Splitting of roton minimum in the \nu=5/2 Moore-Read state

TL;DR

This paper predicts a splitting in the roton mode of the /2 Moore-Read quantum Hall state caused by Majorana modes, suggesting optical spectroscopy could detect non-abelian anyonic excitations.

Contribution

It introduces a calculation of the dynamical structure factor revealing a fermionic degree of freedom-induced splitting in the roton mode for the /2 state.

Findings

Splitting of the roton mode due to Majorana fermions.

Potential experimental detection via optical spectroscopy.

Evidence for non-abelian anyons in quantum Hall systems.

Abstract

We calculate the dynamical structure factor of the \nu=5/2 non-abelian quantum Hall state in the dipole approximation, valid for large momenta. Due to the fact that both quasi-particles (qps) and quasi-holes (qhs) have an internal Majorana degree of freedom, a qp-qh pair has a fermionic degree of freedom which can be either empty or occupied, and leads to a splitting of the roton mode. Observation of this splitting by means of finite wavelength optical spectroscopy could provide evidence for Majorana modes in the \nu=5/2 quantum Hall state.