Imaging magnetoelectric subbands in ballistic constrictions

We perform scanning gate experiments on ballistic constrictions in the presence of small perpendicular magnetic fields. The constrictions form the entrance and exit of a circular gate-defined ballistic stadium. Close to constrictions we observe sets of regular fringes creating a checker board pattern. Inside the stadium conductance fluctuations governed by chaotic dynamics of electrons are visible. The checker board pattern allows us to determine the number of transmitted modes in the constrictions forming between the tip-induced potential and gate-defined geometry. Spatial investigation of the fringe pattern in a perpendicular magnetic field shows a transition from electrostatic to magnetic depopulation of magnetoelectric subbands. Classical and quantum simulations agree well with different aspects of our observations.