Low frequency imaginary impedance at the superconducting transition of 2H-NbSe$_2$

The superconducting transition leads to a sharp resistance drop in a temperature interval that can be a small fraction of the critical temperature T$_c$. A superconductor exactly at T$_c$ is thus very sensitive to all kinds of thermal perturbations, including the heat dissipated by the measurement current. We show that the interaction between electrical and thermal currents leads to a sizeable imaginary impedance at frequencies of order of tens of Hz at the resistive transition of single crystals of the layered material 2H-NbSe$_2$. We explain the result using models developed for transition edge sensors. By measuring under magnetic fields and at high currents, we find that the imaginary impedance is strongly influenced by the heat associated with vortex motion and out-of-equilibrium quasiparticles.