We study effects of the oft-neglected cubic Dresselhaus spin-orbit coupling (i.e., directly proportional p3) in GaAs/AlGaAs quantum dots. Using a semiclassical billiard model, we estimate the magnitude of the spin-orbit induced avoided crossings in a closed quantum dot in a Zeeman field. Using previous analyses based on random matrix theory, we calculate corresponding effects on the conductance through an open quantum dot. Combining our results with an experiment on an 8 microm2 quantum dot [D. M. Zumbühl, Phys. Rev. B 72, 081305 (2005)10.1103/PhysRevB.72.081305] suggests that (1) the GaAs Dresselhaus coupling constant gamma is approximately 9 eV A3, significantly less than the commonly cited value of 27.5 eV A3, and (2) the majority of the spin-flip effects can come from the cubic Dresselhaus term.
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