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

TL;DR

This paper provides a unified theoretical framework for understanding daughter states in quantum Hall systems at half-integer fillings, revealing their topological properties, experimental signatures, and relation to parent states using composite fermion models.

Contribution

It introduces a comprehensive description of daughter states as bosonic quantum Hall states formed by composite-fermion pairs, extending the understanding of pairing channels in quantum Hall effects.

Findings

All daughter states can be described within a unified composite fermion framework.

Hall conductance measurements can identify the topological order of even-denominator plateaus.

A trial wavefunction for a specific daughter state at filling factor 6/11 is proposed.

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.