High-impedance contacts made on the surface of Sr$_{0.88}$La$_{0.12}$CuO$_2$ superconducting thin films systematically display a zero-bias anomaly. We consider two-level systems (TLS) as the origin of this anomaly. We observe that the contribution of
some TLS to the contact resistance is weakened by a magnetic field. We show that this could result from the increase of the TLS relaxation rate in the superconducting state, due to its ability to create pairs of quasiparticles out of the condensate, when located close to the surface of the film.
We have used the electric--field effect to modulate the resistivity of the surface of underdoped Sr$_{0.88}$La$_{0.12}$CuO$_{2+x}$ thin films, allowing opposite modifications of the electron and hole density in the CuO$_2$ planes, an original situati
on with respect to conventional chemical doping in electron-doped materials. When the Hall effect indicates a large contribution of a hole band, the electric--field effect on the normal state resistivity is however dominated by the electrons, and the superconducting transition temperature increases when carriers are transfered from holes to electrons.
The resistance noise in a Bi_2Sr_2CaCu_2O$_{8+delta}$ thin film is found to increase strongly in the underdoped regime. While the increase of the raw resistance noise with decreasing temperature appears to roughly track the previously reported pseudo
gap temperature for this material, standard noise analysis rather suggests that the additional noise contribution is driven by the proximity of the superconductor-insulator transition.
