Phase Transition in Coulomb Glasses

Díaz‐Sánchez, A.; Ortuño, M.; Pérez‐Garrido, A.; Cuevas, E.

doi:10.1002/(sici)1521-3951(200003)218:1<11::aid-pssb11>3.0.co;2-y

phys. stat. sol. (b)

2000

DOI: 10.1002/(sici)1521-3951(200003)218:1<11::aid-pssb11>3.0.co;2-y

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Phase Transition in Coulomb Glasses

A. Díaz‐Sánchez

M. Ortuño

A. Pérez‐Garrido

et al.

Abstract: We search for the phase transition and the nature of the low temperature phase for different models of the Coulomb glass and different dimensionalities. We do this with the help of several statistical parameters of the overlap between different many‐particle states, first introduced to investigate the spin glass transition and related to the Edwards‐Anderson order parameter. We calculate numerically these parameters in dependence on the temperature and system size for very low temperatures. Then we apply scali… Show more

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Cited by 10 publications

(3 citation statements)

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“…Glass phase -Several works have searched for a GP by measuring the parameter [( n i − 1/2) 2 ] av [11] or higher cumulants of the overlap between two replicas [15]. We measure instead the glass CL ξ …”

mentioning

confidence: 77%

“…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].…”

mentioning

confidence: 98%

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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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mentioning

confidence: 77%

mentioning

confidence: 98%

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

Goethe

Palassini

2009

Phys. Rev. Lett.

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show abstract

“…[8][9][10][11][12] An order parameter, similar to the Edwards-Anderson order parameter used for spin glass systems, was proposed for the electron glass in an attempt to find a glass transition. Though a non-zero value of the order parameter was found, critical behavior was absent in the numerical studies.…”

mentioning

confidence: 99%

Electrical transport studies of quench condensed Bi films at the initial stage of film growth: A structural transition and the possible formation of electron droplets

Rosario¹,

Liu²

2002

Phys. Rev. B

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The electrical transport properties of amorphous Bi films prepared by sequential quench deposition have been studied in situ. A superconductor-insulator (S-I) transition was observed as the film was made increasingly thicker, consistent with previous studies. Unexpected behavior was found at the initial stage of film growth, a regime not explored in detail prior to the present work. As the temperature was lowered, a positive temperature coefficient of resistance (dR/dT > 0) emerged, with the resistance reaching a minimum before the dR/dT became negative again. This behavior was accompanied by a non-linear and asymmetric I − V characteristic. As the film became thicker, conventional variable-range hopping (VRH) was recovered. We attribute the observed crossover in the electrical transport properties to an amorphous to granular structural transition. The positive dR/dT found in the amorphous phase of Bi formed at the initial stage of film growth was qualitatively explained by the formation of metallic droplets within the electron glass. 73.50.-h, 74.40.+k

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Numerical study of the equilibrium thermodynamics of the Coulomb glass

Goethe¹,

Palassini²

2009

Ann. Phys.

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PACS 64.70ph, 75.10.Nr We discuss the results of large-scale Monte Carlo simulations of the lattice Coulomb glass model. Using the Exchange Monte Carlo algorithm we are able to equilibrate the system to very low temperature and obtain evidence against the existence of an equilibrium glass transition in three dimensions (3D). We also discuss results for the 3D Random Field Ising model that highlight the role of the interaction range. Finally, we report results for the 2D Coulomb glass, which show a behaviour very similar to the 3D case. A long-standing question in the study of disordered systems is whether the slow nonequilibrium dynamics observed in Coulomb glasses (CG) (for recent work see, e.g., [1,2] and references therein) reflects an underlying equilibrium transition to a glass phase [3]. This question was recently revived in mean-field studies [4][5][6] that predict the existence of an equilibrium glass phase in the 3D CG model with random site energies (RSE) [7]. This is a nontrivial prediction since the transition breaks no symmetry of the Hamiltonian, but only the so-called replica symmetry, similarly to the spin-glass transition in mean-field spin glasses [8]. In the usual interpretation of a replica symmetry-broken (RSB) phase, the configuration space splits into many thermodynamic states, or "valleys" separated by diverging free-energy barriers.Numerical searches for an equilibrium glass phase in the CG have been hampered by computational difficulties and by the lack of a simple order parameter [3,9]. In the RSB scenario, the order parameter is the full distribution P (q) of overlaps between states, which is a delta function in the fluid phase and has finite support in the glass phase. Menashe et al. [10] argued against a glass phase from the system-size dependence of the equilibration time of Monte Carlo (MC) simulations in 2D. Numerical evidence for a transition was found for the special case of positional disorder without RSE at half-filling [9,11,12]. However, since this model exhibits particle-hole symmetry, the glass phase need not be of the RSB kind. A similar situation occurs in short-range spin glasses, where in 3D and in the absence of an external field the existence of a spin-glass phase, described by an Edwards-Anderson order parameter, is well established [13, 16] but does not necessarily imply RSB. The spin-glass analogous of the glass transition in the CG model with RSE would be the much-debated Almeida-Thouless transition in the presence of a field [8].Recently, Surer et al. [14] and the authors [15] simulated the CG lattice model with RSE in 3D with the Exchange Monte Carlo (EMC) algorithm, a method widely used for spin glasses and other systems with rugged free-energy landscapes, which allows equilibrium to be reached at much lower temperatures than in previous work [9,10]. Both Surer et al. and us found evidence against the existence of a glass transition by computing a suitably defined finite-size correlation length (see below), an observable previously used as a test for phase...

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Phase Transition in Coulomb Glasses

Cited by 10 publications

References 9 publications

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

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

Electrical transport studies of quench condensed Bi films at the initial stage of film growth: A structural transition and the possible formation of electron droplets

Numerical study of the equilibrium thermodynamics of the Coulomb glass

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