Transitions from Composite Fermi Liquid to Moore-Read States in Weyl Semimetals

Abstract: Weyl semimetals represent a significant class of topological gapless materials in three dimensions and have been shown to exhibit three-dimensional quantum Hall effect. However, existing research mainly focuses on scenarios without interactions. Recent studies suggest that the fractional quantum Hall effect can arise in a Weyl semimetal with a one-third filled Landau level under a magnetic field. However, it remains unclear whether more exotic states, such as composite Fermi liquid and MooreRead states, can appear at half filling. Here we surprisingly find the existence of composite Fermi liquid, Moore-Read states and charge density waves in the same Weyl-orbit-based Landau level of a Weyl semimetal and their transitions induced by varying the distance between Weyl points. We attribute these transitions to a significant change in the single-particle wave functions of the Landau level as the distance between Weyl points is varied. Finally, we demonstrate that a transition from composite Fermi liquid to Moore-Read states can be induced by tuning the direction of a magnetic field, a process that is more experimentally accessible.