Quantum depinning of a pancake vortex from a columnar defect

We consider the problem of the depinning of a weakly driven $(F\ll F_c)$ pancake vortex from a columnar defect in a Josephson-coupled superconductor, where $F$ denotes the force acting on the vortex ${(F}_c$ is the critical force). The dynamics of the vortex is supposed to be of the Hall type. The Euclidean action $S_{\mathrm{Eucl}}\mathrm{}\left(T\right)\mathrm{}$ is calculated in the entire temperature range; the result is universal and does not depend on the detailed form of the pinning potential. We show that the transition from quantum-to-classical behavior is second-order like with the temperature $T_c$ of the transition scaling like $F^{4/3}$. Special attention is paid to the regime of applicability of our results, in particular, the influence of the large vortex mass appearing in the superclean limit is discussed.