Asymmetric spatial structure of zero modes for birefringent Dirac fermions

TL;DR

This paper investigates zero energy modes in a model with birefringent Dirac fermions, revealing an unusual vortex configuration where length scales vary arbitrarily without affecting quantum number fractionalization.

Contribution

It introduces a novel vortex configuration in birefringent Dirac fermion systems and analyzes the asymmetric spatial structure of zero modes with numerical validation.

Findings

Length scales of zero modes can be arbitrarily varied.

Quantum number fractionalization remains unaffected.

Numerical results confirm theoretical predictions.

Abstract

We study the zero energy modes that arise in an unusual vortex configuration involving both the kinetic energy and an appropriate mass term in a model which exhibits birefringent Dirac fermions as its low energy excitations. We find the surprising feature that the ratio of the length scales associated with states centered on vortex and anti-vortex topological defects can be arbitrarily varied but that fractionalization of quantum numbers such as charge is unaffected. We discuss this situation from a symmetry point of view and present numerical results for a specific lattice model realization of this scenario.