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arXiv 1707.07352cond-mat.str-el
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二维金属量子临界点附近的光学电导率:“推广的Drude公式”的地位

Optical conductivity of a two-dimensional metal near a quantum-critical point: the status of the "extended Drude formula"

Andrey V. Chubukov, Dmitrii L. Maslov

摘要:

量子临界点附近金属的光学电导率不仅通过散射时间而且通过有效质量依赖于频率,这在量子临界点附近获得奇异的频率依赖性。我们检查这一论断,通过计算图解的光学电导率,$σ' (Ω)$,附近的量子点和自旋密度波(SDW)的量子临界点(QCP)在2D。如果不考虑当前顶点的重整化,则$σ' (Ω)$通过准粒子剩余$Z$(等于我们近似中的裸质量和重整化质量的比率)和输运散射率$γ_{\text{tr}}$表示为$σ' (Ω)\propto Z^2 γ_{\text{tr}}/Ω^2$。对于一个连续的QCP($γ_{\text{tr}}\proptoΩ^{4/3}$和$Z\proptoΩ^{1/3}$),该公式表明$σ'(Ω)$将趋于恒定在$Ω\to 0$。我们明确地表明,$σ' (Ω)$的实际行为是不同的,由于强重整化的当前顶点,这抵消了$Z^2$的一个因素。因此,$σ' (Ω)$发散为$1/Ω^{2/3}$,正如早期的作品所描述的那样。在SDW的情况下,我们考虑两个贡献的导电性:从热点和从费米表面的“不冷不热”的地区。热点贡献不受顶点重整化的影响,但它是次导致的不冷。对于后者,我们认为,一个因素的$Z^2$再次取消顶点校正。因此,SDW QCP处的$σ' (Ω)$随着$1/Ω$向下缩放到最低频率。

英文摘要:

The optical conductivity of a metal near a quantum critical point (QCP) is expected to depend on frequency not only via the scattering time but also via the effective mass, which acquires a singular frequency dependence near a QCP. We check this assertion by computing diagrammatically the optical conductivity, $σ' (Ω)$, near both nematic and spin-density wave (SDW) quantum critical points (QCPs) in 2D. If renormalization of current vertices is not taken into account, $σ' (Ω)$ is expressed via the quasiparticle residue $Z$ (equal to the ratio of bare and renormalized masses in our approximation) and transport scattering rate $γ_{\text{tr}}$ as $σ' (Ω)\propto Z^2 γ_{\text{tr}}/Ω^2$. For a nematic QCP ($γ_{\text{tr}}\proptoΩ^{4/3}$ and $Z\proptoΩ^{1/3}$), this formula suggests that $σ'(Ω)$ would tend to a constant at $Ω\to 0$. We explicitly demonstrate that the actual behavior of $σ' (Ω)$ is different due to strong renormalization of the current vertices, which cancels out a factor of $Z^2$. As a result, $σ' (Ω)$ diverges as $1/Ω^{2/3}$, as earlier works conjectured. In the SDW case, we consider two contributions to the conductivity: from hot spots and from"lukewarm" regions of the Fermi surface. The hot-spot contribution is not affected by vertex renormalization, but it is subleading to the lukewarm one. For the latter, we argue that a factor of $Z^2$ is again cancelled by vertex corrections. As a result, $σ' (Ω)$ at a SDW QCP scales as $1/Ω$ down to the lowest frequencies.

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