Low-temperature quantum diffusion of light particles in solids

Abstract

A general survey of the theoretical description of low-temperature tunnelling diffusion of light interstitial particles in normal-conducting metals, superconducting metals, and in insulators is given. Both the regimes of incoherent (mean free path of diffusion smaller than the distance between interstitial sites) and coherent diffusion (mean free path larger than the distance of interstitial sites) are discussed. For the regime of incoherent diffusion it is shown that the behaviour of the low-temperature tunnelling rates of the light particles is to a great extent determined by so-called energy asymmetry parameters which describe the static energy shifts between the ground states of adjacent interstitial sites. These static energy shifts are caused by lattice inhomogenities. Depending on the strength of the coupling of the light particles to the electron and phonon system of the crystal different regions of behaviour are found. This is demonstrated with the help of temperature-energy asymmetry ‘phase’ diagrams of low-temperature quantum diffusion. It is argued that the regime of coherent tunnelling diffusion has to be further divided into a regime of band diffusion of a localized particle (small polaron) and a regime of Bloch propagation. In the first case the thermal de Broglie wavelength of the light particles is smaller than the distance between the interstitial sites and in the latter case it is larger. The transition from the regime of incoherent diffusion to the regime of coherent diffusion is discussed. Some remarks concerning the differences between positron diffusion and diffusion of the heavier light particles are made.