Zvi Ovadyahu reported on the absorption rate in strongly localized Anderson insulators.
The bottom line message of the talk was to provide evidence that the electron-electron inelastic scattering rate in Anderson insulators is strongly suppressed from its value in the less disordered, diffusive regime. This may be an indication of the physics of many-particle localization in strongly disordered systems.
The material under investigation was InOx, one of the standard materials in which electron glassiness is studied. An electron glass is an Anderson insulator where all relevant single particle states are localized. Coulomb interactions are very important due to the absence of standard screening. Thus there are strong and long ranged interactions, as far as screening due to gates or thermal excitations can be neglected. The frustration between disorder and Coulomb interactions produces a glassy state.
All samples studied for the present purpose were 2d, crystalline In2O{3-x} films, measured at 4K where they are in the hopping regime (resistances ~10 MOhm). This specific variety of InOx was chosen because all its parameters are known, being close to a free electron system (unlike the amorphous systems).
The basic glassy or out-of-equilibrium phenomenon in InOx is the slow logarithmic relaxation of conductance with time after a quench from high T. Other ways to excite the system include non-Ohmic fields, or raising the bath temperature, both of which make the conductance quickly jump upwards, and then slowly increase further. Upon undoing the perturbation the conductance jumps down and relaxes back logarithmically towards the previous state. Both excitations have qualitatively similar effects.
The system was excited with non-Ohmic fields of various frequencies, to pump energy into the system. Thereby the power was adjusted in such a way as to keep the initial jump of conductance constant. The frequency range covered 23 Hz up to15.5 MHz.
A first interesting result concerns the apparent energy, as a proxy for which the initial conductance after the downjump is taken. Apparently, the absorbed energy depends on the frequency: it starts decreasing for frequencies of order 10^5 Hz and higher. The meaning of this characteristic scale frequency was not explored further here.
The focus of the talk was rather on the rate of e-e inelastic processes. An upper bound for the latter was obtained by considering the heat balance in the steady state under non-Ohmic excitation. This allows to obtain a good estimate of the heat removal rate from the electrons. Ovadyahu argues that in the steady state, it must be an upper bound on the inelastic collision rate, which controls absorption (otherwise the system would absorb more energy and come to a steady state with higher heat removal rate). His finding is that the inelastic rate in the insulator is as small as gamma= 3.5*10^5 Hz, as compared to measured rates of the order of 10^11/s in the diffusive regime.
The large difference must almost inevitably be blamed on localization and the associated discreteness in the insulator (the single particle level spacing is 100-10^4 K!). From this point of view the experiments seem to be consistent with tendencies expected in systems featuring manybody localization, as proposed by Basko et al.. Remarkably, the (near) discreteness seems to hold despite the presence of strong, long range interactions, which are in principle expected to destroy the discreteness of the spectrum and delocalize the many body excitations (see, Fleishman and Anderson).
A possible element of an explanation may be that these excitations are indeed delocalized, but have a very low diffusivity because dipolar interactions in 3d are only marginally long range which is the case of critical hopping, discussed in Anderson '58.
Blogged by Markus Mueller
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