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热电材料可以将热能转换为电能，在能量采集、热电制冷和热力发电机等领域有着广阔的应用前景，但实现材料的热电性能大幅度提高仍然是一个挑战。硅材料是半导体工业的基石，广泛应用于集成电路及太阳能电池中。晶体硅具有很高的功率因子，但其高晶格热导率（室温时热导率约为150 W/mK）限制了它在热电领域的应用(室温下ZT<0.01)。然而，二维材料的出现打破了这一局限，它们以其优异的各向异性传输特性和微弱的范德华力，激发了人们对于硅和锗在其二维层状结构中潜在显著热电特性的浓厚兴趣。
Fig 1 Selection rules of electron-phonon scattering. Irreducible representations for C1 and V1 − valley of electron initial states, final states and acoustic phonon modes involved in intravalley and intervalley el-ph interactions for (a) LB and (b) LHD Si/Ge. The red dotted lines separate the intravalley and intervalley scattering.
来自复旦大学的张浩副教授、温州大学邵和助副研究员与南京邮电大学王增旭研究团队，利用第一性原理和群论探究了二维硅锗同素异形体中温度诱导效应以及全电声耦合作用修正的晶格热导率和热电优值。该工作利用群论构建了二维硅/锗同素异形体中载流子谷内和谷间散射的全景选择定则，发现与第一性原理数值计算的结果完全一致。结果表明，由于LHD Si/Ge中镜面对称性的存在，使得电声散射中平面外的ZA模式被完全禁止。同时在LHD Si/Ge中，无论是谷间散射还是谷内散射，大多数利用声学声子的散射通道都被禁止，导致电声散射中声学支模式贡献较小。但是，对于LB Si/Ge，只有利用LA声子的谷内散射和利用ZA和LA的谷间散射被禁止，从而使得声学支在电声耦合总散射率中表现出和光学支相当的贡献。
Fig. 2 Three-phonon scattering channels. The calculated three-phonon scattering channels for (a) LB Si, (b) LB Ge, (c) LHD Si and (d) LHD Ge. (e) The calculated proportion of different three-phonon scattering channels of aaa, aao, aoo, and ooo for LB Si, LB Ge, LHD Si, and LHD Ge.
对于声子-声子相互作用，三声子散射通道的选择定则表明，在二维硅/锗同素异形体中，三声子相互作用的相空间P3主要由光学声子模式的发射过程所主导，LB和LHD Si/Ge中较大的光学声子带宽和光学平带分别导致了显著的声学-光学-光学（aoo）和光学-光学-光学（ooo）散射相空间。此外，温度诱导效应引起的非谐性变化随温度升高而加剧，特别是在LHD Ge中，声-光声子带隙的消失导致群速度和格林艾森常数显著增加。研究比较了三声子与四声子散射率，发现温度效应在大部分声子频率区域中显著增加了模式分辨的四声子相互作用与三声子相互作用之间的比率，这一发现有助于解释LB和LHD Si/Ge中低热导率的原因。
Fig. 3 Four-phonon scattering rates.
在这一基础上，作者通过考虑全电声耦合及高阶非谐声子-声子相互作用，对这些材料的热电性能进行了精确评估，发现LHD Si和LB Ge在700 K下的最大ZT值分别达到1.06和0.66，显著超过了它们相应的体相材料。研究成果不仅为二维硅/锗同素异形体的物理性质和应用潜力提供了更全面的理解，也可能激发对其他材料中声子输运机制的广泛研究。
Fig.4 Thermoelectric properties. Figures of merits zT as a function of carrier concentrations from 300 K to 700 K for (a) LB Si, (b) LB Ge, (c) LHD Si, (d) LHD Ge. (e) PFs and (f) zT values of LB and LHD Si/Ge compared to that of typical materials.
该文近期发表于npj Computational Materials 10：2(2024)，英文标题与摘要如下，点击左下角“阅读原文”可以自由获取论文PDF。
Full-landscape selection rules of electrons and phonons and temperature-induced effects in 2D silicon and germanium
allotropes 
Le Shu, Yujie Xia, Ben Li, Lei Peng, Hezhu Shao, Zengxu Wang, Yan Ce, Heyuan Zhu & Hao Zhang
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 temperature-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.
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