Theory Advances Next-Generation Even-Denominator States at Filling Factors

Researchers are increasingly focused on understanding even-denominator quantum Hall states, potentially unlocking pathways to realising non-Abelian topological orders. Misha Yutushui (Weizmann Institute of Science, University of Cologne) and David F. Mross, alongside David F. Yutushui, present a new theoretical framework for these ‘next-generation’ states, recently observed in experiments with gallium arsenide and bilayer graphene at filling factors such as 1/2, 1/4 and 1/6. This work is significant because it not only analyses the fundamental properties of these states , including their quasiparticles and edge transport , but also establishes clear distinctions between them and previously proposed Bonderson-Slingerland states, predicting which phase will dominate under specific conditions. Crucially, the team demonstrates the topological stability of interface modes remains unaffected by flux attachment, offering a powerful tool for characterising these exotic quantum systems.

This work is significant because it not only analyses the fundamental properties of these states, including their quasiparticles and edge transport, but also establishes clear distinctions between them and previously proposed Bonderson-Slingerland states, predicting which phase will dominate under specific conditions.

Even-denominator Quantum Hall State Theory Explained—a fascinating glimpse

This nuanced understanding of energy level preferences provides crucial insight into the stability and behaviour of these exotic quantum states under varying conditions. The most direct observable for this distinction is the thermal Hall conductance, though challenges with its measurement and interpretation have spurred the search for alternative probes. This work proposes upstream-noise measurements as a viable alternative, corroborating previous findings that identified a PH-Pfaffian topological order at ν = 5/2. The research extends this analysis to other even-denominator fillings, such as ν = 3/8 and 3/10, where similar questions regarding competing topological orders arise, and plateaus cannot be explained by weakly interacting composite fermion superfluids.

This theoretical framework views these states as strongly interacting composite fermions forming half-filled states, generalising the understanding of half-integer quantum Hall states and their experimental signatures to these next-generation systems. This energetic preference offers a pathway for experimental verification of the dominant phase present in a given system. Data shows that the quasiparticle content of an Abelian topological order is efficiently encoded in a K-matrix and a charge vector, with the filling factor determined by ν = tT K−1t. The team derived that the attachment of 2p fluxes modifies the K-matrix as K = K∗ + 2pttT, while the charge vector remains unchanged. Importantly, the determinant of K is related to that of K∗ by det K = (1 + 2pν∗) det K∗, indicating a potential increase in the number of distinct quasiparticle excitations with flux attachment when |1 + 2pν∗| 1. Acknowledging limitations, the authors note that their analysis doesn’t rely on specific assumptions about the filling factor, maintaining applicability across various next-generation states. They also highlight the equivalence between next-generation states and particle-hole conjugates of first-generation states, suggesting alternative descriptions of the same topological phase.