Theory of hot-electron magnetophonon resonance in quasi-two-dimensional quantum-well structures

The linear and nonlinear (dc) electrical transport parallel to the walls of a quantum well, with a magnetic field B=Bz^ applied normal to its barriers, is considered for an electron-phonon system, using the formalism of nonlinear response theory [Phys. Rev. B 40, 5632 (1989)] developed previously. The structurally confined electron gas is assumed to interact with bulk phonons. Explicit expressions for hot-electron magnetophonon resonances are obtained for polar-LO-phonon scattering by computing the electric-field-dependent conductivity formula defined in the Ohm’s-law form of a nonlinear electric current. Certain values of the electric field induce transitions of the carriers between neighboring Landau levels and the maxima of the ordinary magnetophonon resonance at weak electric field evolve to minima and vice versa. The conductivity (and hence the current) oscillates as a function of the magnetic field with electric-field-induced resonances occurring in the hot-electron regime when P${\mathrm{\omega }}_{\mathit{c}}$=${\mathrm{\omega }}_{\mathit{L}}^{\mathrm{*}}$, where ${\mathrm{\omega }}_{\mathit{c}}$ and ${\mathrm{\omega }}_{\mathit{L}}^{\mathrm{*}}$ are the cyclotron and effective phonon frequencies, respectively, and P is an integer. These peak positions are shifted to the higher B side from the ordinary magnetophonon resonance peaks at P${\mathrm{\omega }}_{\mathit{c}}$=${\mathrm{\omega }}_{\mathit{L}}$, where ${\mathrm{\omega }}_{\mathit{L}}$ is the bare phonon frequency. The shift of the resonance peaks is proportional to F. Unlike the three-dimensional system, additional subsidiary resonance peaks are predicted even under very weak electric fields whenever the interelectric subband transitions are allowed to take place for a relevant energy separation between two subbands, leading to an additional oscillatory behavior. The possibility of these interelectric transitions is also discussed. The dependence of the conductivity (or current), energy relaxation rate, and Landau-level broadening on the electric and magnetic fields, the thickness of the well, and the temperature is shown explicitly. Some of the results obtained here are in accordance with those available in the literature.