Massless and massive particle-in-a-box states in single-and bi- layer graphene

Electron transport through short, phase-coherent metal–graphene–metal devices occurs via resonant transmission through particle-in-a-box-like states defined by the atomically-sharp metal leads. We study the spectrum of particle-in-a-box states for singleand bi-layer graphene, corresponding to massless and massive two-dimensional (2-D) fermions. The density of states D as a function of particle number n shows the expected relationships D(n) ~ n1/2 for massless 2-D fermions (electrons in single-layer graphene) and D(n) ~ constant for massive 2-D fermions (electrons in bi-layer graphene). The single parameters of the massless and massive dispersion relations are found, namely Fermi velocity vF = 1.1 × 106 m/s and effective mass m = 0.032 me, where me is the electron mass, in excellent agreement with theoretical expectations.