Rock salt has

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

Rock salt has ωTO/2π=4.9 THz\omega_{TO}/2\pi=4.9\,\mathrm{THz}, εs=5.9\varepsilon_s=5.9 and ε∞=2.34\varepsilon_\infty=2.34. Neglect phonon damping. ((a)) Starting from c2q2=ε(ω)ω2c^2q^2=\varepsilon(\omega)\omega^2 with Chapter 18's ionic permittivity, show that ω2\omega^2 satisfies ε∞ω4−(εsωTO2+c2q2)ω2+c2q2ωTO2=0\varepsilon_\infty\omega^4-(\varepsilon_s\omega_{TO}^2+c^2q^2)\omega^2+c^2q^2\omega_{TO}^2=0. Show also that no real qq exists for ωTO<ω<ωLO\omega_{TO}<\omega<\omega_{LO}, with ωLO2=(εs/ε∞) ωTO2\omega_{LO}^2=(\varepsilon_s/\varepsilon_\infty)\,\omega_{TO}^2. ((b)) At the wavevector where the uncoupled light line ω=cq/ε∞\omega=cq/\sqrt{\varepsilon_\infty} crosses ωTO\omega_{TO}, find the two polariton frequencies ω±/2π\omega_\pm/2\pi in THz, and show that ω+ω−=ωTO2\omega_+\omega_-=\omega_{TO}^2 there. ((c)) Compare the splitting (ω+−ω−)/2π(\omega_+-\omega_-)/2\pi with (ωLO−ωTO)/2π(\omega_{LO}-\omega_{TO})/2\pi, and say what would happen to the splitting if εs\varepsilon_s were equal to ε∞\varepsilon_\infty.

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