Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate

TL;DR

This paper presents a real-space formulation of exciton condensates in bilayer graphene, revealing that vortices can bind zero modes and exhibit fractionalization, with implications for charge properties and topological features.

Contribution

It introduces a real-space approach to analyze vortices in bilayer graphene exciton condensates and demonstrates the existence of zero modes bound to vortices in the continuum limit.

Findings

Oddly-quantized vortices bind exactly one zero mode per valley.

Zero modes are split in the lattice model due to intervalley mixing.

Numerical diagonalization confirms the zero modes and their properties.

Abstract

A real-space formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly-quantized vortex in this condensate binds exactly one zero mode per valley index of the bilayer. In the full lattice model the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties.