Tractable framework for phase transitions in phase-fluctuating disordered two-dimensional superconductors: Applications to bilayer MoS2 and disordered InOx thin films

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 T=0+ 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 Tc and the gap-closing temperature T*. 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 Δ(0) and consequently Tc and T*. Remarkably, applications to bilayer MoS2 [Nat. Nanotechnol. 14, 1123 (2019)] and disordered InOx 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.

Source-reported materials — not catalogue approval

Similar papers