Electrons near the Fermi energy in a strongly-disordered systems, such as amorphous semiconductors , are localized in space. As a result, the Coulomb interaction between the electrons is unscreened. The unscreened Coulomb interaction reorganizes the electronic structure in a fundamental way --- it opens a soft gap in the single-particle density of states near the Fermi energy [1,2]. Crucially, this "Coulomb gap" is unrelated to symmetry breaking or band folding but a genuine result of strong correlation.

In this talk, I will walk the audience through the classic paper by Efros and Shklovskii [1]. I will show that a very simple and elegant argument can convincingly show the existence of the Coulomb gap and determine its size and shape. Next, I will show that the Coulomb gap modifies Mott's law for variable-range hopping. Finally, I will briefly discuss the experimental verification of these predictions in amorphous films [3,4].

References:

1. A. L. Efros and B. Shklovskii, "Coulomb gap and low temperature conductivity of disordered systems", J. Phys. C 8, L49 (1975).
2. A. L. Efros, "Coulomb gap in disordered systems", J. Phys. C 9, 2021 (1976).
3. J. G. Massey and Mark Lee, "Direct Observation of the Coulomb Correlation Gap in a Nonmetallic Semiconductor, Si: B", Phys. Rev. Lett. 75, 4266 (1995).
4. V. Yu. Butko, J. F. DiTusa, and P. W. Adams, "Coulomb Gap: How a Metal Film Becomes an Insulator", Phys. Rev. Lett. 84, 1543 (2000).