Aging effects in an anderson insulator

Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets

We identify the key features of Kardar-Parisi-Zhang (KPZ) universality class in the fluctuations of the wave density logarithm in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit an algebraic scaling with distance characterized by an exponent of 1/3, and a Tracy-Widom probability distribution of the fluctuations. Additionally, within a directed polymer picture of KPZ physics, we identify the dominant contribution of a directed path to the wave packet density and find that its transverse fluctuations are characterized by a roughness exponent 2/3. Leveraging on this connection with KPZ physics, we verify that an Anderson localized wave packet in 2D exhibits a stretched exponential correction to its well-known exponential localization.

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.

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.

Glassy properties of the Bose-glass phase of a one-dimensional disordered Bose fluid

We study a one-dimensional disordered Bose fluid using bosonization, the replica method, and a nonperturbative functional renormalization-group approach. The Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale, quantum tunneling between these metastable states leads to a rounding of the nonanalyticity in a quantum boundary layer that encodes the existence of rare superfluid regions responsible for the ω^{2} behavior of the (dissipative) conductivity in the low-frequency limit. These results can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.

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}].

Glassy Properties of Anderson Localization: Pinning, Avalanches, and Chaos

I present the results of extensive numerical simulations, which reveal the glassy properties of Anderson localization in dimension two at zero temperature: pinning, avalanches, and chaos. I first show that strong localization confines quantum transport along paths that are pinned by disorder but can change abruptly and suddenly (avalanches) when the energy is varied. I determine the roughness exponent ζ characterizing the transverse fluctuations of these paths and find that its value ζ=2/3 is the same as for the directed polymer problem. Finally, I characterize the chaos property, namely, the fragility of the conductance with respect to small perturbations in the disorder configuration. It is linked to interference effects and universal conductance fluctuations at weak disorder and more spin-glass-like behavior at strong disorder.

Evidence for thermal activation in the glassy dynamics of insulating granular aluminum conductance

Insulating granular aluminum is one of the proto-typical disordered insulators whose low temperature electrical conductance exhibits ubiquitous non-equilibrium phenomena. These include slow responses to temperature or gate voltage changes, characteristic field effect anomalies and ageing phenomena typical of a glass. In this system the influence of temperature on the glassy dynamics has remained elusive. A similar situation was met in insulating indium oxide and it was concluded that in high carrier density Anderson insulators, electronic slow relaxations essentially proceed via activationless processes. In this work we experimentally demonstrate that thermal effects do play a role and that the slow dynamics in granular aluminum is subject to thermal activation. We show how its signatures can be revealed and activation energy distributions can be extracted, providing a promising grasp on the nature of the microscopic mechanism at work in glassy Anderson insulators. We explain why some of the experimental protocols previously used in the literature fail to reveal thermal activation in these systems. Our results and analyses call for a reassessment of the emblematic case of indium oxide, and question the existence of purely activationless dynamics in any of the systems studied so far.

Electronic crystal growth

Interacting atoms or molecules condense into liquid, and, when cooled further, they form a crystal. The time evolution of the atomic or molecular ordering has been widely studied as a nonequilibrium emergence of order from a supercooled liquid or a glass. Interacting electrons in a variety of correlated electron systems also form crystals, but observing the time evolution of electronic crystallization has been experimentally challenging. Here, working with an organic conductor exhibiting a supercooled charge liquid or charge glass as a metastable state, we observed electronic crystal growth through resistivity and nuclear magnetic resonance measurements. The temperature profile of the crystal growth is similar to those observed in classical systems and reveals two distinct regimes for the mechanism of electronic crystallization.

Nonmonotonic Aging and Memory Retention in Disordered Mechanical Systems

We observe nonmonotonic aging and memory effects, two hallmarks of glassy dynamics, in two disordered mechanical systems: crumpled thin sheets and elastic foams. Under fixed compression, both systems exhibit monotonic nonexponential relaxation. However, when after a certain waiting time the compression is partially reduced, both systems exhibit a nonmonotonic response: the normal force first increases over many minutes or even hours until reaching a peak value, and only then is relaxation resumed. The peak time scales linearly with the waiting time, indicating that these systems retain long-lasting memory of previous conditions. Our results and the measured scaling relations are in good agreement with a theoretical model recently used to describe observations of monotonic aging in several glassy systems, suggesting that the nonmonotonic behavior may be generic and that athermal systems can show genuine glassy behavior.

