Coulomb Glass Research Articles

Phase-ordering kinetics of the asymmetric Coulomb glass model.

We present results for phase-ordering kinetics in the Coulomb glass (CG) model, which describes electrons on a lattice with unscreened Coulombic repulsion. The filling factor is denoted by K∈[0,1]. For a square lattice with K=0.5 (symmetric CG), the ground state is a checkerboard with alternating electrons and holes. In this paper, we focus on the asymmetric CG where K≲0.5, i.e., the ground state is checkerboard-like with excess holes distributed uniformly. There is no explicit quenched disorder in our system, though the Coulombic interaction gives rise to frustration. We find that the evolution morphology is in the same dynamical universality class as the ordering ferromagnet. Further, the domain growth law is slightly slower than the Lifshitz-Cahn-Allen law, L(t)∼t^{1/2}, i.e., the growth exponent is underestimated. We speculate that this could be a signature of logarithmic growth in the asymptotic regime.

Effect of screening on the relaxation dynamics in a Coulomb glass

Effect of screening on the relaxation dynamics in a Coulomb glass

Superconducting dome by tuning through a van Hove singularity in a two-dimensional metal

Chemical substitution is a promising route for the exploration of a rich variety of doping- and/or disorder-dependent collective phenomena in low-dimensional quantum materials. Here we show that transition metal dichalcogenide alloys are ideal platforms to this purpose. In particular, we demonstrate the emergence of superconductivity in the otherwise metallic single-layer TaSe2 by minute electron doping provided by substitutional W atoms. We investigate the temperature and magnetic field dependence of the superconducting state of Ta1-δWδSe2 with electron doping (δ) using variable temperature (0.34–4.2 K) scanning tunneling spectroscopy (STS). We unveil the emergence of a superconducting dome spanning 0.003 < δ < 0.03 with a maximized critical temperature of 0.9 K, a significant increase from that of bulk TaSe2 (TC = 0.14 K). Superconductivity emerges from an increase of the density of states (DOS) as the Fermi surface approaches a van Hove singularity due to doping. Once the singularity is reached, however, the DOS decreases with δ, which gradually weakens the superconducting state, thus shaping the superconducting dome. Lastly, our doping-dependent measurements suggest the development of a Coulomb glass phase triggered by disorder due to W dopants.

A comparison of modified extremal optimization algorithm vs quenching for electron glass system optimization

Coulomb glass or electron glass refers to a system of localized electrons interacting via unscreened Coulomb interactions. The electrons are localized on a square lattice site, and the site's energies are random. This model was mainly used to represent amorphous and compensated semiconductors at high disorders and low temperatures. Recently, the model has been used to model granular systems, an array of nanocrystals, and graphene. In this work, we have obtained the ground state of an electron glass model in two dimensions using a modified extremal optimization. The work is done for disorders less than the critical disorder and at half-filling. For this case, the ground state has anti-ferromagnetic ordering, unlike the high disorder case. This allows us to check the efficiency of our new algorithm.The results are compared with quenching using Monte Carlo simulation. In the electron glass model, the number of electrons is conserved, and the interaction is long-ranged. Extremal optimization was developed to obtain the ground state of short-ranged spin systems with a non-conserved magnetization. The algorithm was extended to find the ground state of a long ranged anti-ferromagnet with conserved magnetization. We show that the efficiency of extremal optimization is comparable to the quenching method. The efficiency for both ways decreases as the disorder is increased. The minimum energy states obtained consist of mainly two large domains when the ground state was not achieved. These meta-stable states are stable, and increasing the run time increases the efficiency only by a small amount. The stability of the domains is analyzed using an activity graph. A comparison of the activity graphs for the same disorder configuration for the two algorithms shows that the formation of a meta-stable state is a general feature independent of the algorithm used. The formation of domain states is more prevalent for specific disorder configurations. These results can be explained in terms of domain formation theory.

Optimization of Coulomb glass system using extremal optimization at small disorder.

Optimization of Coulomb glass system using extremal optimization at small disorder.

Optimization of Coulomb glass system using quenching and annealing at small disorders

Abstract In this paper we have used Monte Carlo simulations to study the two dimensional Coulomb glassmodel at half filling. The simulations were carried out using the Metropolis algorithm at zero and small finite disorder. We have used two protocols namely quenching and annealing to find the ground state of the system. In the quenching protocol at zero disorder, we looked at the effect of temperature on the efficiency of finding the ground state. The efficiency does not improve by decreasing the temperature. Since efficiency for quenching protocol was very low, we then used the annealing protocol to find the minimum energy state of the system. The annealing protocol was much more efficient than the quenching procedure. At finite disorder less than the critical disorder, the efficiency of the quenching protocol decreased compared to the zero disorder case. These results have been discussed in terms of domain theory and the density of states.

