Renormalization-group approach to layered superconductors

A renormalization-group theory for a system consisting of coupled superconducting layers as a model for typical high-temperature superconductors is developed. In a first step the electromagnetic interaction over infinitely many layers is taken into account, but the Josephson coupling is neglected. In this case the corrections to two-dimensional behavior due to the presence of the other layers are very small. Next, renormalization-group equations for a layered system with very strong Josephson coupling are derived, taking into account only the smallest possible Josephson vortex loops. The applicability of these two limiting cases to typical high-temperature superconductors is discussed. Finally, it is argued that the original renormalization-group approach by Kosterlitz is not applicable to a layered system with intermediate Josephson coupling.