Excitron Transport in Mixed Crystals: Quantum Percolation

Abstract

Two-component mixed crystals are interesting and important systems for studying exciton transport. At high temperatures, a hopping description of exciton dynamics is thought to be adequate.¹ Considering excitations on only one species of molecule, and assuming that the hopping rates for these active sites are nonzero only for nearest neighbor pairs, this then defines a classical percolation problem.² That is, if the fraction of active sites is p, then for p less than a critical value p_c, only finite clusters of active molecules exist and no long-range transport is possible. However, if p > p_c, an infinite cluster exists, and long-range transport occurs. It is known that for a 2-d square lattice p_c ≅ 0.59, while for a 3-d simple cubic lattice p_c ≅ 0.31.