Criticality in optical properties of the Drude and Drude-Sommerfeld metals around the plasma frequencies for high carrier concentrations
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2026
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| author | Behera, Bikram Keshari Bhattacharyya, Rhitabrata Biswas, Shyamal |
| author_facet | Behera, Bikram Keshari Bhattacharyya, Rhitabrata Biswas, Shyamal |
| contents | We have analytically determined the attenuation constant of the Drude metal for the entire range of frequency ($0<ω<\infty$) of an electromagnetic (plane) wave incident on it within a single framework of classical electrodynamics. Here, by the Drude metal, we mean an electrical conductor that obeys the Drude model for the conduction electrons. We further consider the conductor to have linear dielectric and magnetic properties (i.e. permittivity $ε>ε_0$ and permeability $μ>μ_0$) due to the bound charges and bound currents in the background. Interestingly, for such a conductor with a high carrier concentration ($ω_pτ\gg1$), we have obtained a simple form of the attenuation constant $k_-\simeq+\sqrt{\frac{με}{2}}\sqrt{ω_p^2-ω^2+|ω_p^2-ω^2|}$ for a wide range of high frequencies below and above plasma frequency $ω_p$. Such a result gives rise to criticality in the conductor's optical properties, such as -- the attenuation constant, group velocity, and complex dielectric constant near around $ω=ω_p$. We have obtained the critical exponents for these quantities. We also have obtained a quantum correction to the optical properties within the Drude-Sommerfeld model with the Thomas-Fermi screening. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_08107 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Criticality in optical properties of the Drude and Drude-Sommerfeld metals around the plasma frequencies for high carrier concentrations Behera, Bikram Keshari Bhattacharyya, Rhitabrata Biswas, Shyamal Strongly Correlated Electrons Statistical Mechanics Optics We have analytically determined the attenuation constant of the Drude metal for the entire range of frequency ($0<ω<\infty$) of an electromagnetic (plane) wave incident on it within a single framework of classical electrodynamics. Here, by the Drude metal, we mean an electrical conductor that obeys the Drude model for the conduction electrons. We further consider the conductor to have linear dielectric and magnetic properties (i.e. permittivity $ε>ε_0$ and permeability $μ>μ_0$) due to the bound charges and bound currents in the background. Interestingly, for such a conductor with a high carrier concentration ($ω_pτ\gg1$), we have obtained a simple form of the attenuation constant $k_-\simeq+\sqrt{\frac{με}{2}}\sqrt{ω_p^2-ω^2+|ω_p^2-ω^2|}$ for a wide range of high frequencies below and above plasma frequency $ω_p$. Such a result gives rise to criticality in the conductor's optical properties, such as -- the attenuation constant, group velocity, and complex dielectric constant near around $ω=ω_p$. We have obtained the critical exponents for these quantities. We also have obtained a quantum correction to the optical properties within the Drude-Sommerfeld model with the Thomas-Fermi screening. |
| title | Criticality in optical properties of the Drude and Drude-Sommerfeld metals around the plasma frequencies for high carrier concentrations |
| topic | Strongly Correlated Electrons Statistical Mechanics Optics |
| url | https://arxiv.org/abs/2605.08107 |