Glassy Dynamics in Disordered Electronic Systems Reveal Striking Thermal Memory Effects

Memory is one of the unique qualities of a glassy system. The relaxation of a glass to equilibrium contains information on the sample's excitation history, an effect often refer to as "aging." We demonstrate that under the right conditions a glass can also possess a different type of memory. We study the conductance relaxation of electron glasses that are fabricated at low temperatures. Remarkably, the dynamics are found to depend not only on the ambient measurement temperature but also on the maximum temperature to which the system was exposed. Hence the system "remembers" its highest temperature. This effect may be qualitatively understood in terms of energy barriers and local minima in configuration space and therefore may be a general property of the glass state.

Percolation, sliding, localization and relaxation in topologically closed circuits

Considering a random walk in a random environment in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the "delocalization" of eigenstates of non-hermitian Hamiltonians has been addressed by Hatano, Nelson, and followers. But we show that for a conservative stochastic process the implied spectral properties are dramatically different. In particular we determine the threshold for under-damped relaxation, and observe "complexity saturation" as the bias is increased.

On relaxations and aging of various glasses

Slow relaxation occurs in many physical and biological systems. "Creep" is an example from everyday life. When stretching a rubber band, for example, the recovery to its equilibrium length is not, as one might think, exponential: The relaxation is slow, in many cases logarithmic, and can still be observed after many hours. The form of the relaxation also depends on the duration of the stretching, the "waiting time." This ubiquitous phenomenon is called aging, and is abundant both in natural and technological applications. Here, we suggest a general mechanism for slow relaxations and aging, which predicts logarithmic relaxations, and a particular aging dependence on the waiting time. We demonstrate the generality of the approach by comparing our predictions to experimental data on a diverse range of physical phenomena, from conductance in granular metals to disordered insulators and dirty semiconductors, to the low temperature dielectric properties of glasses.

Huge (but finite) time scales in slow relaxations: beyond simple aging

Experiments performed in the last years demonstrated slow relaxations and aging in the conductance of a large variety of materials. Here, we present experimental and theoretical results for conductance relaxation and aging for the case-study example of porous silicon. The relaxations are experimentally observed even at room temperature over time scales of hours, and when a strong electric field is applied for a time tw, the ensuing relaxation depends on tw. We derive a theoretical curve and show that all experimental data collapse onto it with a single time scale as a fitting parameter. This time scale is found to be of the order of thousands of seconds at room temperature. The generic theory suggested is not fine-tuned to porous silicon, and thus we believe the results should be universal, and the presented method should be applicable for many other systems manifesting memory and other glassy effects.

Localization, anomalous diffusion, and slow relaxations: a random distance matrix approach

We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such as the diffusion of particles, slow relaxations in glasses, and scalar phonon localization. Using a combination of a renormalization group procedure and a direct moment calculation, we find the eigenvalue distribution density (i.e., the spectrum), for low densities, and the localization properties of the eigenmodes, for arbitrary dimension. Finally, we discuss the physical implications of the results.

Slow relaxations and aging in the electron glass

Glassy systems are ubiquitous in nature. They are characterized by slow relaxations to equilibrium without a typical time scale, aging, and memory effects. Understanding this has been a long-standing problem in physics. We study the aging of the electron glass, a system showing remarkable slow relaxations of the conductance. We find that the appropriate broad distribution of relaxation rates leads to a universal relaxation of the form log(1 + t_{w}/t) for the common aging protocol, where t_{w} is the length of time the perturbation driving the system out of equilibrium was on, and t the time of measurement. These results agree well with several experiments performed on different glassy systems, and examining different physical observables, for times ranging from seconds to several hours. The suggested theoretical framework appears to offer a paradigm for aging in a broad class of glassy materials.

Density of states and critical behavior of the Coulomb glass

We present zero-temperature simulations for the single-particle density of states of the Coulomb glass. Our results in three dimensions are consistent with the Efros and Shklovskii prediction for the density of states. Finite-temperature Monte Carlo simulations show no sign of a thermodynamic glass transition down to low temperatures, in disagreement with mean-field theory. Furthermore, the random-displacement formulation of the model undergoes a transition into a distorted Wigner crystal for a surprisingly broad range of the disorder strength.

