Chap 23 Optical properties of metals and inelastic

Chap 23 Optical properties of metals and inelastic scattering • Propagation of EM wave • Plasma wave • Optical properties • Angle resolved photo-emission Dept of Phys M. C. Chang

Attenuation of EM wave (I) • Attenuation of plane wave due to n. I • Reflectivity (or reflectance, normal direction)

Attenuation of EM wave (II) • Decay of intensity (energy density) • Power loss (per unit volume) • dielectric function for metal • Penetration depth

(A) Low frequency (Hagen-Ruben’s) regime ωτ<<1 τ ～ 10 -13~10 -14 ∴ω can be as large as 100 GHz Plasma edge (H. W. ) transparent Dressel and Gruener, p. 99, 308

ωτ >>1 EM wave is damped Longitudinal EM wave (plasma) EM wave propagates with phase velocity Plasma edge Signal blocked

Plasma wave For copper, n=8 1022 /cm 3 A simple picture of plasma oscillation: ωp=1. 6× 1016/s, λp=1200 A (ultraviolet) εcore correction Al 15. 3 e. V bulk plasmon 10. 3 e. V surface plasmon

Dynamic susceptibility (long wavelength limit) (chap 20) For longitudinal EM wave → Energy dispersion for the plasma wave Collective excitation vs quasiparticle (e-h pair) excitation in metal plasma excitation decays into pair excitations e-h continuum 2 D: for long wavelength There is NO plasma gap

Optical properties of alkali metals Drude peak Reσ for Na, K, and Rb Fermi energy Na: 3. 24 e. V K: 2. 12 e. V Rb: 1. 85 e. V 0. 64 εF N. V. Smith PRB 2 2840 1970 n=(ε 0+4πiσ/ω)1/2 Absorption ～ Im(n) ～ Re(σ) T. Inagaki et al , Phys. Rev. B 13, 5610 (1976).

Tremblay A. M. - N-corps, p. 114

Optical properties of noble metals Cu: low threshold (2 e. V, orange) d →s copper s →s Ag: high threshold (4 e. V, ultraviolet) d →s Empty lattice http: //www. webexhibits. org/causesofcolor/9. html