MAGNETOPHONON RESONANCES IN QUANTUM WIRES

A theory of magnetophonon resonances in quantum wires is presented. The magnetoconductivity sigma(xx) calculated using the Kubo formula is found to consist of two types of contribution; one is related to the current carried by the 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, sigma(e-ph), is directly proportional to the coupling constant-alpha of the electron-optical-phonon interaction, whereas the latter, sigma(po), is found to be inversely proportional to alpha. At resonances, sigma(e-ph) exhibits maxima and sigma(po) minima. For weak confinement potential, i.e., for wide quantum wires, sigma(e-ph) is dominant and total magnetoconductivity sigma(xx) 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, sigma(xx) is dominated by sigma(po), resulting in minima in an extremely strong confinement potential.