Composite fermion duality for half-filled multicomponent Landau Levels

TL;DR

This paper explores the duality and particle-hole symmetry in multicomponent half-filled Landau levels, showing how different theoretical descriptions converge and analyzing phase transitions and emergent phenomena in quantum Hall systems.

Contribution

It demonstrates the equivalence of particle-hole symmetric pairing and electron exciton condensates in bilayer systems using Dirac fermion theory and RG analysis, extending to multicomponent systems.

Findings

Particle-hole symmetric interlayer pairing matches the electron exciton condensate phase.

RG analysis indicates a smooth transition from decoupled Fermi liquids to exciton condensate.

Derived phases include a $Z_2$ gauge theory with spin-half visons and symmetry-enforced gaplessness for even component systems.

Abstract

We study the interplay of particle-hole symmetry and fermion-vortex duality in multicomponent half-filled Landau levels, such as quantum Hall gallium arsenide bilayers and graphene. For the $\nu{=}1/2{+}1/2$ bilayer, we show that particle-hole-symmetric interlayer Cooper pairing of composite fermions leads to precisely the same phase as the electron exciton condensate realized in experiments. This equivalence is easily understood by applying the recent Dirac fermion formulation of $\nu{=}1/2$ to two components. It can also be described by Halperin-Lee-Read composite fermions undergoing interlayer $p_x{+}ip_y$ pairing. An RG analysis showing strong instability to interlayer pairing at large separation $d\rightarrow \infty$ demonstrates that two initially-decoupled composite Fermi liquids can be smoothly tuned into the conventional bilayer exciton condensate without encountering a phase transition. We also discuss multicomponent systems relevant to graphene, derive related phases including a $Z_2$ gauge theory with spin-half visons, and argue for symmetry-enforced gaplessness under full SU$(N_f)$ flavor symmetry when the number of components $N_f$ is even.