Two-dimensional Coulomb Glass Research Articles

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.

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.

Critical behavior of the two-dimensional Coulomb glass at zero temperature

The lattice model of Coulomb Glass in two dimensions with box-type random field distribution is studied at zero temperature for system size upto $96^{2}$. To obtain the minimum energy state we annealed the system using Monte Carlo simulation followed by further minimization using cluster-flipping. The values of the critical exponents are determined using the standard finite size scaling. We found that the correlation length $\xi$ diverges with an exponent $\nu=1.0$ at the critical disorder $W_{c} = 0.2253$ and that $\chi_{dis} \approx \xi^{4-\bar{\eta}}$ with $\bar{\eta}=2$ for the disconnected susceptibility. The staggered magnetization behaves discontinuously around the transition and the critical exponent of magnetization $\beta=0$. The probability distribution of the staggered magnetization shows a three peak structure which is a characteristic feature for the phase coexistence at first-order phase transition. In addition to this, at the critical disorder we have also studied the properties of the domain for different system sizes. In contradiction with the Imry-Ma arguments, we found pinned and non-compact domains where most of the random field energy was contained in the domain wall. Our results are also inconsistent with Binder's roughening picture.

Structural relaxation and aging scaling in the Coulomb and Bose glass models

We employ Monte Carlo simulations to study the relaxation properties of the two-dimensional Coulomb glass in disordered semiconductors and the three-dimensional Bose glass in type-II superconductors in the presence of extended linear defects. We investigate the effects of adding non-zero random on-site energies from different distributions on the properties of the correlation-induced Coulomb gap in the density of states (DOS) and on the non-equilibrium aging kinetics highlighted by the density autocorrelation functions. We also probe the sensitivity of the system's equilibrium and non-equilibrium relaxation properties to instantaneous changes in the density of charge carriers in the Coulomb glass or flux lines in the Bose glass.

Nonlinear conductivity of two-dimensional Coulomb glasses

We have studied the nonlinear conductivity of two-dimensional Coulomb glasses. We have used a Monte Carlo algorithm to simulate the dynamic of the system under an applied electric field $E$. We found that in the nonlinear regime the site occupancy in the Coulomb gap follows a Fermi-Dirac distribution with an effective temperature $T_{\rm eff}$, higher than the phonon bath temperature $T$. The value of the effective temperature is compatible with that obtained for slow modes from the generalized fluctuation-dissipation theorem. The nonlinear conductivity for a given electric field and $T$ is fairly similar to the linear conductivity at the corresponding $T_{\rm eff}$. We found that the dissipated power and the effective temperature are related by an expression of the form $(T_{\rm eff}^\alpha-T^\alpha)T_{\rm eff}^{\beta-\alpha}$.

Optically driven Mott-Hubbard systems out of thermodynamic equilibrium

We have studied the nonlinear conductivity of two-dimensional Coulomb glasses. We have used a Monte Carlo algorithm to simulate the dynamic of the system under an applied electric field E. We have compared results for two different models: a regular square lattice with only diagonal disorder and a random array of sites with diagonal and off-diagonal disorder. We have found that for moderate fields the logarithm of the conductivity is proportional to reproducing experimental results. We have also found that in the nonlinear regime the site occupancy in the Coulomb gap follows a Fermi-Dirac distribution with an effective temperature Teff higher than the phonon bath temperature T.

Non-linear conductivity in Coulomb glasses

We have studied the nonlinear conductivity of two-dimensional Coulomb glasses. We have used a Monte Carlo algorithm to simulate the dynamic of the system under an applied electric field E. We have compared results for two different models: a regular square lattice with only diagonal disorder and a random array of sites with diagonal and off-diagonal disorder. We have found that for moderate fields the logarithm of the conductivity is proportional to √ E/T 2 , reproducing experimental results. We have also found that in the nonlinear regime the site occupancy in the Coulomb gap follows a Fermi-Dirac distribution with an effective temperature Teff higher than the phonon bath temperature T . c

Slow relaxation and equilibrium dynamics in a two-dimensional Coulomb glass: Demonstration of stretched exponential energy correlations

