Magnetophonon resonances in quasi-one-dimensional wires

It is shown that the confinement of electrons in quantum wires of width W ({~}0.1 {μ}m) much larger than the magnetic length lB and much smaller than the mean free path lₑ (lB{}W{}lₑ), modeled with a parabolic potential of frequency {Ω}, leads to a shift of the magnetophonon resonance peaks to smaller magnetic fields. The usual resonance condition ω_LO=Pωc, where P is an integer and ωLO and ωc are the optical-phonon frequency and cyclotron frequency, respectively, becomes ω_LO=Pω ̃ \~, with {ω} ̃ \~{}{} equal to (ωc²+Ω²{)}1/2$. The magnetoconductivity ${{σ}}ₓₓ$ decreases when the confinement becomes stronger (when the width decreases). Level broadening and finite-thickness corrections are taken into account.