Efficiency of extremal optimization to find the ground state of Coulomb glass system at small disorder

Efficiency of extremal optimization to find the ground state of Coulomb glass system at small disorder

Critical behavior of the specific heat in Ti-Si amorphous alloys at the metal-insulator transition

In this paper, we report the measurements of specific heat of an amorphous $Ti_{9.5}Si_{90.5}$ alloy located very close to the critical point of the metal-insulator transition. In the presence of a magnetic field, the specific heat is dominated by the Schottky anomaly caused by magnetic moments associated with the dangling bonds in the matrix of amorphous Si. Subtraction of this contribution exposes the behavior of the electronic specific heat coefficient $\gamma$. The coefficient is temperature-independent above 2 K and is, in order of magnitude, close to the value expected in the absence of electron-electron interactions. In the temperature range 0.4-1.5 K, the coefficient $\gamma$ shows an anomalous downturn, which can be approximated by the dependence $\gamma\left(T\right)=\gamma_0ln{(T/T_0)}$, with $T_0\approx0.2$ K . In a companion paper, we found that the Hall coefficient in Ti-Si alloys is affected by the electron-electron interaction up to much higher temperature of 150 K and also varies critically across the metal-insulator transition. We compare our results with theoretical predictions for three models, which can potentially explain the anomalous behavior of the specific heat: generalized non-linear $\sigma$ model, Coulomb glass, and many-body localization.

Quantum Coulomb glass on the Bethe lattice

We study the Coulomb glass emerging from the interplay of strong interactions and disorder in a model of spinless fermions on the Bethe lattice. In the infinite coordination number limit, strong interactions induce a metallic Coulomb glass phase with a pseudogap structure at the Fermi energy. Quantum and thermal fluctuations both melt this glass and induce a disordered quantum liquid phase. We combine self-consistent diagrammatic perturbation theory with continuous time quantum Monte-Carlo simulations to obtain the complete phase diagram of the electron glass and to characterize its dynamical properties in the quantum liquid, as well as in the replica symmetry broken glassy phase. Tunneling spectra display an Efros-Shklovskii pseudogap upon decreasing temperatures, but the density of states remains finite at the Fermi energy due to residual quantum fluctuations. Our results bear relevance to the metallic glass phase observed in Si inversion layers.

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.

Two-Dimensional-Dirac Surface States and Bulk Gap Probed via Quantum Capacitance in a Three-Dimensional Topological Insulator.

BiSbTeSe2 is a 3D topological insulator (3D-TI) with Dirac type surface states and low bulk carrier density, as donors and acceptors compensate each other. Dominating low-temperature surface transport in this material is heralded by Shubnikov-de Haas oscillations and the quantum Hall effect. Here, we experimentally probe and model the electronic density of states (DOS) in thin layers of BiSbTeSe2 by capacitance experiments both without and in quantizing magnetic fields. By probing the lowest Landau levels, we show that a large fraction of the electrons filled via field effect into the system ends up in (localized) bulk states and appears as a background DOS. The surprisingly strong temperature dependence of such background DOS can be traced back to Coulomb interactions. Our results point at the coexistence and intimate coupling of Dirac surface states with a bulk many-body phase (a Coulomb glass) in 3D-TIs.

Two-Dimensional Coulomb Glass as a Model for Vortex Pinning in Superconducting Films

A glass model of vortex pinning in highly disordered thin superconducting films in magnetic fields $B \ll H_{c2}$ at low temperatures is proposed. Strong collective pinning of a vortex system realized in disordered superconductors that are close to the quantum phase transition to the insulating phase -- such as $\mathrm{In O}_x$, $\mathrm{Nb N}$, $\mathrm{Ti N}$, $\mathrm{Mo Ge}$, nano-granular aluminium, and others -- is considered theoretically for the first time. Utilizing the replica trick developed for the spin glass theory, we demonstrate that such vortex system is in non-ergodic state of glass type with large kinetic inductance per square $L_K$. Distribution function of local pinning energies is calculated, and it is shown that it possesses a wide gap, i.e. the probability to find a weakly pinned vortex is extremely low.

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.

Growth of domains for two dimensional Coulomb glass

In this paper we study the growth of domains in two dimensional Coulomb glass at low disorders. Coulomb glass is a system in which electrons interact via long ranged unscreened Coulomb interactions. We have quenched the system from high temperature to a temperature well below the critical temperature. The quenching is done using Monte Carlo simulation via Kawasaki dynamics. We have studied the structure factor at zero and small disorder. Although the dynamics slows down for finite disorder, the structure factor shows Porod Law at zero and finite disorder. The Porod law is well established growth law obeyed by systems with short range interactions at zero disorder. We have also studied the density of states evolution with time. The density of states devolpes a gap as the domains are formed. The gap deepens as the domain size increases with time.

