Electronic zero modes of vortices in Hall states of gapped graphene

TL;DR

This paper investigates whether vortices in gapped graphene Hall states can host zero-energy electron modes, potentially leading to fractional charge, in the context of recent observations of phase transitions.

Contribution

It analyzes the conditions under which vortices in gapped graphene can support zero modes, exploring their potential for fractional charge in magnetic and pseudo-magnetic fields.

Findings

Vortices can host zero-energy modes under certain conditions.

Zero modes depend on the nature of the gapped state and external fields.

Implications for fractional charge in graphene vortices.

Abstract

Recent observation of a metal-insulator phase transition in the $\nu=0$ Hall state of graphene has inspired the idea that charge carriers in the metallic state could be fractionally charged vortices. We examine the question of whether vortices in particular gapped states of graphene and subject to external magnetic and pseudo-magnetic fields could have the mid-gap zero mode electron states which would allow them to be charged.