The behaviour of the propagating and evanescent modes of a 2D quantum wire in a perpendicular magnetic field

The modes of a 2D quantum wire in a perpendicular magnetic field are studied in detail for the real electron energies which are appropriate in nanostructure scattering problems. Propagating and evanescent modes are considered for both asymmetric and symmetric confining potentials. The symmetry of the mode functions and the real and imaginary parts of k are investigated in both cases. For asymmetric potentials the evanescent k values usually have non-zero real parts. For symmetric potentials purely imaginary k values also appear when epsilon is just below a propagation threshold. Calculated wavefunctions and dispersion curves for both Re(k) and Im(k) are presented for simple examples of both cases and the transformation from one to the other is described. The total current carried by an arbitrary superposition of modes (both propagating and evanescent) is calculated. The part of the current carried by interfering evanescent modes involves a complex analogue of the group velocity. (C) 1997 Academic Press Limited.