Avalanches in the Relaxation Dynamics of Electron Glasses

Abstract

We study the zero-temperature relaxation dynamics of an electron glass model with single-electron hops. We find numerically that in the charge rearrangements (avalanches) triggered by displacing an electron, the number of electron hops has a scale-free, power-law distribution up to a cutoff diverging with the system size N , independently of the disorder strength and provided hops of arbitrary length are allowed. In avalanches triggered by the injection of an extra electron, the distribution does not have a power-law limit, but its mean diverges non-trivially with N . In both cases, the avalanche statistics is well reproduced by a branching process model, that assumes independent hops. Qualitative differences with avalanches in infinite-range spin glasses and related systems are discussed.

Numerical observation of a glassy phase in the three-dimensional Coulomb glass

“…Numerically, a Coulomb gap in agreement with the ES theory has been observed in multiple studies. However, there is no consensus in the vast numerical work [31,[33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] on the existence of a thermodynamic transition into a glassy phase. Nonequilibrium approaches suggest the existence of glassy behavior; however, thermodynamic simulations have failed to detect a clear transition.…”

Electron glass effects in amorphous NbSi films

“…When thermal effect and Coulomb interactions compete, the density-of-states at the Fermi level remains finite and the naive application of Thomas-Fermi theory gives a screening length that goes like 1/T [43]. Numerical simulations at T = 0 found that a charge injection in an electron glass triggers an electronic avalanche which size scales with the size of the system [30,31]. This divergence of the screening length at low T was actually experimentally inferred from the T study of the background relaxation in granular Al films [38].…”

“…In granular Al films, only the 10 nm-thick layer of the film closest to the gate insulator is electrically disturbed by a V g change [28], while the disturbance extends to more than 70 nm in a-InOx films [29], indicating markedly different length scales in the two systems. The large penetration length observed in InOx films was taken as an experimental evidence for electronic avalanches found after a charge injection in numerical simulations of Coulomb glass models [30,31]. However, they seem to contradict the very short screening lengths sometimes invoked in this system [13,29].…”