N$$ \mathcal{N} $$ -extended D = 4 supergravity, unconventional SUSY and graphene

We derive a 2+1 dimensional model with unconventional supersymmetry at the boundary of an 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, K and K′. The two valleys correspond to the two independent sectors of the OSp(p|2) × 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.