Conductance oscillations related to the eigenenergy spectrum of a quantum dot in weak magnetic fields

The electron transport through a quantum dot, defined by the electrostatic potential of four Schottky gates on top of a GaAs-${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{-}\mathit{x}}$As heterostructure, was studied experimentally. The dot was connected to the surrounding two-dimensional electron gas by two variable quantum point contacts. The conductance, measured either as a function of gate voltage or magnetic field, showed characteristic variations: conductance maxima recurrently appear when the gate voltage is varied and conductance maxima are observed to shift approximately linearly in position when the magnetic field is varied. The measurement is compared with a transport model, where the eigenenergy spectrum is calculated for an isolated perfectly circular disk, with qualitative agreement regarding the characteristic variations of conductance and in Fourier power spectra of magnetoconductance. The conductance variations are related to the density of states at the Fermi energy. They cannot be attributed to single levels because the number of electrons in the dot was too large (approximately 1700 electrons), but originate from a shell structure with coincident energy levels.