Phonon transport in Cu2GeSe3 : Effects of spin-orbit coupling and higher-order phonon-phonon scattering

Much attention has been focused on understanding the mechanism of low lattice thermal conductivity in Cu-based diamondlike thermoelectric compounds. For ${\mathrm{Cu}}_{2}\mathrm{Ge}{\mathrm{Se}}_{3}$, the underlying origin of low lattice thermal conductivity remains to be clarified. In this work, the first-principles calculations are employed to systematically investigate the effects of spin-orbit coupling, higher-order phonon-phonon scattering, phonon wavelike tunneling, temperature-induced renormalization of phonon and phonon-phonon interaction, and volumetric expanse on the phonon transport of ${\mathrm{Cu}}_{2}\mathrm{Ge}{\mathrm{Se}}_{3}$. We show that the spin-orbit coupling results in no detectable change on the phonon frequencies, compared with those obtained without spin-orbit coupling, while it induces slight increase in both Gr\"uneisen parameter and lattice thermal conductivity of ${\mathrm{Cu}}_{2}\mathrm{Ge}{\mathrm{Se}}_{3}$, and the underlying mechanism is thoroughly analyzed. With the fourth-order phonon scattering and temperature-induced renormalization, the calculated lattice thermal conductivities are well consistent with the experimental results. Due to the enhanced four-phonon scattering process, there are remarkable reductions for the thermal conductivity. In ${\mathrm{Cu}}_{2}\mathrm{Ge}{\mathrm{Se}}_{3}$, the coherences term ${\ensuremath{\kappa}}_{c}$ contributes increasingly to the total lattice thermal conductivity when temperature arises. And after considering the effects of temperature-induced renormalization and higher-order phonon-phonon interactions, the ${\ensuremath{\kappa}}_{c}$ would provide $\ensuremath{\sim}5%$ and above 25% of total conductivity at 300 and 800 K, respectively. Our finding clarifies the mechanism of low thermal conductivity in ${\mathrm{Cu}}_{2}\mathrm{Ge}{\mathrm{Se}}_{3}$, and benefits the design of similar Cu-based diamondlike materials in thermoelectric applications.