We have simulated energy relaxation and equilibrium dynamics in Coulomb glasses using the random energy lattice model. We show that in a temperature range where the Coulomb gap is already well developed $(T=0.03--0.1)$, the system still relaxes to an equilibrium behavior within the simulation time scale. For all temperatures $T$, the relaxation is slower than exponential. Analyzing the energy correlations of the system at equilibrium $C(\ensuremath{\tau})$, we find a stretched exponential behavior, $C(\ensuremath{\tau})={e}^{\ensuremath{-}{(\ensuremath{\tau}/{\ensuremath{\tau}}_{0})}^{\ensuremath{\gamma}}}$. We study the temperature dependence of ${\ensuremath{\tau}}_{0}$ and $\ensuremath{\gamma}$. ${\ensuremath{\tau}}_{0}$ is shown to increase faster than exponentially with decreasing $T$. $\ensuremath{\gamma}$ is proportional to $T$ at low temperature and approaches unity for high temperature. We define a time ${\ensuremath{\tau}}_{\ensuremath{\gamma}}$ from these stretched exponential correlations and show that this time corresponds well with the time required to reach equilibrium. From our data it is not possible to determine whether ${\ensuremath{\tau}}_{\ensuremath{\gamma}}$ diverges at any finite temperature, indicating a glass transition, or whether this divergence happens at zero temperature. While the time dependence of the system energy can be well fitted by a random walker in a harmonic potential for high temperatures $(T=10)$, this simple model fails to describe the long time scales observed at lower temperatures. Instead we present an interpretation of the configuration space as a structure with fractal properties and the time evolution as a random walk on this fractal-like structure.

Effective Temperature in Relaxation of Coulomb Glasses

We study relaxation in two-dimensional Coulomb glasses up to macroscopic times. We use a kinetic Monte Carlo algorithm especially designed to escape efficiently from deep valleys around metastable states. We find that, during the relaxation process, the site occupancy follows a Fermi-Dirac distribution with an effective temperature much higher than the real temperature T. Long electron-hole excitations are characterized by T(eff), while short ones are thermalized at T. We argue that the density of states at the Fermi level is proportional to T(eff) and is a good thermometer to measure it. T(eff) decreases extremely slowly, roughly as the inverse of the logarithm of time, and it should affect hopping conductance in many experimental circumstances.

Nonequilibrium Relaxations and Aging Effects in a Two-Dimensional Coulomb Glass

The relaxations of conductivity have been studied in the glassy regime of a strongly disordered two-dimensional electron system in Si after a temporary change of carrier density during the waiting time tw. Two types of response have been observed: (a) monotonic, where relaxations exhibit aging, i.e., dependence on history, determined by tw and temperature; (b) nonmonotonic, where a memory of the sample history is lost. The conditions that separate the two regimes also have been determined.

Quantum and frustration effects on fluctuations of the inverse compressibility in two-dimensional Coulomb glasses

We consider interacting electrons in a two-dimensional quantum Coulomb glass, and investigate by means of the Hartree-Fock approximation the combined effects of the electron-electron interaction and the transverse magnetic field on fluctuations of the inverse compressibility. Preceding systematic study of the system in the absence of a magnetic field identified the source of the fluctuations, interplay of disorder and interaction, and effects of hopping. Revealed in sufficiently clean samples with strong interactions is an unusual right-biased distribution of the inverse compressibility, which is neither of Gaussian nor Wigner-Dyson type. While in most cases weak magnetic fields tend to suppress fluctuations, in relatively clean samples with weak interactions fluctuations are found to grow with the magnetic field. This is attributed to the localization properties of the electron states, which may be measured by the participation ratio and the inverse participation number. It is also observed that at the frustration where the Fermi level is degenerate, localization or modulation of electrons is enhanced, raising fluctuations. Strong frustration in general suppresses effects of the interaction on the inverse compressibility and on the configuration of electrons.

Thermodynamic fluctuations of site energies and occupation numbers in the two-dimensional Coulomb glass

Thermodynamic fluctuations of site energies and occupation numbers in the two-dimensional Coulomb glass

Localization in one- and two-dimensional quantum Coulomb glasses

Localization in one- and two-dimensional quantum Coulomb glasses

Conductivity of the two-dimensional Coulomb glass

We studied by computer simulation the effects of Coulomb interactions on the properties of strongly localized Anderson insulators. We took full account of many-body effects by considering the many-electron configurations of the system rather than single-particle states. We developed an algorithm to obtain the configurations and energies of the low-lying system states, and from there the conductivity. At low-temperatures T, we found that the conductivity was proportional to exp(-${\mathrm{T}}_{0}$/T${)}^{1\mathrm{/}2}$. Many-electron transitions were seen to be important at very low temperatures. In this regime, ${\mathrm{T}}_{0}$\ensuremath{\approx}0.61, which is much smaller than predicted by one-electron theory. Experimental results which use the predicted ${\mathrm{T}}_{0}$ to obtain localization radii must therefore be reinterpreted.

Monte Carlo simulation of hopping conduction in two-dimensional Coulomb glasses

We have carried out a Monte Carlo simulation of the conductivity of a two-dimensional strongly localized interacting system. A plot of dlog sigma /dlogT versus T, on a double logarithmic scale, clearly shows two distinct regimes, one activated at high T and a non-activated one at low T. The conductivity exponent in this later regime is close to 1/2 , in agreement with Efros and Shklovskii's predictions (1984), although the characteristic temperature T0'; is about a factor of two smaller than predicted.