电子-电子相互作用导致的等离激元光导率与阻尼
Optical conductivity and damping of plasmons due to electron-electron interaction
AI总结：
本文重新推导电子-电子相互作用下的光导率实部，澄清二维电子气阻尼标度争议，并推广至三维电子气与掺杂单层石墨烯。
摘要：
我们重新审视了由电子-电子相互作用导致的等离激元阻尼问题。等离激元线宽可与电荷极化率的虚部相关，或等价地与光导率的实部 Reσ(q,ω) 相关。我们首先通过标准的半经典 Boltzmann 方程处理该问题，证明二维（2D）电子气的 Reσ(q,ω) 在 ω≪T 时按 q²T²/ω⁴ 标度，这与文献[1]和[2]的结果一致，但与文献[3]不符；后者认为 Reσ(q,ω) ∝ q²T²/ω²。为解决这一分歧，我们使用文献{mishchenko:2004}的原始方法，针对任意 ω/T 比值重新推导 Reσ(q,ω)，并表明尽管后一项确实存在，但它相对于 q²T²/ω⁴ 项是次阶的。我们分别用电子液体的剪切黏度和体黏度，对主导项和次阶项给出物理解释。我们还计算了三维（3D）电子气和掺杂单层石墨烯的 Reσ(q,ω)。我们发现，在所有其他参数相同的情况下，有限温度对石墨烯中的等离激元线宽影响最强，在 ω≪T 时其按 T⁴ln T 标度。
英文摘要：
We re-visit the issue of plasmon damping due to electron-electron interaction. The plasmon linewidth can related to the imaginary part of the charge susceptibility or, equivalently, to the real part of the optical conductivity, $\mathrm{Re}σ(q,ω)$. Approaching the problem first via a standard semi-classical Boltzmann equation, we show that $\mathrm{Re}σ(q,ω)$ of two-dimensional (2D) electron gas scales as $q^2T^2/ω^4$ for $ω\ll T$, which agrees with the results of Refs. [1] and [2] but disagrees with that of Ref. [3], according to which $\mathrm{Re}σ(q,ω) \propto q^2T^2/ω^2$. To resolve this disagreement, we re-derive $\mathrm{Re}σ(q,ω)$ using the original method of Ref. {mishchenko:2004} for an arbitrary ratio $ω/T$ and show that, while the last term is, indeed, present, it is subleading to the $q^2T^2/ω^4$ term. We give a physical interpretation of both leading and subleading contributions in terms of the shear and bulk viscosities of an electron liquid, respectively. We also calculate $\mathrm{Re}σ(q,ω)$ for a three-dimensional (3D) electron gas and doped monolayer graphene. We find that, with all other parameters being equal, finite temperature has the strongest effect on the plasmon linewidth in graphene, where it scales as $T^4\ln T$ for $ω\ll T$.
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