Abstract:

A broad range of disordered materials contain electronic states that are spatially well localized. Usual approaches to simulation of ac conductivity of these materials rely on Kubo's formula which expresses the ac conductivity in terms of the mean square displacement of a diffusing carrier. Such approaches therefore assume that carriers are in equilibrium and that they are only slightly perturbed by external alternating electric field. In [1] we obtain the expression for the optical conductivity in a material with localized electronic states and weak electron-phonon or electron-impurity interaction which is valid for any nonequilibirum state of the electronic subsystem prior to the action of electric field. Particularly, in the case of incoherent nonequilibrium state of the electronic subsystem, the optical conductivity is entirely expressed in terms of the positions of electronic states, their nonequilibrium populations, and Fermi's golden rule transition probabilities between the states. The same mathematical form of the expression is valid both in the case of electron-phonon and electron-impurity interaction. Moreover, our result for the nonequilibrium optical conductivity has the same form as the expressions previously obtained for the case of equilibrium. Our results are expected to be valid at sufficiently high frequencies, such that the period of the electric field is much smaller than the carrier relaxation time. We apply the derived expressions to two model systems, a simple one-dimensional Gaussian disorder model and the model of a realistic three-dimensional organic polymer material obtained using previously developed multiscale methodology. We note that the simple one-dimensional model captures the essential features of the mobility spectrum of a more realistic system.

[1] V. Janković and N. Vukmirović, Phys. Rev. B 90, 224201 (2014).