Level spacing distributions and elastic hopping in the Coulomb glass

Talamantes, J.; Pollak, M.; Elam, L.

doi:10.1209/epl/i1996-00143-x

Cited by 31 publications

(52 citation statements)

References 11 publications

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“…The same conclusion was drawn from density-matrix RG studies [13] and exact diagonalizations [14] in 1D. In contrast, for 2D models in the localized regime [15,16] it was found that interactions lead to a delocalization. Up to now it has been unclear whether these inconsistent results are due to being in different parameter regions (weak vs. strong disorder), different quantities studied (conductance, manyparticle level statistics or charge stiffness), or long-range vs. short-range interactions.…”

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confidence: 68%

Do Interactions Increase or Reduce the Conductance of Disordered Electrons? It Depends!

1998

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We investigate the influence of electron-electron interactions on the conductance of two-dimensional disordered spinless electrons. We present an efficient numerical method based on diagonalization in a truncated basis of Hartree-Fock states to determine with high accuracy the low-energy properties in the entire parameter space. We find that weak interactions increase the d.c. conductance in the strongly localized regime while they decrease the d.c. conductance for weak disorder. Strong interactions always decrease the conductance. We also study the localization of single-particle excitations at the Fermi energy which turns out to be only weakly influenced by the interactions. 71.55.Jv, 72.15.Rn, 71.30.+h The influence of electron-electron interactions on the transport in disordered electronic systems has been investigated intensively within the last two decades [1,2]. Recently, the problem has reattracted a lot of attention after experimental [3] and theoretical [4] results challenged established opinions.It is well accepted [5] that non-interacting electrons in three dimensions (3D) undergo a localizationdelocalization transition at finite disorder. In contrast, all states are localized in 2D and 1D even for infinitesimal weak disorder [6]. However, today it is believed that the metal-insulator transition (MIT) in most experimental systems cannot be explained based on noninteracting electrons. The metallic phase of disordered interacting electrons has been studied intensively within the perturbative renormalization group (RG) [2] leading to a qualitative analysis of the MIT and the identification of different universality classes. One of the results is that the lower critical dimension of the MIT is d − c = 2 as it is for non-interacting electrons. Therefore it came as a surprise when experiments [3] on Si-MOSFETs revealed indications of a MIT in 2D. Since these experiments are performed at low electron density where the Coulomb interaction is particularly strong compared to the Fermi energy, interaction effects are a likely reason for this MIT. A complete understanding has, however, not yet been obtained. Explanations were suggested based on the perturbative RG [7], non-perturbative effects [8], or the transition being a superconductor-insulator transition rather than a MIT [9].Theoretically, surprising results have been obtained for just two interacting particles in the insulating regime [4]. It was found that two particles can form a pair whose localization length is much larger than that of a single particle. Later an even larger delocalization was suggested for clusters of three or more particles [10]. In the case of a repulsive electron-electron these delocalized states have rather high energy, thus their relevance for the low-energy properties of a degenerate system is not clear. It has been argued that the many-particle problem can be reduced to a few interacting quasiparticles above the Fermi surface [11]. This is, however, only possible, if the interactions do not change the nature of the ground s...

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confidence: 68%

Do Interactions Increase or Reduce the Conductance of Disordered Electrons? It Depends!

1998

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“…However, in this method neither disorder nor interactions are treated completely and different results obtained this way contradict each other. Recently, localization in an interacting disordered system was investigated 13 by the numerical analysis of the manybody spectrum of small clusters from which the authors inferred a delocalizing influence of the interactions.…”

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confidence: 99%

Quantum Coulomb glass within a Hartree-Fock approximation

1997

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We study the influence of electron-electron interactions on the electronic properties of disordered materials. In particular, we consider the insulating side of a metal-insulator transition where screening breaks down and the electron-electron interaction remains long-ranged. The investigations are based on the quantum Coulomb glass, a generalization of the classical Coulomb glass model of disordered insulators. The quantum Coulomb glass is studied by decoupling the Coulomb interaction by means of a Hartree-Fock approximation and exactly diagonalizing the remaining localization problem. We investigate the behavior of the Coulomb gap in the density of states when approaching the metal-insulator transition and study the influence of the interaction on the localization of the electrons. We find that the interaction leads to an enhancement of localization at the Fermi level. 71.55.Jv, 72.15.Rn, 71.30.+h

