Thermodynamic Theory of Disordered 2D Superconductors

Understanding the roles of phase fluctuation and disorder in superconducting phase transition has intrigued researchers for decades and continues to be a topic of enormous interest in related topics such as in two-dimensional (2D) superconductors, high-𝑇𝑐 superconductors, and charge-density-waves. Here starting from a purely microscopic model, we develop a self-consistent thermodynamic theory for disordered 2D superconductors by incorporateing the superconducting gap as well as quantum and thermal phase fluctuations in the presence of the long-range Coulomb interactions. The simulation based on this theory successfully predicts the existence of long-range superconducting order in the 2D limit even when temperature is raised to above zero Kelvin, but the emerging large thermal phase fluctuations with further increasing temperature destroy the gap before the BCS transition. The inhomogeneous quantum phase fluctuations with increasing disorder leads to a mixed state of superconducting and normal-state islands. It is demonstrated that a robust superconductivity can survive at low temperature even in the presence of a high degree of disorder, a prerequisite of the superconducting-insulating transition. The results from the theory successfully explain many of the recent experimental observations of the superconductors in the 2D limit, and the theory can potentially be utilized to understand a broad range of phase transitions including transition mechanisms in high-𝑇𝑐 superconductors, formation of charge density waves, displacive quantum paraelectrics, etc.