Competition of Pairing and Nematicity in the Two-Dimensional Electron Gas

Abstract: Due to its extremely rich phase diagram, the two-dimensional electron gas exposed to perpendicular magnetic field has been the subject of intense and sustained study. One particularly interesting problem in this system is that of the half-filled Landau level, where the Fermi sea of composite fermions, a fractional quantum Hall state arising from a pairing instability of the composite fermions, and the quantum Hall nematic were observed in the half-filled $N=0$, $N=1$, and $N \geq 2$ Landau levels, respectively. Thus different ground states developed in different half-filled Landau levels. This situation has recently changed, when evidence for both the paired fractional quantum Hall state and the quantum Hall nematic was reported in the half-filled $N=1$ Landau level. Furthermore, a direct quantum phase transition between these two ordered states was found. These results highlight an intimate connection between pairing and nematicity, a topic of current interest in several strongly correlated systems, in a well-understood and low disorder environment.