Coulomb gap in the one-particle density of states in three-dimensional systems with localized electrons

Abstract

The one-particle density of states (1P-DOS) in a system with localized electron states vanishes at the Fermi level due to the Coulomb interaction between electrons. Derivation of the Coulomb gap uses stability criteria of the ground state. The simplest criterion is based on the excitonic interaction of an electron and a hole and leads to a quadratic 1P-DOS in the three-dimensional (3D) case. In 3D, higher stability criteria, including two or more electrons, were predicted to exponentially deplete the 1P-DOS at energies close enough to the Fermi level. In this paper we show that there is a range of intermediate energies where this depletion is strongly compensated by the excitonic interaction between single-particle excitations, so that the crossover from quadratic to exponential behavior of the 1P-DOS is retarded. This is one of the reasons why such exponential depletion was never seen in computer simulations.

Observation of Coulomb gap in the quantum spin Hall candidate single-layer 1T’-WTe2

“…For our tunneling spectroscopy measurement, the d I /d V curves near the E F can be fitted very well with the linear format of a soft gap, as shown in Fig. 4c 37,38 . Considering the case that the gap is in a linear shape and always pinned at the E F , a Coulomb gap is strongly suggested.…”

“…In the 2D case, the DOS near the Fermi energy can be qualitatively given as: 37,38 at T  = 0 K, where ε represents the energy with respect to the Fermi energy E F . The Coulomb gap in the DOS can be observed experimentally at low enough temperatures, such that thermal excitations do not wash it out.…”

Marginal Stability in Structural, Spin, and Electron Glasses

“…[50]. However, when multiparticle stability constraints are enforced, the pseudo-gap might be suppressed beyond the bound α = d−1, in particular in d ≥ 3 dimensions [2,53], where stability with respect to soft compact dipolar excitations has to be considered, on top of single charge excitations. Such a tendency is observed in numerical studies of the distribution of single site excitations [11,54].…”

Structural relaxation and aging scaling in the Coulomb and Bose glass models

“…Earlier work by Efros et al [42] focused on random site energies ϕ i from a uniform distribution of certain width, while here we investigate different energy distributions to conclude their effects on the system's properties. We consider cases with zero random on-site energies (ϕ i = 0) and others where the on-site energies are taken from either a normalized Gaussian or a flat distribution of zero mean and different widths w.…”

“…These mean-field arguments assume single-particle hops and that all sites are evenly distributed within the energy interval , whereas in fact multi-particle hops play an important role in the system and sites often cluster [33]. Therefore, γ mf represents a lower bound for the exponent γ [42], for which Möbius, Richter, and Drittler obtained deviations from the predicted mean-field results [41].…”