Energy gap in graphene nanoribbons with structured external electric potentials

Abstract

The electronic properties of graphene zig-zag nanoribbons with electrostatic potentials along the edges are investigated. Using the Dirac-fermion approach, we calculate the energy spectrum of an infinitely long nanoribbon of finite width $w$, terminated by Dirichlet boundary conditions in the transverse direction. We show that a structured external potential that acts within the edge regions of the ribbon, can induce a spectral gap and thus switches the nanoribbon from metallic to insulating behavior. The basic mechanism of this effect is the selective influence of the external potentials on the spinorial wavefunctions that are topological in nature and localized along the boundary of the graphene nanoribbon. Within this single particle description, the maximal obtainable energy gap is $E_{\max }\propto \pi \hslash v_{\mathrm{F}}/w$, i.e., $\approx 0.12$\,eV for $w=$15\,nm. The stability of the spectral gap against edge disorder and the effect of disorder on the two-terminal conductance is studied numerically within a tight-binding lattice model. We find that the energy gap persists as long as the applied external effective potential is larger than $\simeq 0.55\times W$, where $W$ is a measure of the disorder strength. We argue that there is a transport gap due to localization effects even in the absence of a spectral gap.

7 pages, 8 figures; minor revisions, 2 references added, published version

References in corpus (19)

• The electronic properties of graphene
• Energy Band Gap Engineering of Graphene Nanoribbons
• Energy Gaps in Graphene Nanoribbons
• Half-Metallic Graphene Nanoribbons
• Chiral tunneling and the Klein paradox in graphene
• Electronic States of Graphene Nanoribbons
• Unconventional Integer Quantum Hall effect in graphene
• A tight-binding approach to uniaxial strain in graphene
• Andreev reflection and Klein tunneling in graphene
• Structure, Stability, Edge States and Aromaticity of Graphene Ribbons
• Conductance quantization and transport gap in disordered graphene nanoribbons
• Edge disorder induced Anderson localization and conduction gap in graphene nanoribbons
• Will Zigzag Graphene Nanoribbon Turn to Half Metal under Electric Field?
• Conductance Quantization in Graphene Nanoribbons
• Electronic transport properties of graphene nanoribbons
• Gauge field for edge state in graphene
• Transverse field effect in graphene ribbons
• Sensory Organ like Response of Zigzag Edge Graphene Nanoribbons
• Aharanov-Bohm effect for the edge states of zigzag carbon nanotubes