Amplitude, phase, and topological fluctuations shaping the complex phase diagram of two-dimensional superconductors

TL;DR

This paper investigates how amplitude, phase, and topological fluctuations influence the phase diagram and thermodynamic properties of two-dimensional superconductors, providing theoretical insights into fluctuation effects near critical temperatures.

Contribution

It introduces a comprehensive framework to include Gaussian and topological vortex fluctuations in determining critical temperatures and phase behavior of 2D superconductors.

Findings

Calculated the beyond-mean-field critical temperature $T_c$ including thermal fluctuations.

Derived the BKT transition temperature $T_{BKT}$ considering vortex-antivortex pairs.

Mapped the $H$-$T$ phase diagram and analyzed heat capacity behavior under fluctuations.

Abstract

We study the amplitude and phase fluctuations of the Ginzburg-Landau quasiorder parameter for superconductors in two spatial dimensions. Starting from the mean-field critical temperature $T_{\mathrm{c}0}$, we calculate the beyond-mean-field critical temperature $T_{\rm c}$ by including thermal fluctuations of the quasiorder parameter within the Gaussian level. Moreover, from our beyond-mean-field results, we derive the Berezinskii-Kosterlitz-Thouless critical temperature $T_{\rm BKT}$, which takes into account topological vortex-antivortex excitations in the phase fluctuations as well as the amplitude fluctuations, to obtain the shifts of transition temperatures. We elucidate how the Gaussian thermal fluctuations and phase fluctuations associated with vortex excitations affect thermodynamic properties by determining the $H$-$T$ phase diagram for a type-II superconductor and computing the critical behaviors of the heat capacity, which are experimentally accessible, allowing the characterization of the cascade of different kinds of fluctuations in 2D superconductors.