Ballistic electrons in an open square geometry: Selective probing of resonant-energy states

We report on the interplay between classical trajectories and quantum-mechanical effects in a square geometry. At low magnetic fields the four-terminal resistance is dominated by phenomena that depend on ballistic trajectories in a classical billiard. Superimposed on these classical effects are quantum interference effects manifested by highly periodic conductance oscillations. Numerical analysis shows that these oscillations are directly related to excitations of particular eigenstates in the square. In spite of open leads, transport through an open cavity is effectively mediated by just a few (or even a single) resonant-energy states. The leads injecting electrons into the cavity play a decisive role in a selection of the particular set of states excited in the dot. The above selection rule sets a specific frequency of the oscillations seen in the experiment.