  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 single- and bi-layer graphene, corresponding to massless and massive
two-dimensional (2d) Fermions.The density of states D as a function of particle
number n shows the expected relations D(n) ~ n1/2 for massless 2d Fermions
(electrons in single-layer graphene) and D(n) ~ constant for massive 2d
Fermions (electrons in bi-layer graphene). The single parameters of the
massless and massive dispersion relations are found, Fermi velocity vF = 1.1 x
106m/s and effective mass m* = 0.032 me, where me is the electron mass, in
excellent agreement with theoretical expectations.
