Little–Parks Effects in Two-Dimensional Superconductors Near the BKT Transition: A Vortex–Charge Duality Theory

When a thin-walled superconducting cylinder or ring is subjected to a magnetic flux, its superconducting transition temperature exhibits a periodic oscillation known as the Little–Parks effect. In recent years, this phenomenon has attracted renewed interest as a probe for unconventional superconductivity. In two-dimensional superconductors, a Berezinskii–Kosterlitz–Thouless (BKT) transition is generally expected. However, the manifestation of the Little–Parks effect in this regime remains poorly understood. In this presentation, I will discuss our recent theoretical study of the Little–Parks effect in two-dimensional superconductors near the BKT transition, formulated within the framework of vortex–charge duality. By mapping the problem onto a Coulomb gas model, we show that the external magnetic flux corresponds to fractional boundary charges in the dual representation. Our theoretical insights are corroborated by detailed Monte Carlo simulations, confirming the robustness of this duality-based picture.