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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2404.12206 |
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| _version_ | 1866915332180934656 |
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| author | Kuzian, R. O. Krasovskii, E. E. |
| author_facet | Kuzian, R. O. Krasovskii, E. E. |
| contents | Attosecond dynamics of electron reflection from a thin film is studied based on a one-dimensional jellium model. Following the Eisenbud-Wigner-Smith concept, the reflection time delay $Δτ_{\rm R}$ is calculated as the energy derivative of the phase of the complex reflection amplitude $r$. For a purely elastic scattering by a jellium slab of a finite thickness $d$ the transmission probability $T$ oscillates with the momentum $K$ in the solid with a period $π/d$, and $Δτ_{\rm R}$ closely follows these oscillations. The reflection delay averaged over an energy interval grows with $d$, but in the limit of $d\to\infty$ the amplitude $r$ becomes real, so $Δτ_{\rm R}$ vanishes. This picture changes substantially with the inclusion of an absorbing potential $-iV_{\rm i}$: As expected, for a sufficiently thick slab the reflection amplitude now tends to its asymptotic value for a semi-infinite crystal. Interestingly, for $V_{\rm i} \ne 0$, around the $T(E)$ maxima, the $Δτ_{\rm R}(E)$ curve strongly deviates from $T(E)$, showing a narrow dip just at the $Δτ_{\rm R}(E)$ maximum for $V_{\rm i}=0$. An analytical theory of this counterintuitive behavior is developed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12206 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Attosecond dynamics of electron scattering by an absorbing layer Kuzian, R. O. Krasovskii, E. E. Materials Science Attosecond dynamics of electron reflection from a thin film is studied based on a one-dimensional jellium model. Following the Eisenbud-Wigner-Smith concept, the reflection time delay $Δτ_{\rm R}$ is calculated as the energy derivative of the phase of the complex reflection amplitude $r$. For a purely elastic scattering by a jellium slab of a finite thickness $d$ the transmission probability $T$ oscillates with the momentum $K$ in the solid with a period $π/d$, and $Δτ_{\rm R}$ closely follows these oscillations. The reflection delay averaged over an energy interval grows with $d$, but in the limit of $d\to\infty$ the amplitude $r$ becomes real, so $Δτ_{\rm R}$ vanishes. This picture changes substantially with the inclusion of an absorbing potential $-iV_{\rm i}$: As expected, for a sufficiently thick slab the reflection amplitude now tends to its asymptotic value for a semi-infinite crystal. Interestingly, for $V_{\rm i} \ne 0$, around the $T(E)$ maxima, the $Δτ_{\rm R}(E)$ curve strongly deviates from $T(E)$, showing a narrow dip just at the $Δτ_{\rm R}(E)$ maximum for $V_{\rm i}=0$. An analytical theory of this counterintuitive behavior is developed. |
| title | Attosecond dynamics of electron scattering by an absorbing layer |
| topic | Materials Science |
| url | https://arxiv.org/abs/2404.12206 |