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

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) ∼ n 1/2 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 υ F = 1.1 × 106 m/s and effective mass m* = 0.032 m e, where m e is the electron mass, in excellent agreement with theoretical expectations.

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Correspondence to Michael Fuhrer.

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Cho, S., Fuhrer, M. Massless and massive particle-in-a-box states in single- and bi-layer graphene. Nano Res. 4, 385–392 (2011). https://doi.org/10.1007/s12274-011-0093-1

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Keywords

  • Fabry-Perot
  • interference
  • ballistic
  • density of states
  • phase-coherent