On valley asymmetry in a topological interaction for quasi-particles

This paper is focused on investigating the effects of a statistical interaction for graphene-like systems, providing Haldane-like properties for topologically trivial lattices. The associated self-energy correction yields an effective next-nearest hopping, inducing the topological phase, whose specific solutions are scrutinized. In the case of an external magnetic field, it leads to a renormalized quasi-particle structure with generalized Landau levels and explicit valley asymmetry. A suitable tool for implementing such achievements is a judicious indefinite metric quantization, leading to advances in field theory foundations. Since the topological behavior is encoded in the radiative corrections, an unequivocal treatment using an integral representation is carefully developed.