狄拉克金属的本征光吸收
Intrinsic optical absorption in Dirac metals
摘要：
狄拉克金属是一种掺杂（门控）狄拉克材料，费米能（$E_\text{F}$）位于导带或价带中。在非相互作用的情况下，只有当入射光子的频率（$Ω$）超过直接（泡利）频率阈值（等于$2E_\text{F}$）时，无带隙狄拉克金属才会发生光吸收。在这项工作中，我们研究，分析和数值计算，电子-电子（$ee$）和电子-空穴（$eh$）的相互作用在二维（2D）和三维（3D）狄拉克金属的光吸收在整个频率范围内低于$2E_\text{F}$的作用。我们表明，对于$Ω\ll E_\text{F}$，光学电导率，$\Reσ(Ω)$，所产生的组合$ee$和某些$eh$散射过程，尺度为$Ω^2\lnΩ$在二维和$Ω^2$在三维，分别为短程（哈伯德）和长程（屏蔽库仑）相互作用。另一种类型的$eh$过程，类似于原子物理学中的Auger-Meitner（AM）过程，开始对$Ω$的贡献高于直接阈值，等于$E_\text{F}$。与先前文献中研究的具有抛物线带的掺杂半导体的情况类似，狄拉克金属中AM对$\Reσ(Ω)$的贡献由阈值奇异性$\Reσ(Ω)\propto (Ω-E_\text{F})^{d+2}$表现，其中$d$是空间维度，$0<Ω-E_\text{F}\ll E_\text{F}$。然而，与掺杂半导体相反，狄拉克金属中的AM贡献完全被$ee$和其他$eh$贡献所掩盖。从数值上讲，$\Reσ(Ω)$恰好在几乎整个$Ω<2E_\text{F}$范围内都很小。这一发现可能对位于$2E_\text{F}$之下的狄拉克金属中的集体模有重要的影响。
英文摘要：
A Dirac metal is a doped (gated) Dirac material with the Fermi energy ($E_\text{F}$) lying either in the conduction or valence bands. In the non-interacting picture, optical absorption in gapless Dirac metals occurs only if the frequency of incident photons ($Ω$) exceeds the direct (Pauli) frequency threshold, equal to $2E_\text{F}$. In this work, we study, both analytically and numerically, the role of electron-electron ($ee$) and electron-hole ($eh$) interactions in optical absorption of two-dimensional (2D) and three-dimensional (3D) Dirac metals in the entire interval of frequencies below $2E_\text{F}$. We show that, for $Ω\ll E_\text{F}$, the optical conductivity, $\Reσ(Ω)$, arising from the combination of $ee$ and certain $eh$ scattering processes, scales as $Ω^2\lnΩ$ in 2D and as $Ω^2$ in 3D, respectively, both for short-range (Hubbard) and long-range (screened Coulomb) interactions. Another type of $eh$ processes, similar to Auger-Meitner (AM) processes in atomic physics, starts to contribute for $Ω$ above the direct threshold, equal to $E_\text{F}$. Similar to the case of doped semiconductors with parabolic bands studied in prior literature, the AM contribution to $\Reσ(Ω)$ in Dirac metals is manifested by a threshold singularity, $\Reσ(Ω)\propto (Ω-E_\text{F})^{d+2}$, where $d$ is the spatial dimensionality and $0<Ω-E_\text{F}\ll E_\text{F}$. In contrast to doped semiconductors, however, the AM contribution in Dirac metals is completely overshadowed by the $ee$ and other $eh$ contributions. Numerically, $\Reσ(Ω)$ happens to be small in almost the entire range of $Ω<2E_\text{F}$. This finding may have important consequences for collective modes in Dirac metals lying below $2E_\text{F}$.
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