Electron–LO-phonon scattering rates in a cylindrical quantum wire with an axial magnetic field: Analytic results

The interaction of electrons with bulk LO phonons in a cylindrical quantum wire is discussed with both intersubband and intrasubband relaxation considered. For processes involving the lowest pair of subbands, a parallel analytic approach leads to good agreement with the numerical calculations. In particular, the effect of an axial magnetic field is determined for intersubband transitions between these two subbands. It is found that for a given radius, there is a critical magnetic field beyond which first-order LO-phonon interactions are forbidden due to energy conservation. Close to the critical fields, fast intersubband relaxation is predicted. These effects are a consequence of the Zeeman splitting of the doubly degenerate states in the presence of the field and the behavior of the one-dimensional density of states.