Transfer matrix in 1D Dirac-like problems

The transfer matrix method is considered to obtain the fundamental properties of 1D Dirac-like problems. The case of 1D problems in monolayer graphene is addressed. The main characteristics of the transfer matrix are analyzed, contrasting them with the ones corresponding to 1D Schrödinger-like problems. Analytic expressions for the transmission coefficient and bound states are obtained. The continuity between bound states and states of perfect transmission is demonstrated in general, and in particular showed for the case of single electrostatic barriers. These findings in principle can be extended to 2D materials with Hamiltonian similar to monolayer graphene such as silicene and transition metal dichalcogenides.