The classical phase space for quantum dots

Abstract

We numerically integrate Hamilton's equations for the classical phase space trajectories of electrons confined in a closed quantum dot. The dot potential contour is obtained numerically via full, 3D spin density functional calculations of a realistic, GaAs-AlGaAs heterostructure based device. We show that the phase space of the dot is mixed and, as a function of increasing energy, becomes increasingly chaotic. We show that this is related to the well-screened, symmetric shape of the potential at low energies and the un-screened, irregular perimeter shape at the Fermi surface. We employ an iterative method to search for periodic orbits in the dot, employing the computed matrizant.