On the dynamic conductivity for an electron-impurity system |
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Authors: | S Fujita JP Riley CC Chen Ching-Lung Ko CS Raju T Yamaguchi |
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Institution: | Centre de recherches mathématiques, Université de Montréal, Montréal, Québec, Canada;Department of Physics, Ohio University, Athens, Ohio, U.S.A.;Department of Physics and Astronomy, State University of New York at Buffalo, Buffalo, New York, U.S.A. |
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Abstract: | The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, ns) and the energy shift Δ(ω, ε, ns) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, ng, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, ns) is smaller than that extrapolated value which the conventional expression γ0 for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ0-γ becomes appreciable when the ratio of the average time between scatterings, τc, to the average duration of a scattering, τd, is 100 or less, that γ (ω, ns) decreases monotonically from its static value γ (0, ns), and becomes vanishingly small in the region ω≈1/τd, and that in the static limit (ω=0), γ=γ01?(2/π) (γ0τd)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ0 as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, ns) for degenerated electrons is calculated. The deviation, σ-σ0, from the conventional expression σ0=(?i) (nee2/M) ω-iΓ0]?1, (ne]=number density of electrons), for 0°K, is appreciable when the ratio τc/τd is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied. |
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