![The epigraphene edge state
a Tight binding band structure of one valley of a 740 nm wide zigzag graphene ribbon that consists of the hyperbolic bulk 1D subbands and the edge state. The edge state is composed of a flat band at E=0 that is localized at the ribbon edge and that merges into two delocalized linear dispersing bands. Original theory predicted that the delocalized branches of the N = 0 subband is a protected edge state for energies between the N = ±1 bulk subbands⁴⁰. b Tight binding band structure where the flat band at energy E = 0 pins the Fermi level EF at E = 0 at the edge. Charges induced near the edge will be depleted by the flatband to produce a Schottky barrier between the edge and the bulk. The resulting electric fields cause band bending so that the Dirac point will be at ℏvFπn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hslash {v}_{F}\sqrt{\pi n}$$\end{document} below the Fermi level, as schematically depicted in (d). c Schematically shows the divergence of the Fermi wavelength at the edge.](https://www.researchgate.net/publication/366400623/figure/fig1/AS:11431281108400185@1671508120310/The-epigraphene-edge-state-a-Tight-binding-band-structure-of-one-valley-of-a-740nm-wide_Q320.jpg)
![Neutral epigraphene characterization
a SEM micrograph of trapezoidal graphene islands that form early in the growth and ultimately coalesce to produce a uniform graphene layer. (Inset) STM image of the epigraphene showing the characteristic hexagonal lattice of graphene at T = 12.5 K. b Raman spectroscopy. Measured spectrum (red) and SiC subtracted spectrum (blue). The 2D peak is typical of a graphene monolayer. c ARPES (beam energy = 200 eV, EF = 197.4 eV) taken at room temperature along K-M-K’ showing characteristic graphene Dirac cones with vF = 1.06 × 10⁶ m/s, with an apex at E = 0 confirming charge neutrality and no detectable anisotropy. d Infrared magneto-spectroscopy. The transitions follow the expected characteristic graphene B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{B}$$\end{document} dispersion (indicated by the red lines) confirming its monolayer character. e Typical scanning tunneling spectrum (T = 4.4 K, Iset = 400 pA at Vbias = 500 mV), showing the characteristic graphene density of states. A linear fit (dashed lines) indicates a doping level |EF – ED| < 6 meV, showing that the graphene is charge neutral. f STS image at a graphene island edge (T = 12.5 K, Iset = 250 pA at Vbias = 2 V) taken at various distances from the edge from SiC to inside the ribbon with a lateral resolution of about 2 nm (traces are displaced vertically for clarity). Note the 0-DoS peak at the edge, similar to that observed in sidewall ribbons⁴³.](https://www.researchgate.net/publication/366400623/figure/fig2/AS:11431281108437466@1671508120354/Neutral-epigraphene-characterization-a-SEM-micrograph-of-trapezoidal-graphene-islands_Q320.jpg)
December 2022
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Nature Communications
Graphene’s original promise to succeed silicon faltered due to pervasive edge disorder in lithographically patterned deposited graphene and the lack of a new electronics paradigm. Here we demonstrate that the annealed edges in conventionally patterned graphene epitaxially grown on a silicon carbide substrate (epigraphene) are stabilized by the substrate and support a protected edge state. The edge state has a mean free path that is greater than 50 microns, 5000 times greater than the bulk states and involves a theoretically unexpected Majorana-like zero-energy non-degenerate quasiparticle that does not produce a Hall voltage. In seamless integrated structures, the edge state forms a zero-energy one-dimensional ballistic network with essentially dissipationless nodes at ribbon–ribbon junctions. Seamless device structures offer a variety of switching possibilities including quantum coherent devices at low temperatures. This makes epigraphene a technologically viable graphene nanoelectronics platform that has the potential to succeed silicon nanoelectronics. Here, the authors show robust edge state transport in patterned nanoribbon networks produced on epigraphene—graphene that is epitaxially grown on non-polar faces of SiC wafers. The edge state forms a zero-energy, one-dimensional ballistic network with dissipationless nodes at ribbon–ribbon junctions.
