Superconductor-insulator quantum phase transition

TL;DR

This paper reviews the superconductor-insulator transition by examining physical phenomena, microscopic theories, experimental data, and nonlinear effects, highlighting areas for future research and recent key findings.

Contribution

It provides a comprehensive, multi-level analysis of the superconductor-insulator transition, integrating phenomenological, microscopic, and experimental perspectives with new insights.

Findings

Discussion of phenomena like Berezinskii-Kosterlitz-Thouless transition

Summary of microscopic approaches including BCS and Bose-Einstein theories

Presentation of nonlinear phenomena near the transition

Abstract

The current understanding of the superconductor-insulator transition is discussed level by level in a cyclic spiral-like manner. At the first level, physical phenomena and processes are discussed which, while of no formal relevance to the topic of transitions, are important for their implementation and observation; these include superconductivity in low electron density materials, transport and magnetoresistance in superconducting island films and in highly resistive granular materials with superconducting grains, and the Berezinskii-Kosterlitz-Thouless transition. The second level discusses and summarizes results from various microscopic approaches to the problem, whether based on the Bardeen-Cooper-Schrieffer theory (the disorder-induced reduction in the superconducting transition temperature; the key role of Coulomb blockade in high-resistance granular superconductors; superconducting fluctuations in a strong magnetic field) or on the theory of the Bose-Einstein condensation. A special discussion is given to phenomenological scaling theories. Experimental investigations, primarily transport measurements, make the contents of the third level and are for convenience classified by the type of material used (ultrathin films, variable composition materials, high-temperature superconductors, superconductor-poor metal transitions). As a separate topic, data on nonlinear phenomena near the superconductor-insulator transition are presented. At the final, summarizing, level the basic aspects of the problem are enumerated again to identify where further research is needed and how this research can be carried out. Some relatively new results, potentially of key importance in resolving the remaining problems, are also discussed.