Wess-Zumino supersymmetric phase and superconductivity in graphene

Agradecimentos: The authors would like to thank the Brazilian agency CNPq for partial financial support. They also thank the anonymous referees for useful suggestions and discussion Abstract: Supersymmetry is expected to exist in nature at high energies, but must be spontaneously broken at ordinary energy scales. The required energy scale in elementary particle physics is currently inaccessible, but condensed matter could furnish low energy realizations of supersymmetry. In graphene, electrons behave as 'relativistic' massless fermions in 1 + 2 dimensions. Here we propose phenomenologically, assuming that some microscopic parameters can be fine-tuned in graphene, the existence of a supersymmetric Wess-Zumino phase. The supersymmetry breaking leads to a superconductor phase, described by a relativistic Ginzburg-Landau phenomenology CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ Aberto