Collective Insulators in the Integer and Fractional Quantum Hall Regimes in the Limit of Low Disorder

The two-dimensional electron gas subject to a perpendicular magnetic field is one of the most extensively studied systems and remains a topic of significant interest in condensed matter physics. The integer quantum Hall effect, resulting from Landau quantization, was one of the first identified topological ground states. This quantization originates from the flat nature of the electronic bands. If, in addition, strong electron-electron interactions are present, a rich variety of more complex topological ground states forms.

Fractional quantum Hall states are examples of complex topological ground states generated by electron-electron interaction. A simple and elegant way to account for the physics of the fractional quantum Hall regime is through the emergent particle called composite fermions. Additionally, electron interactions can lead to the formation of collective insulating phases, where bulk electrons form charge-ordered structures and become localized by sample disorder. Due to their charge-ordered nature, these states can be characterized by symmetry-breaking in the bulk. Charge-ordered bulk states were first predicted and observed in the extreme quantum limit at extremely low filling factors, named high-field Wigner solids. More complex collective insulating states, where multiple electrons cluster, called the bubble phase, were later predicted by numerical calculations. These bubble phases were soon confirmed by magnetotransport measurements featuring the reentrant integer quantum Hall effect and also by other experimental techniques.

Between the high-field Wigner solid and the second Landau level lies a regime dominated mainly by composite fermions, where numerous fractional quantum Hall states have been observed. Although multi-electron bubble phases are not expected in the lowest Landau level, numerical calculations suggest that an integer quantum Hall Wigner solid may emerge in the flanks of the integer quantum Hall state at filling factors deviating slightly from the integer number. Indeed, multiple experimental techniques have probed solid-phase behavior in this regime, However, transport evidence remains limited, and it remains an open question whether features observed in multi-electron bubble phases also manifest in these states.

Moreover, composite fermions, despite experiencing a reduced effective magnetic field, display similarities to electrons. As a result, charge-ordered composite fermion phases are also expected to form. Indeed, at sufficiently small filling factors, the high-field composite fermion Wigner solid is energetically favored over the electronic Wigner solid. Additionally, although not previously probed experimentally, Hartree-Fock numerical calculations predict the existence of multi-composite fermion bubble phases.

In this dissertation, we present our research on several collective insulating states in both the integer and fractional quantum Hall regimes at the lowest Landau level. Chapter 2 details our study of the integer quantum Hall Wigner solid. Here, we present the magnetotransport behavior of several latest-generation GaAs samples. In both samples, we observe reentrant integer quantum Hall states, which we interpret as integer quantum Hall Wigner solids, in the flanks of the ν = 1 integer quantum Hall state. The charge-ordered nature of this localization is further confirmed by the non-monotonic temperature dependence of the longitudinal resistance, a characteristic commonly used to indicate the solid nature of bubble phases. Interestingly, at base temperatures, the reentrant states and the integer quantum Hall states between them merge into a single plateau, suggesting a continuous transition from a randomly localized ground state to a collective insulating ground state. To further probe this phase crossover, we construct phase stability diagrams and calculate the thermal activation energies from the data. We also conduct a quantitative comparison between the samples. Furthermore, we perform a large-signal non-linear measurement suggesting this Wigner solid may have a different depinning mechanism than the bubble phases observed at higher Landau levels.

Chapter 3 provides experimental evidence for a novel ground state between the fractional quantum Hall states at ν = 5/3 and ν = 8/5, which we believe can be described as a bubble phase of composite fermions. This novel phase features a new phenomenon, the reentrant fractional quantum Hall state, where the Hall resistance is re-quantized to a fractional value rather than an integer value, as seen in the reentrant integer quantum Hall effect. This is the first observation of such a reentrant fractional quantum Hall state, which we interpret as a composite fermion bubble phase, a strongly correlated insulating phase. We present the magnetotransport data from a high-quality GaAs sample and discuss the possible candidate ground states for this reentrant behavior. Our analysis suggests that this phase is a bubble phase of composite fermions, based on the observed fractional statistics and supported by Hartree-Fock numerical calculations.