Interaction and localization are two fundamental pillars in understanding the physics of solid-state systems. In quantum Hall systems, through the application of a strong magnetic field, the kinetic energy of the electrons can be quenched sufficiently so that the dominant energy scale is the Coulomb repulsion between electrons. The strong electron-electron correlations lead to exotic physics like the many-body liquid phase, called the fractional quantum Hall states (FQHSs) and many-body solid phase, namely the Wigner crystal (WC). However, the inherent disorder in the material deters the development of such novel states and leads to deviations from ideal behavior.

Recent improvements in molecular beam epitaxy have enabled the growth of extremely pure, ultra-high-quality GaAs crystals. In this talk, I will present my PhD research on the interplay of interaction and disorder in GaAs two-dimensional electron systems, particularly in the limit of very low disorder. For the case of strongly correlated liquids, we observe that only certain transitions between the FQHSs obey the theoretically predicted localization physics, where composite fermions, the emergent quasiparticle in FQHSs, are non-interacting. In the limit of weak disorder, we find that composite fermions themselves can be interacting, and so, there are departures from localization theories for FQHSs. Moving on to the WC regime, the ultra-high sample purity facilitates the formation of extremely large WC domains. Consequently, the energy gap of the WC state, one of the most fundamental parameters characterizing the WC, is now in excellent quantitative agreement with theoretical models that do not include disorder in calculations. However, the presence of the residual disorder plays a significant role when the WC is forced to move under the application of a driving DC-current. Surprisingly, we observe that less-disordered WCs exhibit new, additional structure in transport and noise measurements, revealing a richer dynamic phase diagram.
 

Adviser: Mansour Shayegan