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arXiv:0711.2668

Collective modes in quantum electron glasses and electron-assisted hopping

Markus Müller, L. B. Ioffe

Published Nov 17, 2007• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.0711.2668

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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.
This paper describes experiments utilizing a unique property of electron glasses to gain information on the fundamental nature of the interacting Anderson-localized phase. The methodology is based on measuring the energy absorbed by the electronic system from alternating electromagnetic fields as a function of their frequency. Experiments on three-dimensional (3D) amorphous indium-oxide films suggest that, in the strongly localized regime, the energy spectrum is discrete and inelastic electron-electron events are strongly suppressed. These results imply that, at low temperatures, electron thermalization and finite conductivity depend on coupling to the phonon bath. The situation is different for samples nearing the metal-insulator transition; in insulating samples that are close to the mobility edge, energy absorption persists to much higher frequencies. Comparing these results with previously studied 2D samples [Ovadyahu, Phys. Rev. Lett. 108, 156602 (2012)] demonstrates that the mean-level spacing (on a single-particle basis) is not the only relevant scale in this problem. The possibility of delocalization by many-body effects and the relevance of a nearby mobility edge (which may be a many-body edge) are discussed.
Understanding the nature of collective charge dynamics in the Coulomb gap phase is essential for revealing the existence of many-body localization. However, the corresponding many-particle excitation spectra remain poorly understood. Here, we present a comprehensive investigation of [Formula: see text]Al and [Formula: see text]Cu nuclear magnetic/quadrupole resonance (NMR/NQR), along with specific heat ([Formula: see text]) measurements, in the p-type semiconductor CuAlO[Formula: see text]. Our study unveils distinct changes in charge dynamics at two crossover temperature scales which separate three regimes associated with Anderson localization of charge carriers: thermally activated transport ([Formula: see text] K) → Mott variable-range hopping (VRH) → Efros–Shklovskii (ES) VRH with Coulomb gap formation ([Formula: see text] K). In the ES VRH regime, we observe a striking divergence in the zero-field [Formula: see text]Cu spin-lattice relaxation rate, [Formula: see text], which is strongly suppressed by an applied magnetic field, indicative of quantum critical charge fluctuations. This is further supported by a distinct magnetic field-dependence of [Formula: see text] deep within the Coulomb gap phase. Taken together, these results provide compelling evidence for the emergence of strong, gapless collective charge fluctuations within the Anderson insulating phase where single-particle excitations are gapped.
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 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.
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.
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.