Coherent states of graphene layer with and without a PT-symmetric chemical potential

In this paper we construct different classes of coherent and bicoherent states for the graphene tight-binding model in presence of a magnetic field, and for a deformed version where we include a $PT$-symmetric chemical potential $V$. In particular, the problems caused by the absence of a suitable ground state for the system is taken into account in the construction of these states, for $V=0$ and for $V\ne 0$. We introduce ladder operators which work well in our context, and we show, in particular, that there exists a choice of these operators which produce a factorization of the Hamiltonian. The role of broken and unbroken $PT$-symmetry is discussed, in connection with the strength of $V$.