Lattice effects in the complex subband dispersion of 2DEG semiconductor waveguide structures subjected to a perpendicular magnetic field

In modeling waveguide magneto-transport experiments (in a quasi-two dimensional electron gas), it is important to have knowledge of the electronic states in a magnetic field perpendicu-lar to the plane of the waveguide confinement potential. We present numerical results, within a lattice model, for the full complex subband dispersion of a rectangular waveguide. The form of our numerical real-subband solutions agrees well with analytical real solutions. However, some of our numerical evanescent solutions have a different topology from the analytic evanescent solutions near the bandedges. We argue that our evanescent solutions, although consistent with the symmetry of the lattice model and mode conservation in the restricted Hilbert space of the discretized Hamiltonian, yield different results that are forbidden in the continuum solutions. This is a concern for numerical solutions.