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XKEYWORD: LO-phonon

# Longitudinal Optical phonons

These are phonons (in which the ...). They interact with electrons by an e.psi interaction term (see Babiker-1992). Babiker-Z-1998 refer only to p-polarised LO-phonons, both confined and interface. There seem to be no s-polarised LO-phonons, either confined or interface.

There can be 'interface LO-phonons' (evanescent phonons) as well in energy ranges where k_L is imaginary -- these are distinct from the (FK) IP-phonons, which are actually phonon-polaritons. These 'interface LO-phonons' are described by decaying exponentials, and so need to be attached to interfaces. In the DC-model where u_z can be non-zero at the interface, and so these interface modes can exist. As they are LO-phonons, they still have an e.psi interaction with electrons. However, a requirement of the HD-model is that atomic displacements u_z is zero at (or near) the interfaces (Ridley-B-1991) if the two layers are sufficiently dissimilar (eg GaAs/AlAs, but not for low Al GaAs/GaAlAs), in which case they will vanish.

The LO mode displacements are

u_x = k_x ( e^{i k_L z} \pm \exp^{-i k_L z} ) e^{ i (k_x x - \omega t) }
u_z = k_L ( e^{i k_L z} \mp \exp^{-i k_L z} ) e^{ i (k_x x - \omega t) }

\phi_{LO} = -i \rho_{LO} ( e^{i k_L z} \pm \exp^{-i k_L z} ) e^{ i (k_x x - \omega t) }


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