Transport study on two-dimensional electrons with controlled short-range alloy disorder.

摘要

Disorder plays an important role in almost all aspects of solid state physics. However, due to the complexity in the nature of disorder, it is usually hard to experimentally study its effect in a controllable way.;We present in this thesis the first systematic study on disorder-related physics in two-dimensional electron systems (2DES). Our samples are modulation doped AlxGa1-xAs-Al 0:3Ga0:7As heterostructures with a broad range of Al impurity concentration x. We have shown that the alloy potential fluctuation in these systems has a range of atomic dimension and amplitude of 1.13eV. The relative weight of short-range alloy disorder increases in samples with larger x.;With the 2DES samples of controlled alloy disorder, we have investigated the quantum Hall plateau-to-plateau transition in the integer quantum Hall regime. We have unambiguously verified that the plateau-to-plateau transition is a universal quantum phase transition, and built up a framework to understand the role that disorder plays in this transition.;When the disorder in the system is dominated by short-range alloy potential fluctuations, we have found a perfect power-law temperature scaling dRxydB&vbm0;B=B c ∝ T-kappa with a universal exponent kappa = 0:42 over two full decades of temperature. The inelastic scattering exponent p is identified to be 2 by an experiment on samples of various sizes. The localization length exponent nu = 2:4 is therefore verified by the experimentally measured values of kappa and p.;In systems with disorder being dominated by long-range Coulomb potential fluctuations, a semi-classical exponent kappa = 0:58 is observed at high temperatures. Below a crossover temperature Tc, the universal exponent kappa = 0:42 is restored, as the quantum phase coherence length becomes much longer than the Coulomb disorder range.;For samples with very high Al concentrations, alloy clustering is likely, and the effective sample size is determined by a hidden length scale related with the cluster size. As a result, the exponent kappa = 0.58 persists into low temperatures until dRxydB&vbm0;B=B c saturates at 65mK, a relatively high temperature.;We have further investigated the physics in the Fractional quantum Hall effect (FQHE) and Wigner crystal regime at high magnetic fields. We have found that alloy disorder does not affect the FQH gaps while it enhances the formation of Wigner crystals. As a result the terminal FQH state in systems with alloy disorder has been shifted to nu = ⅓. More excitingly, we have observed the nu = 1 reentrant integer quantum Hall effect, which is a direct manifestation of the particle-hole symmetry in the Wigner crystal phase of the lowest Landau level.;In both regimes, we have therefore found that the range of disorder plays critical roles. Our experimental methods with controlled short-range alloy disorder have been proved to be powerful in the investigation of disorder-related physics.