$\mathcal{N}$-Extended $D=4$ Supergravity, Unconventional SUSY and Graphene

TL;DR

This paper develops a boundary model with unconventional supersymmetry derived from 4D supergravity, providing a top-down approach to describe electronic properties of graphene-like materials at the Dirac points.

Contribution

It introduces a novel 2+1D boundary model with extended supersymmetry from supergravity, linking torsion parameters to graphene mass terms.

Findings

Boundary model captures electronic properties of graphene.

Valleys correspond to independent sectors related by parity.

Mass parameters are identified with substrate torsion.

Abstract

We derive a $2+1$ dimensional model with unconventional supersymmetry at the boundary of an ${\rm AdS}_4$ $\mathcal{N}$-extended supergravity, generalizing previous results. The (unconventional) extended supersymmetry of the boundary model is instrumental in describing, within a top-down approach, the electronic properties of graphene-like 2D materials at the two Dirac points, ${\bf K}$ and ${\bf K}'$. The two valleys correspond to the two independent sectors of the ${\rm OSp}(p|2)\times {\rm OSp}(q|2)$ boundary model in the $p=q$ case, which are related by a parity transformation. The Semenoff and Haldane-type masses entering the corresponding Dirac equations are identified with the torsion parameters of the substrate in the model.