Dynamics of edge Majorana fermions in $\nu=\frac{5}2$ fractional quantum Hall effects

TL;DR

This paper investigates the dynamics of edge Majorana fermions in the $ u=5/2$ fractional quantum Hall effect, revealing a linear dispersion due to coupling with charged modes, a novel insight into their behavior.

Contribution

It demonstrates that charged-neutral mode coupling causes linear dispersion of edge Majorana fermions, challenging previous assumptions about their dynamics.

Findings

Neutral modes are confirmed to be chiral.

P-wave pairing does not affect neutral mode dynamics.

Coupling leads to velocity proportional to charged mode wave vector.

Abstract

Commencing with the composite fermion description of the $\nu=5/2$ fractional quantum Hall effect, we study the dynamics of the edge neutral Majorana fermions. We confirm that these neutral modes are chiral and show that a conventional p-wave pairing interaction between CFs does not contribute to the dynamics of the edge neutral fermions. We find an important bilinear coupling between the charged and neutral modes. We show that owing to this coupling, the dispersion of the neutral modes is linear and their velocities are proportional to the wave vector of the charged mode. This dynamic origin of the motion of the edge Majorana fermions was never expected before.