A Lorentz-violating low-energy model for the bilayer graphene

In this work, we propose a model with Lorentz symmetry violation which describes the electronic low energy limit of AA-bilayer graphene (BLG) system. The AA-type bilayer is known to preserve linear dispersion relation layer in limit. theoretical shows that BLG system, time-like vector can be associated separation and contributes eigenstates. Based on these properties, describe $(2+1)$-dimensional space-time fermionic quasi-particles emerge low-energy introduction Lorentz-violating parameter, analogy $(3 + 1)$-dimensional Standard Model Extension (SME). Moreover, study consequences coupling electromagnetic field, show via effective action photon acquires massive spectrum. Finally, using hydrodynamic approach collisionless limit, one finds LSV generates new kind anomalous thermal current vortexes system vector.