Zero-bias anomalies on Sr$_{0.88}$La$_{0.12}$CuO$_2$ thin films

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.