Full-landscape selection rules of electrons and phonons and temperature-induced effects in 2D silicon and germanium allotropes

Abstract The electron-phonon (el-ph) and phonon-phonon interactions play crucial roles in determining the electronic and thermal transport properties of materials. Using the group theory and ab-initio calculations, we have derived the full-landscape selection rules for intravalley and intervalley scattering for carriers in 2D silicon and germanium allotropes with low buckled (LB) and large honeycomb dumbbell (LHD) structures, showing dominant role of optical modes in total el-ph coupling in LHD Si/Ge due to most el-ph scattering channels via acoustic modes blocked by symmetries. Remarkably, we show that due to the relatively large optical phonon bandwidth and “bunching effect" of acoustic phonon bands, the selection rules of three-phonon interactions reveal the dominant ooo and aoo channels in LHD and LB Si/Ge, respectively, and the temprature-induced effects significantly increase the ratio between mode-resolved four-phonon interactions and three-phonon interactions in most of the phonon-frequency region, finally leading to the low thermal conductivities in both LB and LHD Si/Ge. Furthermore, we observe the anomalous temperature-dependent thermal conductivities in LHD Ge, resulted from the vanishing quasi-acoustic-optical phonon gap under the temperature-induced effects. By considering full el-ph coupling and higher-order anharmonic phonon-phonon interactions, the maximal thermoelectric figures of merits in LHD Si and LB Ge are found to reach 1.06 and 0.66 at 700 K, respectively, significantly surpassing their bulk counterparts. Our work is poised to stimulate wide-ranging exploration into phonon transport across diverse materials, and benefits both fundamental knowledge and advanced technologies of 2D Si/Ge allotropes.