Transmission Line Analogy for Wave Propagation in Graphene-Based Structures

Quantum mechanical wave phenomena in semiconductor multilayer structures are described with the effective-mass Schrödinger equation. Up until now, we have focused on the similarity between the effective-mass Schrödinger equation and Maxwell's equations, and we have effectively utilized transmission-line theory as a means of analysis and design of quantum mechanical wave phenomena. On the other hand, wave phenomena in graphene are described with the massless Dirac equation; accordingly, treating it with circuit theory necessitates using a generalized transmission line theory. In this paper, it is shown that the generalized transmission line theory can be effectively used to treat quantum mechanical wave phenomena in graphene multilayer structures. Our results show that the wave phenomena in graphene can be treated with a equivalent transmission line with characteristic impedances that differs according to the propagation directions. Based on the proposed method, some numerical simulations of the wave propagation in graphene multilayer structures were performed, and the appropriateness of the proposed method was verified.