Magnetophonon resonances in quantum wires

A theory of magnetophonon resonances in quantum wires is presented. The magnetoconductivity σₓₓ calculated using the Kubo formula is found to consist of two types of contribution; one is related to the current carried by one electron hopping motion between the localized cyclotron orbits through the electron-phonon interaction, and the other is caused by the current carried by electron motion affected by the confinement potential. The former, σ_e-ph, is directly proportional to the coupling constant {α} of the electron--optical-phonon interaction, whereas the latter, σₚₒ is found to be inversely proportional to {α}. At resonances, σ_e-ph exhibits maxima and σₚₒ minima. For weak confinement potential, i.e., for wide quantum wires, σ_e-ph is dominant and total magnetoconductivity σₓₓ shows maxima at resonances as pointed out by Vasilopoulos et al. [Phys. Rev. B 40, 1810 (1989)]. On the other hand, in the case of strong confinement potential, or in narrow quantum wires, σₓₓ is dominated by σₚₒ, resulting in minima in an extremely strong confinement potential.