Symmetry of magnetoconductance fluctuations of quantum dots in the nonlinear response regime

We investigate the symmetry of magnetoconductance fluctuations of phase-coherent, two-terminal quantum dots in the nonlinear regime of transport. Specifically, we consider open, ballistic quantum dots (electron billiards) with and without symmetry axes parallel and perpendicular to the current direction and formulate a set of novel symmetry relations not observed in devices with lower symmetry. We experimentally confirm these relations, demonstrating that high-quality materials and modern semiconductor technology allow the fabrication of devices with almost perfect symmetry. Small deviations from the intended symmetry, presumably due to impurities and fabrication limitations, do exist and can be detected. We also take into account circuit-induced asymmetries of the measured conductance due to bias-dependent depletion and demonstrate that this effect can be experimentally distinguished from rectification effects that are due to a lack of device symmetry. Some open questions regarding the role of a magnetic field in the nonlinear regime of transport are highlighted.