History-dependent relaxation and the energy scale of correlation in the Electron-Glass

We present an experimental study of the energy-relaxation in Anderson-insulating indium-oxide films excited far from equilibrium. In particular, we focus on the effects of history on the relaxation of the excess conductance dG. The natural relaxation law of dG is logarithmic, namely dG=-log(t). This may be observed over more than five decades following, for example, cool-quenching the sample from high temperatures. On the other hand, when the system is excited from a state S_{o} in which it has not fully reached equilibrium to a state S_{n}, the ensuing relaxation law is logarithmic only over time t shorter than the time t_{w} it spent in S_{o}. For times t>t_{w} dG(t) show systematic deviation from the logarithmic dependence. It was previously shown that when the energy imparted to the system in the excitation process is small, this leads to dG=P(t/t_{w}) (simple-aging). Here we test the conjecture that `simple-aging' is related to a symmetry in the relaxation dynamics in S_{o} and S_{n}. This is done by using a new experimental procedure that is more sensitive to deviations in the relaxation dynamics. It is shown that simple-aging may still be obeyed (albeit with a modified P(t/t_{w})) even when the symmetry of relaxation in S_{o} and S_{n} is perturbed by a certain degree. The implications of these findings to the question of aging, and the energy scale associated with correlations are discussed

Electric Field Effect in Ultrathin Films near the Superconductor-Insulator Transition

The effect of an electric field on the conductance of ultrathin films of metals deposited on substrates coated with a thin layer of amorphous Ge was investigated. A contribution to the conductance modulation symmetric with respect to the polarity of the applied electric field was found in regimes in which there was no sign of glassy behavior. For films with thicknesses that put them on the insulating side of the superconductor-insulator transition, the conductance increased with electric field, whereas for films that were becoming superconducting it decreased. Application of magnetic fields to the latter, which reduce the transition temperature and ultimately quench superconductivity, changed the sign of the reponse of the conductance to electric field back to that found for insulators. We propose that this symmetric response to capacitive charging is a consequence of changes in the conductance of the a-Ge layer, and is not a fundamental property of the physics of the superconductor-insulator transition as previously suggested.Comment: 4 pages text, 4 figure

Anomalous Hopping Exponents of Ultrathin Films of Metals

The temperature dependence of the resistance R(T) of ultrathin quench-condensed films of Ag, Bi, Pb and Pd has been investigated. In the most resistive films, R(T)=Roexp(To/T)^x, where x=0.75. Surprisingly, the exponent x was found to be constant for a wide range of Ro and To in all four materials, possibly implying a consistent underlying conduction mechanism. The results are discussed in terms of several different models of hopping conduction.Comment: 6 pages, 5 figure

Time Dependent Development of the Coulomb Gap

We show that the time development of the Coulomb gap in a Coulomb glass can involve very long relaxation times due to electron rearrangement and hopping. We find that an applied magnetic field reduces the rate of electron hopping and, hence, Coulomb gap formation. These results are consistent with recent conductance experiments on thin semiconducting and metallic films.Comment: 4 pages, Latex, 3 encapsulated postscript figure

Electrical transport studies of quench condensed Bi films at the initial stage of film growth: Structural transition and the possible formation of electron droplets

The electrical transport properties of amorphous Bi films prepared by sequential quench deposition have been studied in situ. A superconductor-insulator (S-I) transition was observed as the film was made increasingly thicker, consistent with previous studies. Unexpected behavior was found at the initial stage of film growth, a regime not explored in detail prior to the present work. As the temperature was lowered, a positive temperature coefficient of resistance (dR/dT > 0) emerged, with the resistance reaching a minimum before the dR/dT became negative again. This behavior was accompanied by a non-linear and asymmetric I-V characteristic. As the film became thicker, conventional variable-range hopping (VRH) was recovered. We attribute the observed crossover in the electrical transport properties to an amorphous to granular structural transition. The positive dR/dT found in the amorphous phase of Bi formed at the initial stage of film growth was qualitatively explained by the formation of metallic droplets within the electron glass.Comment: 7 pages, 6 figure

Manifestation of ageing in the low temperature conductance of disordered insulators

We are interested in the out of equilibrium phenomena observed in the electrical conductance of disordered insulators at low temperature, which may be signatures of the electron coulomb glass state. The present work is devoted to the occurrence of ageing, a benchmark phenomenon for the glassy state. It is the fact that the dynamical properties of a glass depend on its age, i.e. on the time elapsed since it was quench-cooled. We first critically analyse previous studies on disordered insulators and question their interpretation in terms of ageing. We then present new measurements on insulating granular aluminium thin films which demonstrate that the dynamics is indeed age dependent. We also show that the results of different relaxation protocols are related by a superposition principle. The implications of our findings for the mechanism of the conductance slow relaxations are then discussed

Evidence of Vortices on the Insulating Side of the Superconductor-Insulator Transition

The magnetoresistance of ultrathin insulating films of Bi has been studied with magnetic fields applied parallel and perpendicular to the plane of the sample. Deep in the strongly localized regime, the magnetoresistance is negative and independent of field orientation. As film thicknesses increase, the magnetoresistance becomes positive, and a difference between values measured in perpendicular and parallel fields appears, which is a linear function of the magnetic field and is positive. This is not consistent with the quantum interference picture. We suggest that it is due to vortices present on the insulating side of the superconductor-insulator transition.Comment: 4 pages, 3 figure

Electron Glass in Ultrathin Granular Al Films at Low Temperatures

Quench-condensed granular Al films, with normal-state sheet resistance close to 10 k$\Omega/\Box$, display strong hysteresis and ultraslow, non-exponential relaxation in the resistance when temperature is varied below 300 mK. The hysteresis is nonlinear and can be suppressed by a dc bias voltage. The relaxation time does not obey the Arrhenius form, indicating the existence of a broad distribution of low energy barriers. Furthermore, large resistance fluctuations, having a 1/f-type power spectrum with a low-frequency cut-off, are observed at low temperatures. With decreasing temperature, the amplitude of the fluctuation increases and the cut-off frequency decreases. These observations combine to provide a coherent picture that there exists a new glassy electron state in ultrathin granular Al films, with a growing correlation length at low temperatures.Comment: RevTeX 3.1, 4 pages, 4 figures (EPS files) (Minor Additions

Electron-Assisted Hopping in Two Dimensions

We have studied the non-ohmic effects in the conductivity of a two-dimensional system which undergoes the crossover from weak to strong localization with decreasing electron concentration. When the electrons are removed from equilibrium with phonons, the hopping conductivity depends only on the electron temperature. This indicates that the hopping transport in a system with a large localization length is assisted by electron-electron interactions rather than by the phonons.Comment: 5 pages, 4 figure