"Massless and massive particle-in-a-box states in single- and bi-layer " by Sungjae Cho and Michael Fuhrer

Article Title

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

Authors

Sungjae Cho, Department of Physics and Center for Nanophysics and Advanced Materials, University of Maryland, College Park, Maryland 20742, USA
Michael Fuhrer, Department of Physics and Center for Nanophysics and Advanced Materials, University of Maryland, College Park, Maryland 20742, USA

Keywords

Fabry–Perot, interference, ballistic, density of states, phase-coherent

Abstract

ABSTRACT 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 (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.