Magnesium oxide has a transverse optical phonon at

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

Magnesium oxide has a transverse optical phonon at ωTO/2π=12.0 THz\omega_{TO}/2\pi=12.0\,\mathrm{THz}, a static permittivity εs=9.65\varepsilon_s=9.65 (Chapter 18) and a high-frequency permittivity ε∞=2.96\varepsilon_\infty=2.96, obtained from its refractive index far above the phonon frequencies (Chapter 19). ((a)) Use the Lyddane-Sachs-Teller relation to find ωLO\omega_{LO}, and hence the wavelength range of MgO's reststrahlen band. ((b)) Find the free electron density nn that a hypothetical free-electron metal (background εb=1\varepsilon_b=1) would need for its unscreened plasma frequency ωp\omega_p to equal the ωLO\omega_{LO} found in part (a). Comment on how this density compares with a typical metal's (102210^{22}-1023 cm−310^{23}\,\mathrm{cm^{-3}}).

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