Fermi Surface Geometry and Optical Conductivity of a 2D Electron Gas near an Ising-Nematic Quantum Critical Point
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| Format: | Preprint |
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2024
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| author | Gindikin, Yasha Chubukov, Andrey V. |
| author_facet | Gindikin, Yasha Chubukov, Andrey V. |
| contents | We analyze optical conductivity of a clean two-dimensional electron system in a Fermi liquid regime near a $T=0$ Ising-nematic quantum critical point (QCP), and extrapolate the results to a QCP. We employ direct perturbation theory up to the two-loop order to elucidate how the Fermi surface's geometry (convex vs. concave) and fermionic dispersion (parabolic vs. non-parabolic) affect the scaling of the optical conductivity, $σ(ω)$, with frequency $ω$ and correlation length $ξ$. We find that for a convex Fermi surface the leading terms in the optical conductivity cancel out, leaving a sub-leading contribution $σ(ω) \propto ω^2 ξ^4 \mathcal{L}$, where $\mathcal{L} = \mathrm{const}$ for a parabolic dispersion and $\mathcal{L} \propto \log{ωξ^3}$ in a generic case. For a concave Fermi surface, the leading terms do not cancel, and $σ(ω) \propto ξ^2$. We extrapolate these results to a QCP and obtain $σ(ω) \propto ω^{2/3}$ for a convex Fermi surface and $σ(ω) \propto 1/ω^{2/3}$ for a concave Fermi surface. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_17392 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fermi Surface Geometry and Optical Conductivity of a 2D Electron Gas near an Ising-Nematic Quantum Critical Point Gindikin, Yasha Chubukov, Andrey V. Strongly Correlated Electrons Mesoscale and Nanoscale Physics We analyze optical conductivity of a clean two-dimensional electron system in a Fermi liquid regime near a $T=0$ Ising-nematic quantum critical point (QCP), and extrapolate the results to a QCP. We employ direct perturbation theory up to the two-loop order to elucidate how the Fermi surface's geometry (convex vs. concave) and fermionic dispersion (parabolic vs. non-parabolic) affect the scaling of the optical conductivity, $σ(ω)$, with frequency $ω$ and correlation length $ξ$. We find that for a convex Fermi surface the leading terms in the optical conductivity cancel out, leaving a sub-leading contribution $σ(ω) \propto ω^2 ξ^4 \mathcal{L}$, where $\mathcal{L} = \mathrm{const}$ for a parabolic dispersion and $\mathcal{L} \propto \log{ωξ^3}$ in a generic case. For a concave Fermi surface, the leading terms do not cancel, and $σ(ω) \propto ξ^2$. We extrapolate these results to a QCP and obtain $σ(ω) \propto ω^{2/3}$ for a convex Fermi surface and $σ(ω) \propto 1/ω^{2/3}$ for a concave Fermi surface. |
| title | Fermi Surface Geometry and Optical Conductivity of a 2D Electron Gas near an Ising-Nematic Quantum Critical Point |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2401.17392 |