The effects of collective pinning on topological order-disorder phase transition in type-II superconducting films

The effects of collective pinning, due to the quenched disorder, on topological order-disorder phase transition in type-II superconducting films have been investigated. It is found that the collective pinning renormalizes the energy and charge of the elementary topological excitations, hence, suppresses the topological order-disorder phase transition temperature, and increases the correlation length of the correlation functions of the order parameter. It is also demonstrated that either increasing the strength of the random correlation of the collective pinning potential, or decreasing the random correlation length of the collective pinning potential reduces the phase transition temperature, and increases the corresponding correlation length of the correlation functions of the order parameter. Our consequences agree with those obtained when the collective pinning is neglected. The application of our results to other relevant two-dimensional models are also discussed.