  First of all, we reconsider the tight - binding model of monolayer graphene,
in which the variations of the hopping parameters are allowed. We demonstrate
that the emergent 2D Weitzenbock geometry as well as the emergent U(1) gauge
field appear. The emergent gauge field is equal to the linear combination of
the components of the zweibein. Therefore, we actually deal with the gauge
fixed version of the emergent 2+1 D teleparallel gravity. In particular, we
work out the case, when the variations of the hopping parameters are due to the
elastic deformations, and relate the elastic deformations with the emergent
zweibein. Next, we investigate the tight - binding model with the varying
intralayer hopping parameters for the multilayer graphene with the ABC
stacking. In this case the emergent 2D Weitzenbock geometry and the emergent
U(1) gauge field appear as well, the emergent low energy effective field theory
has the anisotropic scaling.
