Identifying the topological order of quantized half-filled Landau levels through their daughter states

Abstract

Fractional quantum Hall states at a half-filled Landau level are believed to carry an integer number $\mathcal{C}$ of chiral Majorana edge modes, reflected in their thermal Hall conductivity. We show that this number determines the primary series of Abelian fractional quantum Hall states that emerge above and below the half-filling point. On a particular side of half-filling, each series may originate from two consecutive values of $\mathcal{C}$, but the combination of the series above and below half-filling uniquely identifies $\mathcal{C}$. We analyze these states both by a hierarchy approach and by a composite fermion approach. In the latter, we map electrons near a half-filled Landau level to composite fermions at a weak magnetic field and show that a bosonic integer quantum Hall state is formed by pairs of composite fermions and plays a crucial role in the state's Hall conductivity.

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Cited by in corpus (7)

• Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• Non-Abelian phases from the condensation of Abelian anyons
• Ordering the topological order in the fractional quantum Hall effect
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene