Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2007-10-03
Physics
Condensed Matter
Disordered Systems and Neural Networks
4 pages Conference Proceedings, Phonons 2007, Paris
Scientific paper
10.1088/1742-6596/92/1/012133
The interaction between two-level systems (TLS) and strain fields in a solid is contained in the diagonal matrix element of the interaction hamiltonian, $\delta$, which, in general, has the expression $\delta=2[\gamma]:[S]$, with the tensor $[\gamma]$ describing the TLS ``deformability'' and $[S]$ being the symmetric strain tensor. We construct $[\gamma]$ on very general grounds, by associating to the TLS two objects: a direction, $\hat\bt$, and a forth rank tensor of coupling constants, $[[R]]$. Based on the method of construction and on the invariance of the expression of $\delta$ with respect to the symmetry transformation of the solid, we conclude that $[[R]]$ has the same structure as the tensor of stiffness constants, $[[c]]$, from elasticity theory. In particular, if the solid is isotropic, $[[R]]$ has only two independent parameters, which are the equivalent of the Lam\'e constants. Employing this model we calculate the absorption and emission rates of phonons on TLSs and show that in isotropic solids, on average, the longitudinal phonons interact stronger with the TLSs than the transversal ones, as it is observed in experiments. We also show that in isotropic solids, a transversal wave leaves unperturbed all the TLSs with the direction contained in one of the two planes that are perpendicular either to the wave propagation direction or to the polarization direction and that a longitudinal strain applied to the solid polarises the TLS ensemble.
Anghel Dragoş-Victor
Galperin Yu. M.
Kuhn Tobias
Manninen Matti
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