Ac hopping conduction at extreme disorder takes place on the percolating cluster.pdf

a r X i v : 0 8 0 1 .0 5 3 1 v 4 [ c o n d - m a t .d i s - n n ] 6 J u n 2 0 0 8 Ac hopping conduction at extreme disorder takes place on the percolating cluster Thomas B. Schr?der and Jeppe C. Dyre DNRF Centre “Glass and Time,” IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark (Dated: June 6, 2008) Simulations of the random barrier model show that ac currents at extreme disorder are carried almost entirely by the percolating cluster slightly above threshold; thus contributions from isolated low-activation-energy clusters are negligible. The effective medium approximation in conjunction with the Alexander-Orbach conjecture leads to an excellent analytical fit to the universal ac con- ductivity with no nontrivial fitting parameters. Recent advances relating to ion conduction in glasses and other disordered solids include the application of multidimensional NMR techniques [1], the introduction of ac nonlinear spectroscopy [2], and elucidations of the high-frequency nearly constant loss [3]. Moreover, it was found that the old idea of ions moving by the vacancy mechanism may well be correct [4], and simulations gave new insight into the mixed-alkali effect [5]. Despite these and other significant advances, important questions re- main unanswered. For instance, it is still not understood what role is played by ion interactions for the conductiv- ity [6], or why the random barrier model (RBM) [7, 8] represents ac conductivity data so well. The latter ques- tion is not answered below, but new simulations and ar- guments are presented that we believe lead to a full un- derstanding of the physics of the RBM in the extreme disorder limit (low temperature limit). Ac conductivity is often studied also for amorphous semiconductors, electronically or ionically conducting polymers, defective crystals of various kinds, polaronic conductors, etc [7, 8]. It is a longstanding observation that all disordered solids have remarkably sim