Confirmation in graphene of wave packet multilooped dynamics related to fractional quantum Hall state

TL;DR

This paper explores the topological origins of fractional quantum Hall states in graphene using cyclotron braid subgroups, linking braid theory with quantum dynamics to explain experimental phenomena.

Contribution

It introduces a topological braid framework to understand fractional quantum Hall effects in graphene, including even denominator fillings and Hall metal states.

Findings

Topological braid approach explains fractional quantum Hall states in graphene.

Carrier mobility influences the emergence of fractional quantum Hall states.

Cyclotron braids relate to multilooped dynamics in quantum Hall phenomena.

Abstract

Cyclotron braid subgroups are defined in order to identify the topological origin of Laughlin correlations in 2D Hall systems. Flux-tubes and vortices for composite fermion constructions are explained in terms of unavoidably multilooped cyclotron braids. A link of braid picture with quasiclassical quantum dynamics is conjectured in order to support the phenomenological model of composite fermions with auxiliary fluxtubes, for Landau level fillings out of 1/p, p odd. The even denominator fractional lowest Landau level fillings, including Hall metal at n = 1/2, are also discussed in cyclotron braid terms. The topological arguments are utilized to explain novel experimentally observed features of the fractional quantum Hall state in graphene including the triggering role of carriers mobility for this collective state.