Half vortex and fractional electrical charge in two dimensions

TL;DR

This paper demonstrates that in two-dimensional Dirac systems, topological half-vortices in the order parameter can host fractional electrical charge of e/2, with potential realization in graphene under magnetic fields.

Contribution

It introduces a new topological defect configuration in 2D Dirac systems that supports fractional charge, and analyzes its properties within an eight-dimensional Dirac Hamiltonian.

Findings

A half-vortex supports a single zero mode and fractional charge e/2.

In graphene, an in-plane magnetic field can induce a phase supporting such vortices.

The phase can emerge even with weak interactions due to excitonic instability.

Abstract

Despite fermion doubling, a two-dimensional quasi-relativistic spin-1/2 system can still lead to true fractionalization of electrical charge, when a massive ordered phase supports a "half-vortex". Such topological defect is possible when the order parameter in form of Dirac mass is described by two $U(1)$ angles, and each of them winds by an angle $\pi$ around a point. We demonstrate that such a mass configuration in an eight-dimensional Dirac Hamiltonian exhibits only a single bound zero mode, and therefore binds the charge of $e/2$. In graphene, for example, such an ordered phase is provided by the easy-plane spin-triplet Kekule valence bond solid. We argue that an application of an in-plane magnetic field can cause an excitonic instability toward such ordered phase, even for weak repulsion, when the on-site, nearest-neighbor and second neighbor components of it are of comparable strengths.