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Register a new userEffects of many-electron jumps in relaxation and conductivity of Coulomb glasses
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A numerical study of the energy relaxation and conductivity of the Coulomb glass is presented. The role of many-electron transitions is studied by two complementary methods: a kinetic Monte Carlo algorithm and a master equation in configuration space method. A calculation of the transition rate for two-electron transitions is presented, and the proper extension of this to multi-electron transitions is discussed. It is shown that two-electron transitions are important in bypassing energy barriers which effectively block sequential one-electron transitions. The effect of two-electron transitions is also discussed.
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A relaxation process, with the associated phenomenology of sound attenuation and sound velocity dispersion, is found in a simulated harmonic Lennard-Jones glass. We propose to identify this process with the so called microscopic (or instantaneous) relaxation process observed in real glasses and supercooled liquids. A model based on the memory function approach accounts for the observation, and allows to relate to each others: 1) the characteristic time and strength of this process, 2) the low frequency limit of the dynamic structure factor of the glass, and 3) the high frequency sound attenuation coefficient, with its observed quadratic dependence on the momentum transfer.
Analytical representations in the time and frequency domains are derived for the most frequently used phenomenological fit functions for non-Debye relaxation processes. In the time domain the relaxation functions corresponding to the complex frequency dependent Cole-Cole, Cole-Davidson and Havriliak-Negami susceptibilities are also represented in terms of $H$-functions. In the frequency domain the complex frequency dependent susceptibility function corresponding to the time dependent stretched exponential relaxation function is given in terms of $H$-functions. The new representations are useful for fitting to experiment.
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, $f(t)=f_0exp[-(t/tau)^beta]$, with the exponent $beta$ increasing with the temperature. The relaxation time follows an Arrhenius behavior divergence when $Tto 0$. A relation between the specific heat and the entropy in the long time regime is found.
We report on the effect of elastic intervalley scattering on the energy transport between electrons and phonons in many-valley semiconductors. We derive a general expression for the electron-phonon energy flow rate at the limit where elastic intervalley scattering dominates over diffusion. Electron heating experiments on heavily doped n-type Si samples with electron concentration in the range $3.5-16.0times 10^{25}$ m$^{-3}$ are performed at sub-1 K temperatures. We find a good agreement between the theory and the experiment.
We have measured the conductivity of high-mobility (001) Si metal-oxide-semiconductor field effect transistors (MOSFETs) over wide ranges of electron densities n=(1.8-15)x10^11cm^2, temperatures T=30mK-4.2K, and in-plane magnetic fields B=0-5T. The experimental data have been analyzed using the theory of interaction effects in the conductivity of disordered 2D systems. The parameters essential for comparison with the theory, such as the intervalley scattering time and valley splitting, have been measured or evaluated in independent experiments. The observed behavior of the conductivity, including its quasi-linear increase with decreasing T down to ~0.4K and its downturn at lower temperatures, is in agreement with the theory. The values of the Fermi- liquid parameter obtained from the comparison agree with the corresponding values extracted from the analysis of Shubnikov-de Haas oscillations based on the theory of magnetooscillations in interacting 2D systems.
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