Resonant angular dependence in a weak magnetic field

Resonant tunnelling in two dimensions via a point impurity in a weak magnetic field is considered. We show that when the scattered electrons' energy is equal to the resonance one (which is the eigenenergy of the impurity), the shift of the tunnelling angle is half of the shift when the system is out of resonance. In particular, the incoming and outgoing angles depend on the impurity's location, and thus allow for its spectroscopy.