Conductivity Relaxations in the Electron Glass

Abstract

There is increased recognition 1,2 of the importance in studying the insulator phase on the insulating side of the transition. For example, the donor susceptibility is found to diverge as the transition is approached from the insulator side and can be related to a diverging localization length. Coulomb interactions are expected to play a significant role in the insulator phase. Efros3 have pointed out a Coulomb gap at T=0. The ground state is complicated and it is recognized to resemble 4,5 that of a glass or spin glass. The analogy with the glassy state arises from competition between the 1/r long-range Coulomb interactions and the randomness of site energies. For these reasons, the system on the localized side is called an electron glass. 4,5 Experimentally the slow relaxation behavior in the ac conductivity5 bears a strong resemblance to magnetization relaxation in spin glasses and dielectric or mechanical relaxations in glasses.6,7 In the critical region and at low temperatures, a conductance dependence σ(ω)=Kωs) with s=0.9 has been found5 from 105 to 102 Hz. The measured donor capacitance C has the frequency dependence ωs−1. Hence the dielectric relaxation function e* ≡e′−ie″ exhibit the dependence ωs−1 (a negative small-power law) in both its real and imaginary parts as ω→0. This “infrared divergence” behavior5,6 of e’ and e” is commonly observed in glasses. In spin-glasses, the spin susceptibility behaves in a similar way. 7 This study of low frequency relaxation in the electron glass ruled out the noninteracting Fermi glass model, and confirmed the importance of Coulomb interactions.5 Calculation of the ac conductivity of the electron glass at zero on finite temperature are restricted to the two-site or pair approximation.3 In our view if ħω≪kT, as is the case in all2,5 low-frequency measurements, a relaxation description of the entire assembly is more appropriate. This is particularly relevant in the critical region.