Triangular Quantum Dots in Magnetic Fields

Abstract

The finite-element method allows one to determine the eigenstates of an electron confined in a two-dimensional infinite well of arbitrary shape under a magnetic field. Here we study triangular billiards, which are known to exhibit singular chaotic properties. We find that the magnetic response varies according to the three different triangle classes determined by the ratio of the angles with respect to π. As the irrationality of the angles increases, the spectra show an increasing number of avoided crossings, smoothing the peaks on the magnetic susceptibility at very low temperatures. Our results suggest that ergodicity appears as the irrationality of the triangles increases.