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

TL;DR

This study investigates the particle-in-a-box states in single- and bi-layer graphene, revealing how their density of states relates to massless and massive 2D Fermions, with results aligning well with theoretical models.

Contribution

It provides experimental characterization of particle-in-a-box states in graphene, determining key parameters like Fermi velocity and effective mass, and compares them to theoretical predictions.

Findings

Density of states scales as n^{1/2} in single-layer graphene

Density of states is constant in bi-layer graphene

Fermi velocity and effective mass match theoretical values

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 (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.