We investigate the influence of quadratic adatom-phonon couplings on the phonon-assisted adatom tunneling on solids based upon the early work of Tonks and Dick. We find that the incoherent tunneling at high temperatures (TTD/3) is not simply thermally activated but described by a rate ij(Latin small letter h with stroke)2exp[-Ea/kBT+Ea2/(kBT)2] where is the renormalized tunneling matrix element, Ea is the conventional activation energy caused by linear adatom-phonon couplings, and Ea is an effective energy arising from the quadratic couplings. We determine the conditions when the activated tunneling behavior is qualitatively altered by the quadratic couplings. As a result of reduced dimensionality, the latter play much more important roles in the tunneling diffusion of hydrogen on metal surfaces than they do in the interstitial tunneling in solids.
ASJC Scopus subject areas
- Condensed Matter Physics