Effect of increasing disorder on the critical behavior of a Coulomb system

Overlin, Michael H.; Wong, Lee A.; Yu, Clare C.

doi:10.1103/physrevb.70.214203

Cited by 19 publications

(32 citation statements)

References 47 publications

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“…consistent with the small values found in simulations on irregular lattices without on-site disorder 55,56 . We expect a similar situation in weakly disordered 2D systems.…”

Section: Glassinesssupporting

confidence: 79%

Memory effect in electron glasses: Theoretical analysis via a percolation approach

Lebanon

Müller

2005

Phys. Rev. B

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We present a theory for the memory effect in electron glasses. In fast gate voltage sweeps it is manifested as a dip in the conductivity around the equilibration gate voltage. We show that this feature, also known as anomalous field effect, arises from the long-time persistence of correlations in the electronic configuration. We argue that the gate voltage at which the memory dip saturates is related to an instability caused by the injection of a critical number of excess carriers. This saturation threshold naturally increases with temperature. On the other hand, we argue that the gate voltage beyond which memory is erased, is temperature independent. Using standard percolation arguments, we calculate the anomalous field effect as a function of gate voltage, temperature, carrier density and disorder. Our results are consistent with experiments, and in particular, they reproduce the observed scaling of the width of the memory dip with various parameters.

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“…consistent with the small values found in simulations on irregular lattices without on-site disorder 55,56 . We expect a similar situation in weakly disordered 2D systems.…”

Section: Glassinesssupporting

confidence: 79%

Memory effect in electron glasses: Theoretical analysis via a percolation approach

Lebanon

Müller

2005

Phys. Rev. B

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“…For W = 0, mean-field theory predicts a stable COP for d = 3 [18,22]. Beyond mean field there is some numerical evidence that the COP survives small positional disorder [6,7] and on-site disorder [23], but neither the phase diagram nor the critical properties have been investigated. Our results are as follows: (i) A COP exists below the (approximate) phase boundary in Fig.…”

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confidence: 99%

“…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].…”

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confidence: 99%

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

Goethe

Palassini

2009

Phys. Rev. Lett.

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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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“…There finite-size scaling (FSS) analysis predicts that the values of the critical exponents are consistent with those of the Ising model with short-range interactions. But at finite disorder, such a transition was seen in three dimensional (3d) CG [1][2][3][4] . Later the phase diagram and the critical properties of 3d CG were also investigated by Goethe and Palassini 5 .…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of the two-dimensional Coulomb glass at zero temperature

2017

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The lattice model of Coulomb Glass in two dimensions with box-type random field distribution is studied at zero temperature for system size upto 96 2 . To obtain the minimum energy state we annealed the system using Monte Carlo simulation followed by further minimization using clusterflipping. The values of the critical exponents are determined using the standard finite size scaling. We found that the correlation length ξ diverges with an exponent ν = 1.0 at the critical disorder Wc = 0.2253 and that χ dis ≈ ξ 4−η withη = 2 for the disconnected susceptibility. The staggered magnetization behaves discontinuously around the transition and the critical exponent of magnetization β = 0. The probability distribution of the staggered magnetization shows a three peak structure which is a characteristic feature for the phase coexistence at first-order phase transition. In addition to this, at the critical disorder we have also studied the properties of the domain for different system sizes. In contradiction with the Imry-Ma arguments, we found pinned and noncompact domains where most of the random field energy was contained in the domain wall. Our results are also inconsistent with Binder's roughening picture.

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Effect of increasing disorder on the critical behavior of a Coulomb system

Cited by 19 publications

References 47 publications

Memory effect in electron glasses: Theoretical analysis via a percolation approach

Memory effect in electron glasses: Theoretical analysis via a percolation approach

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

Critical behavior of the two-dimensional Coulomb glass at zero temperature

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