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

The Efros–Shklovskii (ES) Coulomb gap in the one-electron density of localized states and the ES law of the variable range hopping conductivity were coined 50 years ago. The theory and its first confirmations were reviewed in the Shklovskii–Efros (SE) monograph published 40-years ago. This paper reviews the subsequent experimental evidence, theoretical advancements, and novel applications of the ES law. 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, I discuss the non-ohmic ES law and the Coulomb gap near insulator–metal transition. Recent developments of other concepts of the SE book are also discussed.