Spin-Orbit Effects in a GaAs Quantum Dot in a Parallel Magnetic Field

We analyze the effects of spin-orbit coupling on fluctuations of the conductance of a quantum dot fabricated in a GaAs heterostructure. Counterintuitively we argue that spin-orbit effects may become important in the presence of a large parallel magnetic field $B_{\parallel }$, even if they are negligible for $B_{\parallel }=0\mathrm{}$. This should be manifest in the level repulsion of a closed dot, and in reduced conductance fluctuations in dots with a small number of open channels in each lead, for large $B_{\parallel }$. Our picture is consistent with the experimental observations of Folk et al.