Off-center rattling triggers high-temperature thermal transport in thermoelectric clathrates: Nonperturbative approach

Abstract

Lattice thermal conductivities ${\ensuremath{\kappa}}_{\mathrm{L}}$ of type-I clathrates encapsulating ``off-center'' guest atoms behave in a way that is sharply different from those of conventional crystals such as on-center type-I clathrates. The latter decreases with increasing temperature according to $1/T$ above a few tens K, while ${\ensuremath{\kappa}}_{\mathrm{L}}$ of off-center clathrates increase $T$ linearly above a few tens of K. Further increasing temperature above $T\ensuremath{\gtrsim}100\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, ${\ensuremath{\kappa}}_{\mathrm{L}}$ saturates without exhibiting appreciable $T$ dependence. In this temperature regime, the standard formulation of ${\ensuremath{\kappa}}_{\mathrm{L}}$ based on the perturbation theory is unfeasible. We herein present a theory of ${\ensuremath{\kappa}}_{\mathrm{L}}$ based on a ``nonperturbative'' approach by taking into account the interaction between nonvibrational off-center rattling states of guest atoms and cage shells. It is remarkable that our theory shows excellent agreement with observed ${\ensuremath{\kappa}}_{\mathrm{L}}(T)$ for off-center clathrates in magnitudes, the cage volume $\mathrm{\ensuremath{\Omega}}$ dependence, and $T$ dependence.