Identification of topological order in the fractional quantum Hall state at ν=1/4

Abstract

The nature of the fractional quantum Hall state at quarter filling in a wide quantum well is still under debate. Both one-component non-Abelian and two-component Abelian orders have been proposed to describe the system. Interestingly, these candidates received support from different experiments under disparate conditions. In this article, we focus on non-Abelian orders from Cooper pairing between composite fermions and the Abelian Halperin-(5,5,3) order. We discuss and predict systematically different experimental signatures to identify them in future experiments. In particular, we address the Mach-Zehnder interferometry experiment and show that it can identify the recently proposed 22111 parton order. arXiv:1909.04265v2 [cond-mat.str-el] 25 Nov 2019 II. ONE-COMPONENT NON-ABELIAN ORDERS FOR ν = 1/4 FQHE

Fractional charge and fractional statistics in the quantum Hall effects

“…Evidence exists for a ν = 1/4 plateau in wide GaAs quantum wells [200][201][202]. The 16-fold way was extended to that filling factor in [203].…”

“…The precise expression for the current depends on the details of statistics [10,160,203,223,224,[226][227][228][229][230] and simplifies greatly for the Laughlin states at zero temperature [223]. Figure 14 illustrates possible transitions between topological charges of the drain at the Laughlin filling factors ν = 1/m.…”

Very high-energy collective states of partons in fractional quantum Hall liquids

“…It would be interesting to further explore the utility of the effective field theory, Eq. ( 8), at describing the gapless composite Fermi liquid states at filling ν=1/(2p) as well as their pairing instabilities that would describe gapped states at these even-denominator fillings [89]. When it comes to gapped states in the vicinity of ν=1/(2p), it would be interesting to perform the wavenumber expansion to one more order and compute the projected static structure factor to the 6th order in momentum expansion.…”

Fractional charge and fractional statistics in the quantum Hall effects

“…(The contradiction with the Byers-Yang theorem would be unavoidable if fractional charges could have Bose or Fermi statistics.) The precise expression for the current depends on the details of statistics [10,151,194,214,215,[217][218][219][220][221] and simplifies greatly for the Laughlin states at zero temperature [214]. Fig.…”