Two-dimensional Coulomb glass as a model for vortex pinning in superconducting films

A glass model of vortex pinning in highly disordered thin superconducting films in magnetic fields $B \ll H_{c2}$ at low temperatures is proposed. Strong collective pinning of a vortex system realized in disordered superconductors that are close to the quantum phase transition to the insulating phase, such as InO$_x$, NbN, TiN, MoGe, and nanogranular aluminum, is considered theoretically for the first time. Utilizing the replica trick developed for the spin glass theory, we demonstrate that such vortex system is in non-ergodic state of glass type with a large kinetic inductance per square $L_K$. The distribution function of local pinning energies is calculated, and it is shown that it possesses a wide gap; i.e., the probability to find a weakly pinned vortex is extremely low.