Phonon transport in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Cu</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>GeSe</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>: Effects of spin-orbit coupling and higher-order phonon-phonon scattering
Hezhu Shao, Daquan Ding, Ying Fang, Wei Song, Jielan Huang, Changkun Dong, Hao Zhang
Abstract
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.