Oliver E. Buckley Condensed Matter Prize Talk: Coulomb gap here, there, and everywhere

In 1975 Alexei Efros and myself discovered that due to electron-electron interactions the density of localized electron states vanishes near the Fermi level as a quadratic function of the energy distance to the Fermi level. We named this phenomenon the Coulomb gap and showed that it leads to the variable range hopping conductivity which depends on the temperature T as exp[-(T_ES/T)^1/2]. This Efros-Shklovskii law was confirmed in hundreds of experimental papers, where in many cases it describes 10⁶ times dynamic range of conductivity. After going through the history and physics of this discovery I will review many new applications of Efros-Shklovskii law beyond lightly doped semiconductors among which the Quantum Hall Effect is the most prominent. I will also dwell on the McMillan-Shklovskii theory of the Coulomb gap emergence across a Metal-Insulator transition and the related question of screening of the Coulomb gap.