Half century of Efros-Shklovskii Coulomb gap. Romance with Coulomb interaction and disorder

TL;DR

This review comprehensively covers 50 years of research on the Efros-Shklovskii Coulomb gap, highlighting experimental validations, theoretical progress, and new applications across various disordered and localized electronic systems.

Contribution

It synthesizes decades of experimental and theoretical advancements, emphasizing recent findings and novel contexts where the ES Coulomb gap is relevant.

Findings

Experimental validation of ES law over four orders of magnitude in conductivity

Observation of Coulomb gap effects in diverse materials like semiconductors and nanocrystals

Discussion of Coulomb gap behavior near insulator-metal transition

Abstract

Efros-Shklovskii (ES) Coulomb gap in density of localized states and ES law of the variable range hopping conductivity were coined 50 years ago. The theory and its first confirmations were reviewed in our monograph 40-years ago. This paper reviews the subsequent experimental evidence, theoretical advancements, and novel applications. Out of hundreds of experimental validations of the ES law in a diverse range of materials, I focus on those where the dynamic range of conductivity exceeds four orders of magnitude. These include three- and two-dimensional semiconductors under both zero and high magnetic fields, localized phases in the quantum Hall effect, granular metals, nanocrystal arrays, and conducting polymers. Additionally, this review discusses the Coulomb gap near insulator-metal transition and in non-ohmic ES law. Recent developments of other concepts of the ES book are also discussed.