Interactions between electrons and lattice vibrations are responsible for a wide range of material properties and applications. Recently, there has been considerable interest in the development of resonant inelastic x-ray scattering (RIXS) as a tool for measuring electron-phonon ($e$-ph) interactions. Here, we demonstrate the ability of RIXS to probe the interaction between phonons and specific electronic states both near to, and away from, the Fermi level. We perform carbon $K$-edge RIXS measurements on graphite, tuning the incident x-ray energy to separately probe the interactions of the ${\pi }^{*}$ and ${\sigma }^{*}$ electronic states. Our high-resolution data reveal detailed structure in the multiphonon RIXS features that directly encodes the momentum dependence of the $e$-ph interaction strength. We develop a Green’s-function method to model this structure, which naturally accounts for the phonon and interaction-strength dispersions, as well as the mixing of phonon momenta in the intermediate state. This model shows that the differences between the spectra can be fully explained by contrasting trends of the $e$-ph interaction through the Brillouin zone, being concentrated at the $\mathrm{\Gamma }$ and $K$ points for the ${\pi }^{*}$ states while being significant at all momenta for the ${\sigma }^{*}$ states. Our results advance the interpretation of phonon excitations in RIXS and extend its applicability as a probe of $e$-ph interactions to a new range of out-of-equilibrium situations.

中文翻译：

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用共振非弹性 X 射线散射探测远离费米能级的电子-声子相互作用

电子和晶格振动之间的相互作用导致了广泛的材料特性和应用。最近，人们对开发共振非弹性 X 射线散射 (RIXS) 作为测量电子声子的工具产生了相当大的兴趣。$\mathrm{电子}$-ph) 互动。在这里，我们展示了 RIXS 探测靠近和远离费米能级的声子和特定电子态之间相互作用的能力。我们执行碳$钾$- 石墨上的边缘 RIXS 测量，调整入射 X 射线能量以单独探测石墨的相互作用 ${\pi }^{*}$ 和 ${\sigma }^{*}$电子状态。我们的高分辨率数据揭示了多声子 RIXS 特征的详细结构，这些特征直接编码了$\mathrm{电子}$-ph 相互作用强度。我们开发了一种格林函数方法来模拟这种结构，它自然地解释了声子和相互作用强度的分散，以及中间状态下声子动量的混合。该模型表明，光谱之间的差异可以通过对比的趋势来充分解释。$\mathrm{电子}$-ph 相互作用通过布里渊区，集中在 $\mathrm{\Gamma }$ 和 $钾$ 点数 ${\pi }^{*}$ 状态同时在所有时刻都很重要 ${\sigma }^{*}$状态。我们的结果推进了对 RIXS 中声子激发的解释，并扩展了其作为$\mathrm{电子}$-ph 相互作用到一系列新的失衡情况。