Scattering from a magnetic strip: Analytic description of transmission and conductance

The transmission and reflection amplitudes for charged particle scattering from a magnetic field in an infinite strip {0xX,-<y<} are obtained analytically, and the conductance per unit transverse length g is given in closed form. It is found that the dimensionless quantity hg/e2k scales with the variable R=X/kL2 (where k2 is the electron energy and L is the magnetic length) and vanishes without residual tunneling if the strip width exceeds the cyclotron diameter (R>2). In the region (0<R<2), g decreases monotonically with R without Aharonov-Bohm oscillations.