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arXiv 1407.0830cond-mat.mtrl-scicond-mat.mes-hall
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石墨烯声子限制电阻率的第一性原理计算:电子-声子相互作用、应变诱导规范场和Boltzmann方程

Phonon-limited resistivity of graphene by first-principle calculations: electron-phonon interactions, strain-induced gauge field and Boltzmann equation

Thibault Sohier, Matteo Calandra, Cheol-Hwan Park, Nicola Bonini, Nicola Marzari, Francesco Mauri

摘要:

石墨烯中的电子-声子耦合被广泛地从第一性原理建模和模拟。我们发现,使用一个准确的声学声子模式的偏振模型是至关重要的,以获得正确的数值结果。在线性响应框架下,在密度泛函理论水平上计算了电子与声学声子模、规范场和形变势之间的相互作用。声学声子的零动量极限被解释为应变模式,允许在GW近似下计算声学规范场参数。研究了电子屏蔽对电子-声子矩阵元的作用。然后,我们解决玻尔兹曼方程半解析石墨烯,包括声学和光学声子散射。结果表明,在Bloch-Grüneisen和均分区域,电子输运主要由未屏蔽的声学规范场决定,而形变势的贡献可以忽略不计,并且是强屏蔽的.通过与实验数据的比较,我们发现声学声子对电阻率的贡献与掺杂和衬底无关。DFT+GW方法低估了这种对电阻率的贡献约30%。在270 K以上,计算的电阻率低估实验一个更严重,低估是在较低的掺杂更大。我们发现,除了远程声子散射,这种分歧的一个可能的解释是电子-电子相互作用,强烈重正化耦合到固有的光学声子模式。最后,在讨论了Matthiessen规则在石墨烯中的有效性之后,我们直接从实验数据中推导出Boltzmann方程的简化解析解,以提取与应变诱导规范场相关的声学声子的耦合。

英文摘要:

Electron-phonon coupling in graphene is extensively modeled and simulated from first principles. We find that using an accurate model for the polarizations of the acoustic phonon modes is crucial to obtain correct numerical results. The interactions between electrons and acoustic phonon modes, the gauge field and deformation potential, are calculated at the DFT level in the framework of linear response. The zero-momentum limit of acoustic phonons is interpreted as a strain pattern, allowing the calculation of the acoustic gauge field parameter in the GW approximation. The role of electronic screening on the electron-phonon matrix elements is investigated. We then solve the Boltzmann equation semi-analytically in graphene, including both acoustic and optical phonon scattering. We show that, in the Bloch-Grüneisen and equipartition regimes, the electronic transport is mainly ruled by the unscreened acoustic gauge field, while the contribution due to the deformation potential is negligible and strongly screened. By comparing with experimental data, we show that the contribution of acoustic phonons to resistivity is doping- and substrate-independent. The DFT+GW approach underestimates this contribution to resistivity by about 30 %. Above 270K, the calculated resistivity underestimates the experimental one more severely, the underestimation being larger at lower doping. We show that, beside remote phonon scattering, a possible explanation for this disagreement is the electron-electron interaction that strongly renormalizes the coupling to intrinsic optical-phonon modes. Finally, after discussing the validity of the Matthiessen rule in graphene, we derive simplified analytical solutions of the Boltzmann equation to extract the coupling to acoustic phonons, related to the strain-induced gauge field, directly from experimental data.

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