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Philosophical Magazine B

Localization and conductance in the quantum Coulomb glass

Michael Schreiber Thomas Vojta

Published Sep 1, 2001• 1 citation
Publisher

Abstract

We consider the combined influence of disorder, electron-electron interactions and quantum hopping on the properties of electronic systems in a localized phase, approaching an insulator-metal transition.The generic models in this regime are the quantum Coulomb glass and its generalization to electrons with spin.After introducing these models we explain our computational method, the Hartree-Fock based diagonalization.We then discuss the conductance and compare spinless fermions and electrons.It turns out that spin degrees of freedom do not play an essential role in the systems considered.Finally, we analyze localization and decay of singleparticle excitations.We find that interactions generically tend to localize these excitations which is a result of the Coulomb gap in the single-particle density of states.

DOI
10.1080/13642810110055724

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We consider the combined influence of disorder, electron-electron interactions and quantum hopping on the properties of electronic systems in a localized phase, approaching an insulator-metal transition.The generic models in this regime are the quantum Coulomb glass and its generalization to electrons with spin.After introducing these models we explain our computational method, the Hartree-Fock based diagonalization.We then discuss the conductance and compare spinless fermions and electrons.It turns out that spin degrees of freedom do not play an essential role in the systems considered.Finally, we analyze localization and decay of singleparticle excitations.We find that interactions generically tend to localize these excitations which is a result of the Coulomb gap in the single-particle density of states.
We consider the combined influence of disorder, electron4ectron interactions and quantum hopping on the properties of electronic systems in a localized phase, approaching an insulator-metal transition. The generic models in this regime are the quantum Coulomb glass and its generalization to electrons with spin. After introducing these models we explain our computational method, the Hartree-Fock-based diagonalization. We then discuss the conductance and compare spinless fermions and electrons. It turns out that spin degrees of freedom do not play an essential role in the systems considered. Finally, we analyse localization and decay of single-particle excitations. We find that interactions generically tend to localize these excitations, which is a result of the Coulomb gap in the single-particle density of states.
We numerically investigate the transport properties of disordered interacting electrons in three dimensions in the metallic as well as in the insulating phases. The disordered many-particle problem is modeled by the quantum Coulomb glass which contains a random potential, long-range unscreened Coulomb interactions and quantum hopping between different sites. We have recently developed the Hartree-Fock based diagonalization (HFD) method which amounts to diagonalizing the Hamiltonian in a suitably chosen energetically truncated basis. This method allows us to investigate comparatively large systems. Here we calculate the combined effect of disorder and interactions on the dissipative conductance. We find that the qualitative influence of the interactions on the conductance depends on the relative disorder strength. For strong disorder interactions can significantly enhance the transport while they suppress the conductance for weak disorder.
Abstract We numerically investigate the transport properties of disordered interacting electrons in three dimensions in the metallic as well as in the insulating phases. The disordered many‐particle problem is modeled by the quantum Coulomb glass which contains a random potential, long‐range unscreened Coulomb interactions and quantum hopping between different sites. We have recently developed the Hartree‐Fock based diagonalization (HFD) method which amounts to diagonalizing the Hamiltonian in a suitably chosen energetically truncated basis. This method allows us to investigate comparatively large systems. Here we calculate the combined effect of disorder and interactions on the dissipative conductance. We find that the qualitative influence of the interactions on the conductance depends on the relative disorder strength. For strong disorder interactions can significantly enhance the transport while they suppress the conductance for weak disorder.
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 dc conductance in the strongly localized regime while they decrease the dc 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.
We study electronic transport in Anderson insulators with strong Coulomb interactions in dimensions d>=2. Close to the metal insulator transition where the single particle localization length is much larger than interparticle-distance, the interactions lead to a strongly correlated quantum glass phase. Even though single particle excitations are localized and the system is insulating, there are collective electronic modes which remain delocalized down to parametrically small energies. These collective excitations serve as a continuous bath which can provide the activation energy for variable range hopping transport. This circumvents the energy conservation problem arising when only discrete particle-hole excitations are present. In contrast to the weak and material-dependent phonon-assisted hopping mechanism, the activation by an electronic bath leads to a nearly universal prefactor e^2/h of the Efros-Shklovskii conductance, as is observed in many recent experiments.
Interplay of electron correlation and randomness is studied by using the Anderson-Hubbard model within the Hartree-Fock approximation. Under the coexistence of short-range interaction and diagonal disorder, we obtain the ground-state phase diagram in three dimensions, which includes an antiferromagnetic insulator, an antiferromagnetic metal, a paramagnetic insulator (Anderson-localized insulator) and a paramagnetic metal. Although only the short-range interaction is present in this model, we find unconventional soft gaps in the insulating phases irrespective of electron filling, spatial dimensions and long-range order, where the single-particle density of states (DOS) vanishes with a power-law scaling in one dimension (1D) or even faster in two dimensions (2D) and three dimensions (3D) toward the Fermi energy. We call it soft Hubbard gap. Moreover, exact-diagonalization results in 1D support the formation of the soft Hubbard gap beyond the mean-field level. The formation of the soft Hubbard gap cannot be attributed to a conventional theory by Efros and Shklovskii (ES) owing the emergence of soft gaps to the long-range Coulomb interaction. Indeed, based on a picture of multivalley energy landscape, we propose a phenomenological scaling theory, which predicts a scaling of the DOS in perfect agreement with the numerical results. We further discuss a correction of the scaling of the DOS by the long-range part of the Coulomb interaction, which modifies the scaling of Efros and Shklovskii. Furthermore, explicit formulae for the temperature dependence of the DC resistivity via variable-range hopping under the influence of the soft gaps are derived. Finally, we compare the present theory with experimental results of SrRu_{1-x}Ti_xO_3.