Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus

Abstract

Recent quantum Hall experiments have observed `daughter states' next to several plateaus at half-integer filling factors in various platforms. These states were first proposed based on model wavefunctions for the Moore-Read state by Levin and Halperin. We show that these daughters and their parents belong to an extensive family tree that encompasses all pairing channels and permits a unified description in terms of weakly interacting composite fermions. Each daughter represents a bosonic integer quantum Hall state formed by composite-fermion pairs. The pairing of the parent dictates an additional number of filled composite-fermion Landau levels. We support our field-theoretic composite-fermion treatment by using the K-matrix formalism, analysis of trial wavefunctions, and a coupled-wire construction. Our analysis yields the topological orders, quantum numbers, and experimental signatures of all daughters of paired states at half-filling and `next-generation' even-denominators. Crucially, no two daughters share the same two parents. The unique parentage implies that Hall conductance measurements alone could pinpoint the topological order of even-denominator plateaus. Additionally, we propose a numerically suitable trial wavefunction for one daughter of the SU(2)${}_2$ topological order, which arises at filling factor $\nu =\frac{6}{11}$. Finally, our insights explain experimentally observed features of transitions in wide-quantum wells, such as suppression of the Jain states with the simultaneous development of half-filled and daughter states.

11 pages, 4 figures

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• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene