Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect

TL;DR

This paper investigates how the GMP density-wave excitation in fractional quantum Hall states splits into more elementary excitations, revealing new insights into the correlations and nature of chiral gravitons in these states.

Contribution

It demonstrates that the GMP mode splits into elementary excitons at specific filling factors, providing a novel understanding of excitations in fractional quantum Hall states.

Findings

GMP mode remains undivided at certain filling factors

GMP mode splits into two gravitons at other filling factors

Splitting offers insights into FQH correlations and chiral gravitons

Abstract

A fundamental manifestation of the nontrivial correlations of an incompressible fractional quantum Hall (FQH) state is that an electron added to it disintegrates into more elementary particles, namely fractionally-charged composite fermions (CFs). We show here that the Girvin-MacDonald-Platzman (GMP) density-wave excitation of the $\nu{=}n/(2pn{\pm }1)$ FQH states also splits into more elementary single CF excitons. In particular, the GMP graviton, which refers to the recently observed spin-2 neutral excitation in the vanishing wave vector limit [Liang {\it et al.}, Nature {\bf 628}, 78 (2024)], remains undivided for $\nu{=}n/(2n{\pm} 1)$ but splits into two gravitons at $\nu{=}n/(4n{\pm} 1)$ with $n{>}1$. A detailed experimental confirmation of the many observable consequences of the splitting of the GMP mode should provide a unique window into the correlations underlying the FQH effect.