Abstract
The static and dynamical properties of electrons confined in quantum-well-wire structures are modified because of the interaction with unconfined phonon modes. The interaction with virtual phonons leads to a mass renormalization, a binding energy, and a nonparabolic energy-momentum relation. Using the improved Wigner-Brillouin perturbation theory, we have investigated the energy-momentum relation for electrons confined in rectangular quantum-well wires of GaAs surrounded by ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As, as a function of the transverse sizes of the wire. There is observed a significant energy lowering when the electron momentum k approaches ${k}_{\mathrm{LO}}$, and this bending over of the dispersion curve increases when the electron confinement is enhanced.
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