Berezinskii-Kosterlitz-Thouless Transition within the Sine-Gordon Approach: The Role of the Vortex-Core Energy

One of the most relevant manifestations of the Berezinskii-Kosterlitz-Thouless transition occurs in quasi-two-dimensional superconducting systems. The experimental advances made in the last decade in the investigation of superconducting phenomena in low-dimensional correlated electronic systems have raised new questions on the nature of the BKT transitions in real materials. A general issue concerns the possible limitations of theoretical predictions based on the XY model, that was studied as a paradigmatic example in the original formulation. Here, we review the work we have done in revisiting the nature of the BKT transition within the general framework provided by the mapping into the sine-Gordon model. While this mapping was already known since long, we recently emphasized the advantages of such an approach to account for new variables in BKT physics. One such variable is the energy needed to create the core of the vortex, that is fixed within the XY model, while it attains substantially different values in real materials. This has interesting observable consequences, especially in the case when additional relevant perturbations are present, as a coupling between stacked two-dimensional superconducting layers or a finite magnetic field.