Nonlinear Screening Theory of the Coulomb Glass

Abstract

A nonlinear screening theory is formulated to study the problem of gap formation and its relation to glassy freezing in classical Coulomb glasses. We find that a pseudo-gap ("plasma dip") in a single-particle density of states begins to open already at temperatures comparable to the Coulomb energy. This phenomenon is shown to reflect the emergence of short range correlations in a liquid (plasma) phase, a process which occurs even in the absence of disorder. Glassy ordering emerges when disorder is present, but this occurs only at temperatures roughly an order of magnitude lower. Our result demonstrate that the formation of the "plasma dip" at high temperatures is a process distinct from the formation of the Efros-Shklovskii (ES) pseudo-gap, which in our model emerges only within the glassy phase.The interplay of interactions and disorder remains one of the most important open problems in condensed matter physics. These effects are most dramatic in disordered insulators, where the pioneering work of Efros and Shklovskii (ES) [1] emphasized the fundamental significance of the long-ranged nature of Coulomb interactions. This work presented convincing evidence that at T = 0 a soft "Coulomb gap" emerges in the single-particle density of states (DOS) which, in arbitrary dimension d, reads( 1) ¿From a general point of view this result is quite surprising. It indicates a power-law distribution of excitation energies, i.e. the absence of a characteristic energy scale for excitations above the ground state. Such behavior is common in models with broken continuous symmetry, where it reflects the corresponding Goldstone modes, but is generally not expected in discrete symmetry models, such as the one used by ES. Here, it may reflect unusually strong frustration behavior inherent to Coulomb interactions in presence of disorder.Indeed, the ES model seems to display several glassy features characterized by a large number of meta-stable states and slow relaxation, as clearly seen in many simulations [2,3,4,5], and even in some experiments [7]. Interestingly, a precursor of the gap begins to appear [4,6] already at relatively high temperatures, while glassy ordering emerges only at much lower T . Similar behavior has been identified even in absence of randomness [8]. Is the physics of the Coulomb gap thus related or is it unrelated to the glassy features of the system? The close connection between the two phenomena was recently demonstrated [9] for a mean-field model of interacting disordered electrons in the limit of large coordination, but the issue remains unresolved for Coulomb systems in finite dimensions where the ES theory applies.To address these important issues in a controlled and precise fashion, we make the following observation which is the main physical point of this letter. We stress that the principal ES result -the emergence of a power-law spectrum -is not specific to low dimensions! Its physical origin and its relation to high temperature anomalies can, therefore, be investigated by the theoretical approaches c...

Memory effect in electron glasses: Theoretical analysis via a percolation approach

“…This conjecture is rather natural in the light of recent theoretical work which suggests that the emergence and the universality of the Coulomb gap are related to a glass transition at a finite T g in these systems 25,26,27 . This opens the appealing perspective of obtaining more detailed information on Coulomb correlations from a quantitative analysis of the memory experiments.…”

“…More theoretical insight can be gained from mean-field theory 26,27 . Let us first discuss the case of strong disorder (γ > 1), which corresponds to most experiments in indium-oxide (n c > ∼ n X ).…”

Anomalous electric‐field effect and glassy behaviour in granular aluminium: electron glass?

“…Although the question of a finite glass transition temperature in real systems is still theoretically debated [41,42,44] and experimentally unanswered, there is a consensus that the relaxation of a Coulomb glass through the low lying metastable states involve multi-electron hops which can have arbitrarily long times.…”

2D-MIT as self-doping of a Wigner–Mott insulator

“…Because the Coulomb interaction is long ranged, these collective modes are very soft, and play an important role in renormalizing the model parameters. It is this strong renormalization of the charge transfer gap e c − e f that pushes the transition to such low density [6] (r s ≫ 1)), in a fashion that is conceptually very similar to the formation of the Coulomb gap [10]. At present, these effects are incorporated in through the choice of the electrostatic parameters of our model.…”

“…In future work, we would like to systematically incorporate these soft collective modes, the effects of which are currently included in a semi-phenomenological fashion. This program can be achieved by a variety of methods, including extended dynamical mean field approaches (EDMFT), by exploiting unique properties of the Coulomb potential, and by employing the techniques recently developed in the Coulomb glass context [10].…”