Two-Dimensional Electron Layers in External Fields: Analysis of the Effects of Non-Separability
Two-dimensional electron layers when placed in external electric and magnetic fields can display interesting features which arise solely due to the non-separability of electronic motions. Through simple, single electron Hamiltonians, we have studied in considerable details the effects of the nonseparability on the eigenvalue structure of two distinct systems. Intersubband cyclotron combined resonances in a quasi-two-dimensional space charge layer as found in metal-oxide-semiconductor sandwiches are studied using "triangular well" approximation. Two alternative basis sets have been pointed out which enable one to obtain analytical matrix elements of the Hamiltonian for all values of the magnitude and the angle of tilt of the applied magnetic field. Yet another basis set, constructed out of some variationally determined parameters, has been indicated which would facilitate the diagonalization of the Hamiltonian. The coupling beween electronic motions normal and parallel to the layer has been found to give rise to deviations in the expected value of the Landau spacings as functions of the tilt angle of the magnetic field. Optical spectra for such systems show some features in qualitative agreement with experiments and other calculations. The system is a prototype of nonseparable problems in two dimensions. Surface state electrons on liquid helium when placed in perpendicular electric and magnetic fields can have a potential well with two minima for the electronic motion normal to the surface. Such double-minimum potential wells also arise for highly excited Rydberg states of atoms in crossed electric and magnetic fields and in certain molecular potential curves. We applied a WKB formalism, modified to treat cases when two of the classical turning points become very close together, to such double-minimum wells and calculated the energy splittings that arise when one is near "degeneracy", that is when either well, considered independently, can support a bound state at the same energy. We have also applied this formalism to many other potential curves considered previously in the literature to test its efficacy, for the first time to our knowledge, against other known methods.
- Pub Date:
- Physics: Atomic