usadel equations. We developed a fully self-consistent approach, taking into account the appropriate boundary conditions at the contacts with the large gap superconducting leads. We have obtained an analytical solution of the Usadel equations for the simplest TES geometry. For a more general situation we discuss numerical solutions. We present the explicit form of the lateral profile of the order parameter for a typical TES sensor as a function of temperature, size and bias current. We calculate current-phase relations and the critical Josephson current, and discuss the important differences between modeling of the TES as either S-S'-S or S-N-S link.