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“…In this model, W/t = e rnn /[r nn (1+ r nn )], so a small difference in r nn implies a comparatively larger one in W/t. This gives W/t ∼ 3, 5,10,20, 40, 90, 200, 500, 1000 for r nn = 4, 5,6,7,8,9,10,11,12, respectively. One must be careful, however, when comparing our results with those of other authors because here W/t = e C /t.…”

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“…While the Hartree Coulomb repulsion introduces an additional random energy and thus enhances localization, the possibility that quantum correlation due to the EEI may act to delocalize the electrons was proposed twenty years ago by Pollak and Knotek [4], and Pollak [5], but a firm answer has not been achieved yet. Computationally, the main difficulty in the finite-electron-density problem is the huge phase space for systems of reasonable size [6]. Existing work [6,7,8,9,10] resorted to various approximations.…”

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“…Computationally, the main difficulty in the finite-electron-density problem is the huge phase space for systems of reasonable size [6]. Existing work [6,7,8,9,10] resorted to various approximations. In contrast, the TIP problem for reasonably large systems can be solved without such approximations: double occupation of sites can be accounted for, spin and exchange included, and the entire phase space can be examined.…”

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Two electrons in a two-dimensional random potential: Exchange, interaction, and localization

Talamantes

Pollak

2000

Phys. Rev. B

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The problem of two electrons in a two-dimensional random potential is addressed numerically. Specifically, the role of the Coulomb interaction between electrons on localization is investigated by writing the Hamiltonian on a localized basis and diagonalizing it exactly. The result of that procedure is discussed in terms of level statistics, the expectation value of the electron-electron separation, and a configuration-space inverse participation number. We argue that, in the interacting problem, a localizationdelocalization crossover in real space does not correspond exactly to a Poisson-Wigner crossover in level statistics.PACS 71.23An; 71.30+h; 71.23−k §1. Introduction. The problem of two interacting particles (TIP) in a random potential has received much attention in the last few years. The focus has been primarily on TIP in one dimension (1D), where most investigators have dealt with particles interacting via an on-site potential. (For a concise summary of the various approaches used, and results obtained, we refer the reader to the articles in ref. [1].) The reason for all the attention (and controversy) is the result, first found by Shepelyansky [2], that the TIP actually propagate coherently through a length much larger than the one-particle localization radius, which can lead to an enhancement of transport [3]. We address the related problem of localization in 2D systems, and how it is affected by a long-range electron-electron interaction (EEI).The more general problem of the interplay between disorder, interaction and quantum tunneling, and their combined effect on electronic localization is not new. While the Hartree Coulomb repulsion introduces an additional random energy and thus enhances localization, the possibility that quantum correlation due to the EEI may act to delocalize the electrons was proposed twenty years ago by Pollak and Knotek [4], and Pollak [5], but a firm answer has not been achieved yet. Computationally, the main difficulty in the finite-electron-density problem is the huge phase space for systems of reasonable size [6]. Existing work [6,7,8,9,10] resorted to various approximations. In contrast, the TIP problem for reasonably large systems can be solved without such approximations: double occupation of sites can be accounted for, spin and exchange included, and the entire phase space can be examined. A motivation for the problem considered here is the ability to make inferences about approximations made in investigations of finite-density and few-electron systems [11,12,13,14,15,16]. We hope furthermore that the work may contribute to insight into the mechanisms at play in the experimental reports on an observed metal-insulator transition (MIT) in 2D [17].In the present paper, we deal with two electrons in a random potential interacting via a long-range Coulomb interaction, and investigate numerically the effect of that EEI on electronic localization. A tool used frequently to assess localization has been the distribution p(s) of nearest-level spacings s. In the absence o...

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Level spacing distributions and elastic hopping in the Coulomb glass

Cited by 31 publications

References 11 publications

Do Interactions Increase or Reduce the Conductance of Disordered Electrons? It Depends!

Do Interactions Increase or Reduce the Conductance of Disordered Electrons? It Depends!

Quantum Coulomb glass within a Hartree-Fock approximation

Two electrons in a two-dimensional random potential: Exchange, interaction, and localization

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