Thermally-activated dynamics of spontaneous perpendicular vortices tuned by parallel magnetic fields in thin superconducting films

We report magneto-transport measurements on a superconducting molybdenum-germanium (MoGe) film of thickness $d$=50 nm in parallel magnetic fields and show evidence of a transition from a Meissner state to a resistive state of spontaneous perpendicular vortices generated by thermal fluctuations above a certain temperature $T>T_v(B)$. Here $T_v$ appears to match the vortex core explosion condition $d\approx 4.4\xi (T_v)$, where $\xi$ is the coherence length. For $T>T_v$, we observed that a nonlinear current-voltage ($IV$) response (Ohmic at low currents and the power law $V\propto I^{\beta }$ at higher $I$) is exponentially dependent on $B^2$. We propose a model in which the resistive state at $T>T_v$ is due to thermally-activated hopping of spontaneous perpendicular vortices tuned by the pairbreaking effect of the parallel $B$. keywords: vortex, vortices, fluxon, flux lattice, mixed state, lower critical field