Phase Diagram, Correlation Gap, and Critical Properties of the Coulomb Glass

Abstract

We investigate the lattice Coulomb glass model in three dimensions via Monte Carlo simulations. No evidence for an equilibrium glass phase is found down to very low temperatures, although the correlation length increases rapidly near T = 0. A charge-ordered phase (COP) exists at low disorder. The transition to this phase is consistent with the Random Field Ising universality class, which shows that the interaction is effectively screened at moderate temperature. For large disorder, the singleparticle density of states near the Coulomb gap satisfies the scaling relation g(ǫ, T ) = T δ f (|ǫ|/T ) with δ = 2.01 ± 0.05 in agreement with the prediction of Efros and Shklovskii. For decreasing disorder, a crossover to a larger effective exponent occurs due to the proximity of the COP. PACS numbers: 64.70ph,75.10.Nr In disordered insulators, the localized electrons cannot screen effectively the Coulomb interaction at low temperature. Therefore, many-electron correlations are important in this regime. The long-range repulsion induces a soft "Coulomb gap" in the single-particle density of states (DOS). Efros and Shklovskii (ES) [1] argued that the gap has a universal form g(ǫ) ∝ |ǫ − µ| δ near the chemical potential µ, with δ ≥ d − 1 in d dimensions, and that a saturated bound δ = d − 1 modifies the variablerange hopping resistivity ln R ∼ T −x from Mott's law x = 1/(d + 1) to x = 1/2. Both the existence of the gap and the crossover to x ≃ 1/2 at low temperature T have been confirmed experimentally and in numerical simulations [2], but the validity of δ = 2 for d = 3 has yet to be firmly established. Pseudo ground-state numerical calculations gave δ = 2.38 [3], δ = 2.7 [4, 5, 6], δ ≤ 2.01 [7], while finite-T simulations obtain δ between 2 and 4.8 [3,5,6] from the filling of the gap as g(µ) ∝ T δ [8, 9, 10].It was also suggested long ago [11] that disordered insulators enter a glass state at low temperature. Ample experimental and numerical evidence of glassy nonequilibrium effects in these systems has been obtained since [12]. However, it remains unclear whether these effects are purely dynamical or reflect an underlying transition to an equilibrium glass phase (GP), and whether there is a link between glassiness and the Coulomb gap. Some evidence for a sharp equilibrium transition to a GP was found in simulations of localized charges with random positions [6,14,15] but not in the presence of on-site disorder [7,15]. In the latter case, the transition would not break any symmetry of the Hamiltonian, similarly to the long-debated Almeida-Thouless transition in spin glasses [16]. These issues have been brought again to the fore by recent mean-field studies [13,17,18,19] which predict a "replica symmetry broken" equilibrium GP below a critical temperature T g in the presence of on-site disorder. In this GP correlations remain critical, which leads to δ = d − 1, and both T g and the gap width ∆ scale as W In this Letter, we investigate these predictions via extensive Monte Carlo (MC) simulations of the Coulomb glass latti...

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