Electron transmission through step- and barrier-like potentials in graphene ribbons

Abstract

The list of textbook tunneling formulas is extended by deriving exact expressions for the transmission coefficient in graphene ribbons with armchair edges and the step-like and barrier-like profiles of site energies along the ribbon. These expressions are obtained by matching wave functions at the interfaces between the regions, where quasiparticles have constant but different potential energies. It is shown that for an $U_0$ high barrier and low-energy electrons and holes, the mode transmission of charge carriers in this type of ribbons is described by the textbook formula, where the constant barrier is replaced by an effective, energy-dependent barrier, $U_0\to U(E)$. For the lowest/highest electron/hole mode, $U(E)$ goes, respectively, to zero and nonzero value in metallic and semiconducting ribbons. This and other peculiarities of through-barrier/step transmission in graphene are discussed and compared with related earlier results.

Edited, misprints corrected

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Cited by in corpus (5)

• Spectrum of $\pi$ Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance
• Controllable spin-dependent transport in armchair graphene nanoribbon structures
• From acene to graphene spectrum of $\pi$ electrons with the use of the Green's function
• Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions
• Influence of chirality on the electron transmission through step-like potential in zigzag, armchair, and (2m,m) carbon nanotubes