Tractable framework for phase transitions in phase-fluctuating disordered two-dimensional superconductors: Applications to bilayer and disordered thin films
Phys. Rev. B 113, 094517 – Published 18 March, 2026
DOI: https://doi.org/10.1103/xy6z-hxcv
Abstract
Starting from the purely microscopic model, we go beyond conventional mean-field theory and develop a self-consistent microscopic thermodynamic framework for disordered 2D superconductors. It incorporates the fermionic Bogoliubov quasiparticles, bosonic Nambu-Goldstone (NG) quantum and thermal phase fluctuations in the presence of long-range Coulomb interactions, and topological Berezinskii-Kosterlitz-Thouless (BKT) vortex-antivortex fluctuations on an equal footing, to self-consistently treat the superconducting gap and superfluid density. This unified phase-fluctuating description naturally recovers the previously known limiting results: the superconducting gap in the 2D limit can remain robust against long-wavelength NG phase fluctuations at due to Coulomb-induced regularization, while the gradual proliferation of BKT fluctuations as the system approaches criticality drives a separation between the global superconducting transition temperature and the gap-closing temperature . In contrast to mean-field theory, which predicts 2D superconductivity to be independent of carrier density and nonmagnetic disorder (Anderson theorem), the incorporation of phase fluctuations generates a density- and disorder-dependent zero-point gap and consequently and . Remarkably, applications to bilayer [Nat. Nanotechnol. 14, 1123 (2019)] and disordered thin films [Nat. Phys. 21, 104 (2025)] quantitatively reproduce key experimental observations in excellent agreement. The framework offers a useful theoretical tool for understanding phase-fluctuation-dominated superconductivity.