Estimate two collective-response features

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Dielectric and optical properties of solids · Dielectric and optical properties of solids

Solid State Physics, Ch Collective and coupled excitations: plasmons, polaritons and polarons

Problem

Estimate two collective-response features, one from a free-electron model and one from phonon data. ((a)) Magnesium metal supplies two conduction electrons per atom, has mass density 1.738×103 kg m−31.738\times10^3\,\mathrm{kg\,m^{-3}} and molar mass 24.31 g mol−124.31\,\mathrm{g\,mol^{-1}}. Treating it as a free-electron gas with background permittivity εb=1\varepsilon_b=1, estimate the unscreened plasma energy ℏωp\hbar\omega_p and the wavelength at which magnesium's reflectivity should fall from near unity (below) to near zero (above). ((b)) Potassium bromide (KBr) has a transverse optical phonon at ωTO/2π=3.05 THz\omega_{TO}/2\pi = 3.05\,\mathrm{THz}, static permittivity εs=4.78\varepsilon_s=4.78 and high-frequency permittivity ε∞=2.34\varepsilon_\infty=2.34. Estimate the wavelength range of its reststrahlen band.

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