In 1975 Alex Efros and myself discovered that due to electron-electron interactions the density of localized electron states vanishes 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 temperature T as exp[-(TES/T)1/2]. This ES law was confirmed in hundreds of experimental papers where in many cases it describes 106 times change of conductivity. After reminding history and physics of this discovery I will review new applications of ES law. The Quantum Hall Effect is the most prominent and dramatic of them. I will also dwell on McMillan-Shklovskii conjecture for evolution of the Coulomb gap across an Insulator-Metal transition.
Watch a recording of the talk here.