We report on transport signatures of eight distinct bubble phases in the N=3 Landau level of an AlxGa1-xAs/Al0.24Ga0.76As quantum well with x=0.0015. These phases occur near partial filling factors ν≈0.2(0.8) and ν≈0.3(0.7) and have M=2 and M=3 electrons (holes) per bubble, respectively. We speculate that a small amount of alloy disorder in our sample helps to distinguish these broken symmetry states in low-temperature transport measurements.

In spite of its ubiquity in strongly correlated systems, the competition of paired and nematic ground states remains poorly understood. Recently such a competition was reported in the two-dimensional electron gas at filling factor ν = 5/2. At this filling factor a pressure-induced quantum phase transition was observed from the paired fractional quantum Hall state to the quantum Hall nematic. Here we show that the pressure-induced paired-to-nematic transition also develops at ν = 7/2, demonstrating therefore this transition in both spin branches of the second orbital Landau level. However, we find that pressure is not the only parameter controlling this transition. Indeed, ground states consistent with those observed under pressure also develop in a sample measured at ambient pressure, but in which the electron-electron interaction was tuned close to its value at the quantum critical point. Our experiments suggest that electron-electron interactions play a critical role in driving the paired-to-nematic transition.

Electrostatic confinement in semiconductors provides a flexible platform for the emulation of interacting electrons in a two-dimensional lattice, including in the presence of gauge fields. This combination offers the potential to realize a wide host of quantum phases. Capacitance spectroscopy provides a technique that allows one to directly probe the density of states of such two-dimensional electron systems. Here, we present a measurement and fabrication scheme that builds on capacitance spectroscopy and allows for the independent control of density and periodic potential strength imposed on a two-dimensional electron gas. We characterize disorder levels and (in)homogeneity and develop and optimize different gating strategies at length scales where interactions are expected to be strong. A continuation of these ideas might see to fruition the emulation of interaction-driven Mott transitions or Hofstadter butterfly physics.