Non-spontaneous symmetry breaking, chaos, and universality in 2D superconducting phase transition

Abstract

This research paper explores the intriguing phenomenon of the superconductor-metal–insulator phase transition in thin films, examining it from a theoretical standpoint. Our study revolves around the proposition that the process of U(1) symmetry breaking in the Landau–Ginzburg theory might not be entirely spontaneous. Building on this insight, we derive critical parameters characterizing the superconducting phase transition. Our findings demonstrate that the application of an electric field can effectively control the phase transition, leading to the suppression of the supercurrent at specific electric potential values, which is consistent with recent research. Furthermore, we have developed a robust relationship for the nonlinear resistivity that accurately simulates experimental measurements below the critical temperature. This derived relation adopts the form of logistic functions, providing a systematic framework to describe the system within the realm of chaos theory. Moreover, we establish a link with the Berezinskii–Kosterlitz–Thouless theory, highlighting the universality of the topological transition. However, this universality breaks down under the influence of multiple control parameters. To delve further into the underlying reasons for the collapse of universality, we turn to the study of Markus–Lyapunov fractals, which offers a deep understanding into the system’s behavior in the presence of varying external influences..