Magnetic field induced inequivalent vortex zero modes in strained graphene

TL;DR

This paper explores how magnetic fields induce inequivalent zero energy vortex modes in strained graphene, affecting charge and magnetization oscillations, and proposes experimental setups to observe these effects.

Contribution

It demonstrates the existence of inequivalent zero modes with different length scales in strained graphene under magnetic fields, and discusses their implications for charge, magnetization, and potential Majorana modes.

Findings

Zero energy states with different length scales in strained graphene vortex cores.

Oscillatory charge and magnetization due to inequivalent zero modes.

Possibility of localizing single Majorana modes near topological defects.

Abstract

Zero energy states in the Dirac spectrum with U(1) symmetric massive vortices of various underlying insulating orders in strained graphene are constructed in the presence of the magnetic field. An easy plane vortex of antiferromagnet and quantum spin Hall orders host two zero energy states, however, with two different length scales. Such inequivalent zero modes can lead to oscillatory charge and magnetization, and their usual quantizations get restored only far from the vortex core. Otherwise, these zero modes can be delocalized from each other by tuning the mutual strength of two fields. One can, therefore, effectively bind a single zero mode in the vortex core. A possible experimental set up to capture signature of this theory in real graphene as well as in optical honeycomb lattices is mentioned. Generalization of this scenario with underlying topological defects of Kekule superconductors can localize a single Majorana mode in the vicinity of the defect-core.