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.

Finite temperature phase transition in the two-dimensional Coulomb glass at low disorders

We present numerical evidence using Monte Carlo simulations of finite temperature phase transition in two dimensional Coulomb Glass lattice model with random site energies at half-filling. For the disorder strengths (W) studied in this paper, we find the existence of charge-ordered phase (COP) below the critical temperature (Tc(W)). Also, the probability distribution of staggered magnetization calculated at each W shows a two-peak structure at their respective critical temperature. Thus the phase transition from fluid to COP as a function of temperature is second order for all W. We find no evidence of a spin glass phase between a fluid and the COP. Further, we have used finite-size scaling analysis to calculate the critical exponents. The critical exponents at zero disorder are different from the one found at finite disorders, which indicates that the disorder is a relevant parameter here. The critical exponent for correlation length ν increases and Tc decreases with increasing disorder. Similar behaviour for ν was seen in the work of Overlin et al. for three dimensional Coulomb Glass model with a positional disorder. Our study also shows that other critical exponents are also a function of disorder.

Logarithmic coarsening in the Coulomb glass.

We present numerical results from a comprehensive Monte Carlo study in two dimensions (d=2) of coarsening kinetics in the Coulomb glass (CG) model at half-filling. The CG model is characterized by spin-spin interactions which are long-range Coulombic and antiferromagnetic. For the nonequilibrium properties studied by us (spatial correlation functions and domain growth laws), we find that domain growth in the CG is analogous to that in the nearest-neighbor random-field Ising model. The domain length scale L(t) shows a crossover from a regime of "power-law growth with a disorder-dependent exponent" [L(t)∼t^{1/z[over ¯]}] to a regime of "logarithmic growth with a universal exponent" [L(t)∼(lnt)^{1/ψ}].

Suppressed density of states in self-generated Coulomb glasses

We investigate the structure of metastable states in self-generated Coulomb glasses. In dramatic contrast to disordered electron glasses, we find that these states lack marginal stability. Such absence of marginal stability is reflected by the suppression of the single-particle density of states into an exponentially soft gap of the form . To analytically explain this behavior, we extend the stability criterion of Efros and Shklovskii to incorporate local charge correlations, in qualitative agreement with our numerical findings. Our work suggests the existence of a new class of self-generated glasses dominated by strong geometric frustration.

Effect of increasing disorder on domains of the 2d Coulomb glass

We have studied a two dimensional lattice model of Coulomb glass for a wide range of disorders at . The system was first annealed using Monte Carlo simulation. Further minimization of the total energy of the system was done using an algorithm developed by Baranovskii et al, followed by cluster flipping to obtain the pseudo-ground states. We have shown that the energy required to create a domain of linear size L in d dimensions is proportional to . Using Imry–Ma arguments given for random field Ising model, one gets critical dimension for Coulomb glass. The investigation of domains in the transition region shows a discontinuity in staggered magnetization which is an indication of a first-order type transition from charge-ordered phase to disordered phase. The structure and nature of random field fluctuations of the second largest domain in Coulomb glass are inconsistent with the assumptions of Imry and Ma, as was also reported for random field Ising model. The study of domains showed that in the transition region there were mostly two large domains, and that as disorder was increased the two large domains remained, but a large number of small domains also opened up. We have also studied the properties of the second largest domain as a function of disorder. We furthermore analysed the effect of disorder on the density of states, and showed a transition from hard gap at low disorders to a soft gap at higher disorders. At , we have analysed the soft gap in detail, and found that the density of states deviates slightly () from the linear behaviour in two dimensions. Analysis of local minima show that the pseudo-ground states have similar structure.

Excitation probability and effective temperature in the stationary regime of conductivity for Coulomb Glasses

AbstractIn this paper, we shall illustrate the numerical calculation of the effective temperature in Coulomb glasses by excitation probability provided that the system has been placed in a stationary state after applying a strong electric field. The excitation probability becomes a better alternative than the occupation probability, which has been classically employed to calculate the effective temperature and characterize the thermodynamics of Coulomb glasses out of equilibrium. This is due to the fact that the excitation probability shows better statistics than the occupation probability. In addition, our simulations show that the excitation probability does not depend on the choice of the chemical potential, which critically affects the occupation probability. Our results allow us to propose the excitation probability as a standard procedure to determine the effective temperature in Coulomb glasses as well as in other complex systems such as spin glasses.