Size quantization of Dirac fermions in graphene constrictions

TL;DR

This paper demonstrates ballistic transport and quantized conductance of Dirac fermions in lithographically-defined graphene constrictions, confirming size quantization and revealing edge physics through experimental data and simulations.

Contribution

It provides the first clear observation of size quantization of Dirac electrons in graphene constrictions, combining experimental results with theoretical modeling.

Findings

Quantized conductance matches Landauer theory at high densities

Magnetic field data confirms size quantization

Bias spectroscopy reveals renormalized Fermi velocity

Abstract

Quantum point contacts (QPCs) are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wave-length in high-quality bulk graphene can be tuned up to hundreds of nanometers, the observation of quantum confinement of Dirac electrons in nanostructured graphene systems has proven surprisingly challenging. Here we show ballistic transport and quantized conductance of size-confined Dirac fermions in lithographically-defined graphene constrictions. At high charge carrier densities, the observed conductance agrees excellently with the Landauer theory of ballistic transport without any adjustable parameter. Experimental data and simulations for the evolution of the conductance with magnetic field unambiguously confirm the identification of size quantization in the constriction. Close to the charge neutrality point, bias voltage spectroscopy reveals a renormalized Fermi velocity ($v_F \approx 1.5 \times 10^6 m/s$) in our graphene constrictions. Moreover, at low carrier density transport measurements allow probing the density of localized states at edges, thus offering a unique handle on edge physics in graphene devices.