Nonlinear transport properties of La$_2$CuO$_4$/ La$_{\mathrm{2-x}}$Sr$_{\mathrm{x}}$ CuO$_4$ heterostructures in the resistive state*

We report measurements of the nonlinear transport properties of oxide heterojunctions La$_{2}$CuO$_{4}$/La$_{\mathrm{2-x}}$Sr$_{\mathrm{x}}$CuO$_{4}$ in the vicinity of the superconducting transition. The transition occurs over a wide temperature range (7-15K) and shifts to lower temperatures in the presence of a magnetic field, as expected. Strongly nonlinear behavior is observed for the $V-I $characteristic. At low bias currents the nonlinearity has a non-thermal origin close to the transition temperature and is strongly sensitive to magnetic fields. Above the middle of the superconducting transition the nonlinear behavior is consistent instead with electron heating with a value of electron-phonon thermal conductance of $\sim$ 10$^{-6}$ W/K per square micron, which is significantly smaller than the thermal conductance of Nb and NbN ultrathin superconducting films. Our results indicate that this novel low-dimensional superconducting material shows great promise for substantial enhancement of direct detection and wide band mixing of radiation.