The current voltage (IV) characteristics of short [with length $L\lesssim \xi \left(T\right)$] and long [$L\gg \xi \left(T\right)$] microbridges are theoretically investigated near the critical temperature of the superconductor. Calculations are made in the nonlocal (local) limit when the inelastic relaxation length due to electron-phonon interactions $L_{in}={\left(D{\tau }_{in}\right)}^{1/2}$ is larger (smaller) than the temperature-dependent coherence length $\xi \left(T\right)$ ($D$ is the diffusion coefficient, ${\tau }_{in}$ is the inelastic relaxation time of the quasiparticle distribution function). We find that, in both limits, the origin of the hysteresis in the IV characteristics is mainly connected with the large time scale over which the magnitude of the order parameter varies in comparison with the time-scale variation of the superconducting phase difference across the microbridge in the resistive state. In the nonlocal limit, the time-averaged heating and cooling of quasiparticles are found in different areas of the microbridge, which are driven, respectively, by oscillations of the order parameter and the electric field. We show that, by introducing an additional term in the time-dependent Ginzburg-Landau equation, it is possible to take into account the cooling effect in the local limit too.

• Received 30 May 2011

DOI:https://doi.org/10.1103/PhysRevB.84.094511