Frequency dependent conductivity of the interrupted strand model

Abstract

We present rigorous results on the frequency dependence of the Kubo-Greenwood conductivity of the interrupted-strand — or bond-percolation model, for which exists strong evidence to be relevant for a class of quasi one-dimensional organic conductors and for some mixed valent complex compounds like K₂Pt(CN)₄ Br_0.30 3H₂O. The model describes a linear sequence of one-dimensional metallic boxes or segments separated from each other by perfectly insulating lattice defects. We used both Lotentzian and “rectangular” averages to obtain the frequency-averaged conductivity as a well-defined physical quantity and found a sharply peaked structure of the conductivity spectrum resulting from the non-zero energy level spacing of one metallic box. Since one has to look very carefully on different frequency average procedures and on the consequences of the energy spectrum of an entire strand one has to precise arguments and results on the low frequency behaviour of the conductivity obtained from numerical considerations recently proposed by P.S. Riseborough.