TUNNELING MAGNETOPLASMON EXCITATIONS IN THE SEMICLASSICAL LIMIT AND INTEGER QUANTUM HALL REGIME FOR DOUBLE-QUANTUM-WELL SYSTEMS

The magnetoplasmon dispersion relation is obtained in the random-phase approximation for a double-quantum-well structure, where the magnetic field is perpendicular to the planes and only the two lowest tunneling states are included in the formalism. Analytic closed-form results are presented in the long and short wavelength limits when tunneling between the quantum wens is included for (a) sere temperature and only the lowest Landau level is occupied and (b) in the semiclassical limit when many Landau levels are occupied and the temperature is finite. In the quantum strong field (QSF) limit, the symmetric mode spectrum, due to in-phase oscillations in the two wells, has a principal magnetoplasmon mode branch and Bernstein-like plasmon resonances which are not affected by tunneling. In the QSF limit, the antisymmetric (out-of-phase) principal and Bernstein-like modes are split by tunneling between the quantum wells. In addition, there is a new antisymmetric mode due entirely to tunneling (tunneling magnetoplasmon) for which there is no counterpart in a single isolated two-dimensional layer. In the semiclassical regime, the symmetric principal magnetoplasmon mode is not affected by tunneling in the long wavelength limit but the symmetric Bernstein-like modes depend on the electron concentration in each individual subband and, as a result, depend on tunneling explicitly. In the semiclassical limit, the tunneling magnetoplasmon is not affected by the magnetic field to lowest order in the long wavelength limit and weakly depends on the magnetic field in the short wavelength limit. Also, in the semiclassical limit, the effect of a magnetic field on the antisymmetric principal and Bernstein-like modes is apparent as a set of hybridized magnetoplasmon modes shifted up and down in energy relative to the tunneling gap by amounts proportional to multiples of the cyclotron energy.