Aging effects across the metal-insulator transition in two dimensions

Aging effects in the relaxations of conductivity of a two-dimensional electron system in Si have been studied as a function of carrier density. They reveal an abrupt change in the nature of the glassy phase at the metal-insulator transition (MIT): (a) while full aging is observed in the insulating regime, there are significant departures from full aging on the metallic side of the MIT, before the glassy phase disappears completely at a higher density n(g): (b) the amplitude of the relaxations peaks just below the MIT, and it is strongly suppressed in the insulating phase. Other aspects of aging, including large non-Gaussian noise and similarities to spin glasses, also have been discussed.

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.

Nonexponential relaxations in a two-dimensional electron system in silicon

The relaxations of conductivity have been studied in a strongly disordered two-dimensional (2D) electron system in Si after excitation far from equilibrium by a rapid change of carrier density ns at low temperatures T. The dramatic and precise dependence of the relaxations on ns and T strongly suggests (a) the transition to a glassy phase as T-->0, and (b) the Coulomb interactions between 2D electrons play a dominant role in the observed out-of-equilibrium dynamics.

QUANTUM MODE-COUPLING THEORY: Formulation and Applications to Normal and Supercooled Quantum Liquids

▪ Abstract  We review our recent efforts to formulate and study a mode-coupling approach to real-time dynamic fluctuations in quantum liquids. Comparison is made between the theory and recent neutron scattering experiments performed on liquid ortho-deuterium and para-hydrogen. We discuss extensions of the theory to supercooled and glassy states where quantum fluctuations compete with thermal fluctuations. Experimental scenarios for quantum glassy liquids are briefly discussed.

Nonlinear screening theory of the Coulomb glass

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 pseudogap ("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 pseudogap, which in our model emerges only within the glassy phase.

Quantum mode-coupling theory for binary mixtures

We extend the quantum mode-coupling theory of neat liquids to the case of binary mixtures, in order to study supercooled liquids where quantum fluctuations may compete with thermal fluctuations. We apply the theory to a generic model of a binary mixture of Lennard-Jones particles. Our treatment may be used to study quantum aging and exotic glass melting scenarios in structural supercooled quantum liquids.

Glass transition and the Coulomb gap in electron glasses

We establish the connection between the presence of a glass phase and the appearance of a Coulomb gap in disordered materials with strongly interacting electrons. Treating multiparticle correlations in a systematic way, we show that in the case of strong disorder a continuous glass transition takes place whose Landau expansion is identical to that of the Sherrington-Kirkpatrick spin glass. We show that the marginal stability of the glass phase controls the physics of these systems: it results in slow dynamics and leads to the formation of a Coulomb gap.

Stress aging in the electron glass

A new protocol for an aging experiment is studied in the electron-glass phase of indium-oxide films. In this protocol, the sample is exposed to a non-Ohmic electric field F for a waiting time t(w) during which the system attempts to reach a steady state (rather than relax towards equilibrium). The relaxation of the excess conductance Delta G after Ohmic conditions are restored exhibits simple aging as long as F is not too large.

Electrical transport of spin-polarized carriers in disordered ultrathin films

Slow, nonexponential relaxation of electrical transport accompanied by memory effects has been induced in quench-condensed ultrathin amorphous Bi films by the application of a parallel magnetic field. This behavior, which is very similar to space-charge limited current flow, is found in extremely thin films well on the insulating side of the thickness-tuned superconductor-insulator transition. It may be the signature of a collective state that forms when the carriers are spin polarized at low temperatures and in high magnetic fields.

Onset of glassy dynamics in a two-dimensional electron system in silicon

The fluctuations of conductivity sigma with time have been studied in a two-dimensional electron system in low-mobility Si inversion layers. The noise power spectrum is approximately 1/f(alpha) with alpha exhibiting a sharp jump at an electron density n(s) = n(g). A huge increase in the relative variance of sigma is observed as n(s) is reduced below n(g), reflecting a dramatic slowing down of the electron dynamics. This is attributed to the freezing of the electron glass. The data strongly suggest that glassy dynamics persists in the metallic phase.