Phase breaking in ballistic quantum dots: Transition from two- to zero-dimensional behavior

We determine the phase-breaking time ${\mathrm{\tau }}_{\mathrm{\phi }}$ of electrons in ballistic quantum dots, from the aperiodic fluctuations observed in their low-temperature magnetoconductance. Our analysis shows that at temperatures close to a degree Kelvin ${\mathrm{\tau }}_{\mathrm{\phi }}$ scales roughly inversely with temperature, reminiscent of electron-electron scattering in two-dimensional disordered systems. At much lower temperatures, however, a saturation in ${\mathrm{\tau }}_{\mathrm{\phi }}$ is observed, with the transition between the two regimes occurring once the thermal smearing becomes smaller than the expected level spacing in the dot. We therefore suggest that the saturation results from a transition from two- to zero-dimensional transport, as the discrete level structure of the dot becomes resolved.