Alternative mechanism in phonon-assisted tunneling

Abstract

The Hamiltonian of the phonon-assisted tunneling problem in crystals contains three fundamental constituents (lattice and tunneling parts and the coupling between them), for which different hierarchical assumptions are possible. In previous theoretical work (e.g., on paraelectric centers) it has always been assumed that the dominating phonon frequency ${\omega }_d$ is much larger than the bare tunneling parameter $\frac{\Delta }{\hslash }$. Although this seems reasonable, the predicted transition rate is by far too small. In this paper we have discussed the competing influence of low-frequency phonons, for which $\hslash {\omega }_d<\Delta$. Here an alternative mechanism takes over, in which the tunneling is effectively transferred to the phonon system. This is discussed. Moreover, a new optimization procedure is given for the multimode problem, which is not confined to the specific mechanism considered here. In our approach the artifice of a static external field is not required. The calculated temperature behavior of the relaxation time turns out to be qualitatively similar to that of the conventional mechanism, but the relevant physical parameters entering the results are quite different. A future unified treatment of high- and low-frequency phonons proves urgent.