Electron-phonon (e–ph) interactions are usually treated in the lowest order of perturbation theory. Here we derive next-to-leading order e–ph interactions, and compute from first principles the associated electron-two-phonon (2ph) scattering rates. The derivations involve Matsubara sums of two-loop Feynman diagrams, and the numerical calculations are challenging as they involve Brillouin zone integrals over two crystal momenta and depend critically on the intermediate state lifetimes. Using Monte Carlo integration together with a self-consistent update of the intermediate state lifetimes, we compute and converge the 2ph scattering rates, and analyze their energy and temperature dependence. We apply our method to GaAs, a weakly polar semiconductor with dominant optical-mode long-range e–ph interactions. We find that the 2ph scattering rates are as large as nearly half the value of the one-phonon rates, and that including the 2ph processes is necessary to accurately predict the electron mobility in GaAs from first principles.

电子-声子 ( e –ph) 相互作用通常以最低阶的微扰理论来处理。在这里，我们推导出次高阶e –ph 相互作用，并根据第一原理计算相关的电子-双声子 (2ph) 散射率。推导涉及两环费曼图的松原和，数值计算具有挑战性，因为它们涉及两个晶体动量的布里渊区积分，并且严重依赖于中间态寿命。使用蒙特卡罗积分和中间态寿命的自洽更新，我们计算并收敛了 2ph 散射率，并分析了它们的能量和温度依赖性。我们将我们的方法应用于 GaAs，这是一种具有主导光学模式长程e -ph 相互作用的弱极性半导体。我们发现 2ph 散射率几乎是单声子率的一半，并且包括 2ph 过程对于根据第一原理准确预测 GaAs 中的电子迁移率是必要的。