# Hopping Processes Explain T-linear Rise of Thermal Conductivity in Thermoelectric Clathrates above the Plateau

## TL;DR

This paper explains the T-linear increase in thermal conductivity of off-center type-I clathrates above the plateau through a hopping mechanism of localized modes, aligning well with experimental observations.

## Contribution

It introduces a hopping mechanism for localized modes that accounts for the T-linear thermal conductivity rise in off-center clathrates, supported by theoretical calculations.

## Key findings

- Hopping of localized modes explains T-linear thermal conductivity rise.
- Calculated results match experimental data for off-center clathrates.
- Both magnitude and temperature dependence are accurately reproduced.

## Abstract

Type-I clathrate compounds with off-center guest ions realize the phonon-glass electron-crystal concept by exhibiting almost identical lattice thermal conductivities $\kappa_{\rm L}$ to those observed in network-forming glasses. This is in contrast with type-I clathrates with on-center guest ions showing $\kappa_{\rm L}$ of conventional crystallines. Glasslike $\kappa_{\rm L}$ stems from the peculiar THz frequency dynamics in off-center type-I clathrates where there exist three kinds of modes classified into extended(EX), weakly(WL) and strongly localized(SL) modes as demonstrated by Liu $et.\,al.$, Phys. Rev. B $\textbf{93}$, 214305(2016). Our calculated results based on the hopping mechanism of SL modes via anharmonic interactions show fairly good agreement with observed ${\it T}$-linear rise of $\kappa_{\rm L}$ above the plateau. We emphasize that both the magnitude and the temperature dependence are in accord with the experimental data of off-center type-I clathrates.