Emergent geometry experienced by fermions in graphene in the presence of dislocations

TL;DR

This paper explores how fermionic quasiparticles in strained graphene experience a different emergent curved space metric than the elastic theory predicts, especially near dislocations, affecting their scattering behavior.

Contribution

It clarifies the relationship between elastic and fermionic metrics in graphene and analyzes the effects of dislocations, including torsion and emergent magnetic fields, on quasiparticle scattering.

Findings

Dislocations carry singular torsion and quantized emergent magnetic flux.

Emergent magnetic flux causes Aharonov-Bohm effect in quasiparticle scattering.

Torsion singularity leads to the Stodolsky effect.

Abstract

In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov - Bohm effect while the torsion singularity results in Stodolsky effect.