Mesoscopic transport and quantum chaos in ballistic quantum dots

This thesis investigates electronic transport in the ballistic, phase-coherent regime. Stadium-shaped quantum dots with quantum point contact leads are fabricated on a GaAs/AlGaAs heterostructure with a size (0.6 {dollar}mu{dollar}m {dollar}times{dollar} 1.3 {dollar}mu{dollar}m) that is smaller than the measured mean free path for impurity scattering {dollar}ell{dollar} = 3.8 {dollar}mu{dollar}m and the measured phase coherence length {dollar}ellsbphi{dollar} = 9.5 {dollar}mu{dollar}m at T = 1.5 K. Magnetotransport measurements at T = 1.5 K reveal a prominent resistance peak centered at zero magnetic field and reproducible, aperiodic conductance fluctuations at finite field. A systematic series of experiments demonstrates that coherent backscattering is the origin of the zero-field resistance peak and that this effect is distinct from conductance fluctuations at finite fields. Coherent backscattering results from constructive interference between pairs of time-reversed electron trajectories scattered from the walls of the device, analogous to weak localization in diffusive systems.; The importance of device shape in determining transport properties in the ballistic limit is investigated by measuring the T = 0.43 K magnetotransport of pairs of quantum dots fabricated in the shape of a circle and a pacman, which is a circle with a central bar. The characteristic magnetic field for both coherent backscattering (B{dollar}sb{lcub}rm c{rcub}{dollar}) and conductance fluctuations (B{dollar}sbalpha{dollar}) are strongly shape-dependent: both are larger by a factor {dollar}geq{dollar}3 in the pacman. Comparison of large and small devices of nominally identical shape shows that characteristic trajectory areas are proportional to the device area. By verifying the relationship B{dollar}sbalphacong 2 rm Bsb{lcub}c{rcub}{dollar}, we show that coherent backscattering and conductance fluctuations are independent yet complementary measures of the characteristic trajectory area.; We measure the detailed dependence of coherent backscattering, with amplitude {dollar}Deltarm Gsb0{dollar} and field scale B{dollar}sb{lcub}rm c{rcub}{dollar}, and conductance fluctuations, with amplitude {dollar}deltarm Gsb{lcub}rms{rcub}{dollar} and field scale B{dollar}sbalpha{dollar}, on the overall dot conductance G{dollar}sb{lcub}rm dot{rcub}{dollar} in the range e{dollar}sp2{dollar}/h to 6 e{dollar}sp2{dollar}/h. We find a parallel between the behavior of coherent backscattering and conductance fluctuations: at T = 1.5 K, both amplitudes {dollar}Deltarm Gsb0{dollar} and {dollar}deltarm Gsb{lcub}rms{rcub}{dollar} rise monotonically versus G{dollar}sb{lcub}rm dot{rcub}{dollar} without showing signs of leveling-off, and both field scales B{dollar}sb{lcub}rm c{rcub}{dollar} and B{dollar}sbalpha{dollar} are roughly constant versus G{dollar}sb{lcub}rm dot{rcub}{dollar}. Semiclassical theory and random matrix theory are unable to account for these results. Below T = 1.5 K, the amplitude of conductance fluctuations {dollar}deltarm Gsb{lcub}rms{rcub}{dollar} is observed to grow more rapidly with decreasing temperature than the size of coherent backscattering {dollar}Deltarm Gsb0{dollar}, suggesting that {dollar}deltarm Gsb{lcub}rms{rcub}{dollar} is attenuated by thermal averaging but that {dollar}Deltarm Gsb0{dollar} is not. Coherent backscattering becomes strikingly sensitive to gate voltage below T {dollar}approx{dollar} 200 mK. This temperature agrees with the average spacing of energy levels in the quantum dot {dollar}Delta/rm ksb{lcub}B{rcub}{dollar} = 160 mK.