(Anti-)de Sitter, Poincar\'{e}, Super symmetries, and the two Dirac points of graphene

TL;DR

This paper explores theoretical correspondences between high-energy physics and graphene, focusing on topological defects like grain boundaries that involve both Dirac points, proposing models with torsion, de Sitter symmetry, and unconventional supersymmetry.

Contribution

It introduces two novel high-energy-theory models linking graphene defects to theories with torsion and supersymmetry, expanding the emergent field theory framework for material defects.

Findings

Proposes a (3+1)-dimensional theory with torsion and Lorentz/de Sitter symmetry.

Links two Dirac points to unconventional supersymmetry with SU(2) symmetry.

Suggests new avenues for including grain boundaries in emergent field theories.

Abstract

We propose two different high-energy-theory correspondences with graphene (and related materials) scenarios, associated to grain boundaries, that are topological defects for which both Dirac points are necessary. The first correspondence points to a $(3+1)$-dimensional theory, with nonzero torsion, with spatiotemporal gauge group $SO(3,1)$, locally isomorphic to the Lorentz group in $(3+1)$ dimensions, or to the de Sitter group in $(2+1)$ dimensions. The other correspondence treats the two Dirac fields as an internal symmetry doublet, and it is linked here with unconventional supersymmetry with $SU(2)$ internal symmetry. Our results are suggestive, rather than conclusive, and pave the way to the inclusion of grain boundaries in the emergent field theory picture associated with these materials, whereas disclinations and dislocations have been already well explored.