The role of defect-induced phonon localization in quantum diffusion

A defect displacement to a nearest site in the crystal lattice is usually accompanied by breaking and reconstitution of fairly strong chemical bonds, which has a strong effect on quantum diffusion. In the present communication, we present a nonperturbative theory, which enables one to properly account for the effect mentioned. The theory is applied to the description of the diffusion of vacancies in cubic lattices. It is shown that the local softening of the lattice by a vacancy produces a low-frequency pseudolocal mode resulting in a strong enhancement of the contribution of the low-frequency phonons to the diffusion. As a consequence, at low temperatures the diffusion coefficient D of vacancies is strongly reduced and its temperature dependence is essentially weakened: instead of the D ∝ T^-9 temperature dependence one gets D ∝ T_κ dependence with κ ∼ 1. The obtained results are in agreement with the experimental data for the diffusion of vacancies in solid helium at low temperatures. © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.