超越Allen-Heine-Cardona：金刚石线宽和线移中的非微扰电子-声子相互作用
Beyond Allen-Heine-Cardona: non-perturbative electron-phonon interactions in the linewidths and lineshifts of diamond
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中文总结 AI 辅助
该研究针对金刚石的线宽与线移，采用非微扰格林函数方法（NPG）克服Allen-Heine-Cardona（AHC）微扰理论的缺陷，证实其能准确描述谱展宽与高阶效应，为相关研究提供可靠框架。
中文摘要 AI 辅助
固体的温度依赖带隙通常通过在壳上评估的微扰Allen-Heine-Cardona（AHC）电子-声子自能来计算。将AHC扩展到任意频率ω以通过戴森方程确定完整谱函数的方法已知会失效，会错误放置卫星峰且在带极值处不产生展宽；而非微扰超胞（SC）方法聚焦于本征值平均而非线形，基于特殊位移的方法无法描述完整线形或简并带的线移。本文采用非微扰格林函数方法（NPG），随机采样畸变的SC构型，由此直接得到包含线移、线宽和不对称性的谱函数，并在重整化带极值处恢复有限谱权重。我们证明，用裸传播子计算的任意阶微扰自能代入戴森方程后，其虚部在裸带隙内消失，会给出错误的谱函数：传播子的自洽性是使带边展宽的关键，NPG通过构造满足该性质且包含所有非泡图。我们还解释了为何SC方法收敛所需的SC远小于微扰理论所需的q网格。对于带隙移动，NPG和壳上AHC结果相当，表明高阶项未显著改变金刚石的重整化；但在谱函数方面，超越裸微扰理论不仅更准确，且是必要的，NPG提供了从第一性原理捕获谱展宽和高阶效应的可靠框架。
英文摘要
The temperature-dependent band gap of solids is usually computed from the perturbative Allen-Heine-Cardona (AHC) electron-phonon self-energy evaluated on-shell. Extending AHC to arbitrary frequency $ω$ to determine the full spectral function via the Dyson equation is known to fail, misplacing satellites and yielding no broadening at band extrema, while non-perturbative supercell (SC) methods have focused on eigenvalue averages rather than lineshapes, and approaches based on special displacements cannot describe the full lineshape, or the lineshift at degenerate bands. Here we use a non-perturbative Green's function method (NPG), stochastically sampling distorted SC configurations, from which the spectral function, including lineshift, linewidth, and asymmetry, follows directly, and we recover finite spectral weight at the renormalized band extrema. We prove that the perturbative self-energy, computed to any order with the bare propagator and introduced into the Dyson equation, has an imaginary part that vanishes within the bare gap, giving incorrect spectral functions: self-consistency of the propagator is essential to broaden the band edges. NPG satisfies this property by construction, and contains all non-bubble diagrams. We also give a simple explanation of why SC methods converge with much smaller SCs than the corresponding $\mathbf{q}$-grids required by perturbation theory. For the band gap shift itself, the NPG and on-shell AHC results are found to be comparable, demonstrating that higher-order terms do not significantly alter the resulting renormalization in diamond. When it comes to the spectral function though, our results show that going beyond bare perturbation theory is not merely more accurate, but necessary, and NPG provides a robust framework to capture spectral broadening and higher-order effects from first principles.
