I-V characteristics of atomically thin superconducting $La_{2-x}Sr_xCuO_4$ films*

I-V characteristics of $La_{2-x}Sr_xCuO_4$ thin films grown by Molecular Beam Epitaxy are studied in a wide range of temperatures in zero magnetic field. Strongly nonlinear response to applied electric current was observed near the superconducting state. At temperatures $T>T_{BKT}$ the observed characteristics have three distinct features: (1) at small currents voltage $V$ is proportional to the current $I$; (2) at higher currents a cubic dependence ($I \sim I^3$) is observed; (3) and even higher currents $V \sim I^\alpha$ with coefficient $\alpha(T)<$ 3, which decreases with the temperature increase. At $T=T_{BKT}$ the coefficient $\alpha=3$. Observed nonlinear response is in-line with Berezinsky--Kosterlitz--Thouless (BKT) theory.