Theory of Next-Generation Even-Denominator States

Abstract

Even-denominator quantum Hall states are leading candidates for realizing non-Abelian topological orders, with the $\nu=\frac{5}{2}$ plateau in GaAs the first and most-studied example. Recent experiments in GaAs and bilayer graphene (BLG) have observed many `next-generation' even-denominator states at filling factors such as $\nu=\frac{3}{4}$, $\frac{3}{8}$, and $\frac{3}{10}$. We develop the theory of these states, including analyses of their bulk quasiparticles, of methods for distinguishing between pairing channels in edge transport measurements, and of their trial wavefunctions. As part of this study, we derive general relations of how flux attachment affects many universal properties of states. In particular, we prove that the topological stability of interface modes is invariant under flux attachment. We compare next-generation paired states to Bonderson-Slingerland states at the same filling factors, and demonstrate that their quasiparticles carry identical charges and obey the same exchange statistics. The next-generation and Bonderson-Slingerland states still describe distinct phases, and we find that the former are energetically favored in the lowest Landau level, while the latter are favored in the first excited level.