Analytical expression for $\pi$-ton vertex contributions to the optical conductivity
Vertex corrections from the transversal particle-hole channel, so-called $\pi$-tons, are generic in models for strongly correlated electron systems and can lead to a displaced Drude peak (DDP). Here, we derive the analytical expression for these $\pi$-tons, and how they affect the optical conductivi...
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2025-04-01
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| author | Juraj Krsnik, Anna Kauch, Karsten Held |
| author_facet | Juraj Krsnik, Anna Kauch, Karsten Held |
| author_sort | Juraj Krsnik, Anna Kauch, Karsten Held |
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| description | Vertex corrections from the transversal particle-hole channel, so-called $\pi$-tons, are generic in models for strongly correlated electron systems and can lead to a displaced Drude peak (DDP). Here, we derive the analytical expression for these $\pi$-tons, and how they affect the optical conductivity as a function of correlation length $\xi$, fermion lifetime $\tau$, temperature $T$, and coupling strength to spin or charge fluctuations $g$. In particular, for $T\rightarrow T_c$, the critical temperature for antiferromagnetic or charge ordering, the dc vertex correction is algebraic $\sigma_{VERT}^{dc}\propto \xi \sim (T-T_c)^{-\nu}$ in one dimension and logarithmic $\sigma_{VERT}^{dc}\propto \ln\xi \sim \nu \ln (T-T_c)$ in two dimensions. Here, $\nu$ is the critical exponent for the correlation length. If we have the exponential scaling $\xi \sim e^{1/T}$ of an ideal two-dimensional system, the DDP becomes more pronounced with increasing $T$ but fades away at low temperatures where only a broadening of the Drude peak remains, as it is observed experimentally, with the dc resistivity exhibiting a linear $T$ dependence at low temperatures. Further, we find the maximum of the DPP to be given by the inverse lifetime: $\omega_{DDP} \sim 1/\tau$. These characteristic dependencies can guide experiments to evidence $\pi$-tons in actual materials. |
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| spelling | doaj-art-47845e5abb024f2da71b417014d659fc2025-08-20T02:24:39ZengSciPostSciPost Physics2542-46532025-04-0118413810.21468/SciPostPhys.18.4.138Analytical expression for $\pi$-ton vertex contributions to the optical conductivityJuraj Krsnik, Anna Kauch, Karsten HeldVertex corrections from the transversal particle-hole channel, so-called $\pi$-tons, are generic in models for strongly correlated electron systems and can lead to a displaced Drude peak (DDP). Here, we derive the analytical expression for these $\pi$-tons, and how they affect the optical conductivity as a function of correlation length $\xi$, fermion lifetime $\tau$, temperature $T$, and coupling strength to spin or charge fluctuations $g$. In particular, for $T\rightarrow T_c$, the critical temperature for antiferromagnetic or charge ordering, the dc vertex correction is algebraic $\sigma_{VERT}^{dc}\propto \xi \sim (T-T_c)^{-\nu}$ in one dimension and logarithmic $\sigma_{VERT}^{dc}\propto \ln\xi \sim \nu \ln (T-T_c)$ in two dimensions. Here, $\nu$ is the critical exponent for the correlation length. If we have the exponential scaling $\xi \sim e^{1/T}$ of an ideal two-dimensional system, the DDP becomes more pronounced with increasing $T$ but fades away at low temperatures where only a broadening of the Drude peak remains, as it is observed experimentally, with the dc resistivity exhibiting a linear $T$ dependence at low temperatures. Further, we find the maximum of the DPP to be given by the inverse lifetime: $\omega_{DDP} \sim 1/\tau$. These characteristic dependencies can guide experiments to evidence $\pi$-tons in actual materials.https://scipost.org/SciPostPhys.18.4.138 |
| spellingShingle | Juraj Krsnik, Anna Kauch, Karsten Held Analytical expression for $\pi$-ton vertex contributions to the optical conductivity SciPost Physics |
| title | Analytical expression for $\pi$-ton vertex contributions to the optical conductivity |
| title_full | Analytical expression for $\pi$-ton vertex contributions to the optical conductivity |
| title_fullStr | Analytical expression for $\pi$-ton vertex contributions to the optical conductivity |
| title_full_unstemmed | Analytical expression for $\pi$-ton vertex contributions to the optical conductivity |
| title_short | Analytical expression for $\pi$-ton vertex contributions to the optical conductivity |
| title_sort | analytical expression for pi ton vertex contributions to the optical conductivity |
| url | https://scipost.org/SciPostPhys.18.4.138 |
| work_keys_str_mv | AT jurajkrsnikannakauchkarstenheld analyticalexpressionforpitonvertexcontributionstotheopticalconductivity |