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

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 wave functions 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 wave functions, 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 wave function for one daughter of the SU(2)2 topological order, which arises at filling factor ν=611. 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.