Electron fractionalization for two-dimensional Dirac fermions

TL;DR

This paper explores how two-dimensional Dirac fermions can exhibit charge fractionalization through topological defects in a field theory, revealing new insights into fractional charge behavior without breaking time-reversal symmetry.

Contribution

It introduces a detailed analysis of fermion-number fractionalization in a (2+1)-D Dirac field theory with complex Higgs and axial gauge fields, including new formulas for fractional charge.

Findings

Fractional charge varies continuously with a parameter in the Hamiltonian.

Presence of half-vortices in axial gauge fields can rationalize fractional charge to 1/2.

Multiple techniques confirm the fractionalization phenomena.

Abstract

Fermion-number fractionalization without breaking of time-reversal symmetry was recently demonstrated for a field theory in $(2+1)$-dimensional space and time that describes the couplings between massive Dirac fermions, a complex-valued Higgs field carrying an axial gauge charge of 2, and a U(1) axial gauge field. Charge fractionalization occurs whenever the Higgs field either supports vortices by itself, or when these vortices are accompanied by half-vortices in the axial gauge field. The fractional charge is computed by three different techniques. A formula for the fractional charge is given as a function of a parameter in the Dirac Hamiltonian that breaks the spectral energy-reflection symmetry. In the presence of a charge $\pm1$ vortex in the Higgs field only, the fractional charge varies continuously and thus can take irrational values. The simultaneous presence of a half-vortex in the axial gauge field and a charge $\pm1$ vortex in the Higgs field re-rationalizes the fractional charge to the value 1/2.