Spectral characteristics of conductance fluctuations in ballistic quantum dots: The influence of finite magnetic field and temperature

We study the influence of finite magnetic field and temperature on the spectral characteristics of the aperiodic fluctuations, observed in the magnetoresistance of GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As ballistic quantum dots. At temperatures well below 1 K, and at sufficiently low magnetic fields, the fluctuations obscure any average features in the magnetoresistance. As the magnetic field is increased, such that the cyclotron orbit size becomes much smaller than the dot dimensions, however, a strong decay in the high-frequency content of the fluctuations, and a simultaneous increase in their correlation field, is observed. We associate this behavior with a suppression of backscattering in the dot, which occurs as well-defined edge states begin to form, and in order to account for our observations we apply simple model, which considers the flux enclosed by skipping orbits localized at the dot walls. Increasing the temperature, the amplitude of the fluctuations is found to decay exponentially, while their correlation field remains roughly unchanged. This scaling is very different from that observed in disordered systems, and is argued to be due to the absence of large-scale disorder in ballistic dots. Finally, we confirm the ballistic nature of transport in the dots by considering the form of the weak localization peak observed at low-field magnetic fields, and discuss our results in relation to theoretical predictions for ballistic dots with chaotic geometries.