Three-dimensional Coulomb Glass Research Articles

Relaxation dynamics of the three-dimensional Coulomb glass model.

In this paper, we analyze the dynamics of the Coulomb glass lattice model in three dimensions near a local equilibrium state by using mean-field approximations. We specifically focus on understanding the role of localization length (ξ) and the temperature (T) in the regime where the system is not far from equilibrium. We use the eigenvalue distribution of the dynamical matrix to characterize relaxation laws as a function of localization length at low temperatures. The variation of the minimum eigenvalue of the dynamical matrix with temperature and localization length is discussed numerically and analytically. Our results demonstrate the dominant role played by the localization length on the relaxation laws. For very small localization lengths, we find a crossover from exponential relaxation at long times to a logarithmic decay at intermediate times. No logarithmic decay at the intermediate times is observed for large localization lengths.

Charge ordering in the three-dimensional Coulomb glass at finite temperatures and low disorders

In this paper, we have studied the three dimensional Coulomb glass lattice model at half-filling using Monte Carlo Simulations. Annealing of the system shows a second-order transition from paramagnetic to charge-ordered phase for zero as well as small disorders. We have also calculated the critical exponents and transition temperature using a finite sizing scaling approach. The Monte Carlo simulation is done using the Metropolis algorithm, which allowed us to study larger lattice sizes. The transition temperature and the critical exponents at zero disorder matched the previous studies within numerical error. We found that the transition temperature of the system decreased as the disorder is increased. The values of critical exponents $\alpha$ and $\gamma$ were less and value of $\nu$ more than the corresponding zero disorder values. The use of large system sizes led to the correct variation of critical exponents with the disorder.

Numerical observation of a glassy phase in the three-dimensional Coulomb glass

The existence of an equilibrium glassy phase for charges in a disordered potential with long-range electrostatic interactions has remained controversial for many years. Here we conduct an extensive numerical study of the disorder-temperature phase diagram of the three-dimensional Coulomb glass model using population annealing Monte Carlo to thermalize the system down to extremely low temperatures. Our results strongly suggest that, in addition to a charge order phase, a transition to a glassy phase can be observed, consistent with previous analytical and experimental studies.

Charge avalanches and depinning in the Coulomb glass: The role of long-range interactions

We explore the stability of far-from-equilibrium metastable states of a three-dimensional Coulomb glass at zero temperature by studying charge avalanches triggered by a slowly varying external electric field. Surprisingly, we identify a sharply defined dynamical ("depinning") phase transition from stationary to nonstationary charge displacement at a critical value of the external electric field. Using particle-conserving dynamics, scale-free system-spanning avalanches are observed only at the critical field. We show that the qualitative features of this depinning transition are completely different for an equivalent short-range model, highlighting the key importance of long-range interactions for nonequilibrium dynamics of Coulomb glasses.

Nonequilibrium relaxation and aging scaling of the Coulomb and Bose glass.

We employ Monte Carlo simulations to investigate the nonequilibrium relaxation properties of the two- and three-dimensional Coulomb glass with different long-range repulsive interactions. Specifically, we explore the aging scaling laws in the two-time density autocorrelation function. We find that, in the time window and parameter range accessible to us, the scaling exponents are not universal, depending on the filling fraction and temperature: As either the temperature decreases or the filling fraction deviates more from half filling, the exponents reflect markedly slower relaxation kinetics. In comparison with a repulsive Coulomb potential, appropriate for impurity states in strongly disordered semiconductors, we observe that, for logarithmic interactions, the soft pseudogap in the density of states is considerably broader, and the dependence of the scaling exponents on external parameters is much weaker. The latter situation is relevant for flux creep in the disorder-dominated Bose glass phase of type-II superconductors subject to columnar pinning centers.

Mean-field theory for the three-dimensional Coulomb glass

We study the low temperature phase of the three-dimensional Coulomb glass within a mean-field approach which reduces the full problem to an effective single site model with a nontrivial replica structure. We predict a finite glass transition temperature ${T}_{c}$, and a glassy low temperature phase characterized by permanent criticality. The latter is shown to assure the saturation of the Efros-Shklovskii Coulomb gap in the density of states. We find this pseudogap to be universal due to a fixed point in Parisi's flow equations. The latter is given a physical interpretation in terms of a dynamical self-similarity of the system in the long time limit, shedding light on the concept of effective temperature. From the low temperature solution we infer properties of the hierarchical energy landscape, which we use to make predictions about the master function governing the aging in relaxation experiments.

Heterogeneous dynamics of the three-dimensional Coulomb glass out of equilibrium

The nonequilibrium relaxational properties of a three-dimensional Coulomb glass model are investigated by kinetic Monte Carlo simulations. Our results suggest a transition from stationary to nonstationary dynamics at the equilibrium glass transition temperature of the system. Below the transition the dynamic correlation functions lose time translation invariance and electron diffusion is anomalous. Two groups of carriers can be identified at each time scale: electrons whose motion is diffusive within a selected time window and electrons that during the same time interval remain confined in small regions in space. During the relaxation that follows a temperature quench an exchange of electrons between these two groups takes place and the nonequilibrium excess of diffusive electrons initially present decreases logarithmically with time as the system relaxes. This bimodal dynamical heterogeneity persists at higher temperatures when time translation invariance is restored and electron diffusion is normal. The occupancy of the two dynamical modes is then stationary and its temperature dependence reflects a crossover between a low-temperature regime with a high concentration of electrons forming fluctuating dipoles and a high-temperature regime in which the concentration of diffusive electrons is high.

Stretched exponential relaxation in the Coulomb glass

The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function, $f(t)=f_0\exp[-(t/\tau)^\beta]$, with the exponent $\beta$ increasing with the temperature. The relaxation time follows an Arrhenius behavior divergence when $T\to 0$. A relation between the specific heat and the entropy in the long time regime is found.

Electrode screening of the Coulomb gap

Abstract Computer simulation of tunnelling into materials with a Coulomb gap is presented. The model system is a three-dimensional Coulomb glass lying to one side of an infinite plane. An equipotential near the plane simulates the electrode, which screens the Coulomb interaction between localized electrons in the Coulomb glass. The depth-dependent one-particle density of states is computed, and the results are then used to obtain the tunnelling conductance of the system as a function of voltage.

Bethe-Peierls-Weiss approximation for the two- and three-dimensional Coulomb glass: zero-temperature and finite-temperature results

The Bethe-Peierls-Weiss approximation is applied to the Coulomb glass Hamiltonian in two and three dimensions. The single-particle density of states (DOS) at zero temperature is calculated analytically; it has a soft Coulomb gap at the Fermi energy. The authors rederive the self-consistent equation of Efros (1975), but not the altered version given by Baranovskii, Efros, Gelmont and Shklovskii (1979). The DOS is independent of the mean occupation number of the sites. These results are compared with numerical simulations of the model. The influence of finite temperatures on the DOS is discussed qualitatively. The Coulomb gap fills with increasing temperature T. For kT smaller than the gap width the DOS at the Fermi energy is proportional to kTD-1.