Applicability of layered sine-Gordon models to layered superconductors: II. The case of magnetic coupling

TL;DR

This paper develops a quantum field theoretical renormalization group approach to analyze vortex dynamics in magnetically coupled layered superconductors, extending previous work on Josephson coupling and providing insights into phase transitions.

Contribution

It introduces a multi-layer sine-Gordon model for magnetically coupled superconductors and analyzes its phase structure using a differential renormalization group method.

Findings

Transition temperature depends on the number of layers, matching known results.

Vortex interactions are derived from the field-theoretical model.

Physical parameters like vortex fugacity are identified and analyzed.

Abstract

In this paper, we propose a quantum field theoretical renormalization group approach to the vortex dynamics of magnetically coupled layered superconductors, to supplement our earlier investigations on the Josephson-coupled case. We construct a two-dimensional multi-layer sine-Gordon type model which we map onto a gas of topological excitations. With a special choice of the mass matrix for our field theoretical model, vortex dominated properties of magnetically coupled layered superconductors can be described. The well known interaction potentials of fractional flux vortices are consistently obtained from our field-theoretical analysis, and the physical parameters (vortex fugacity and temperature parameter) are also identified. We analyse the phase structure of the multi-layer sine--Gordon model by a differential renormalization group method for the magnetically coupled case from first principles. The dependence of the transition temperature on the number of layers is found to be in agreement with known results based on other methods.