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

Abstract

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...

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

“…However, at the extremes of the energy regime, the opposite appears to happen -the wavefunctions for the interacting system are more localized, at least in configuration space. (It has been shown [26] that EEI can, under certain conditions enhance either localization or delocalization, and this in fact has been found to be the case [10].) We discuss the enhanced localization at the band edges in the context of [26] [26], so the effect on localization depends on which is enhanced more.…”

“…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.…”

“…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.…”

Possible robust insulator-superconductor transition on solid inert gas and other substrates

“…11 This shows that the conductance of a disordered film depends on interplay between interaction and disorder. 21 We caution that since our experiments are limited to 1.8 K, we cannot rule out the possibility that a film which appears to be the last film on the insulating side, may, at lower temperature turn out to be superconducting. 15 .…”

“…20 It has been shown that interactions may increase or decrease the conductance of a disordered 2D electron systemweak interactions increase the dc conductance in the localized regime while they decrease the conductance in the diffusive regime. 21 Strong interactions were always found to decrease the conductance. These considerations motivated our experiments.…”