Non-homogeneous magnetic field induced magnetic edge states and their   transport in a quantum wire
  The spectrum of magnetic edge states and their transport properties in the presence of a perpendicular non-homogeneous magnetic field in a quantum wire formed by a parabolic confining potential are obtained. Systems are studied where the magnetic field exhibits a discontinuous jump in the transverse direction and changes its sign, strength, and both sign and strength at the magnetic interface. The energy spectra and wave functions of these systems, the corresponding group velocities along the interface and the particle average positions normal to the interface are calculated. The resistance of the quantum wire in the presence of such a magnetic interface is obtained both in the ballistic and the diffusive regimes as a function of the Fermi energy and of the homogeneous background magnetic field. The results are compared with those for the case of a homogeneous field. 
S. M. Badalyan and F. M. Peeters