Spectrum of $\pi$-electrons in Graphene As a Macromolecule

Abstract

We report the exact solution of spectral problem for a graphene sheet framed by two armchair- and two zigzag-shaped boundaries. The solution is found for the $\pi$ electron Hamiltonian and gives, in particular, a closed analytic expression of edge-state energies in graphene. It is shown that the lower symmetry of graphene, in comparison with $C_{6h}$ of 2D graphite, has a profound effect on the graphene band structure. This and other obtained results have far going implications for the understanding of graphene electronics. Some of them are briefly discussed.

Revised in connection with publication in PRL, editing

References in corpus (5)

• Electronic Properties of Disordered Two-Dimensional Carbon
• Electronic States of Graphene Nanoribbons
• Conductance quantization in mesoscopic graphene
• Quantum dots in graphene
• Zero modes and the edge states of the honeycomb lattice

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• Non-local exchange effects in zigzag edge magnetism of neutral graphene nanoribbons
• A Gate-Induced Switch in Zigzag Graphene Naoribbons and Charging Effects
• Hidden correlation between absorption peaks in achiral carbon nanotubes and nanoribbons
• Spectrum of pi electrons in bilayer graphene nanoribbons and nanotubes: an analytical approach
• Electrical manipulation of the edge states in graphene and the effect on the quantum Hall transport
• Dependence of transport on adatom location for armchair-edge graphene nanoribbons
• Large Berry phases in layered graphene
• From acene to graphene spectrum of $\pi$ electrons with the use of the Green's function
• Quantum Conductance of Achiral Graphene Ribbons and Carbon Nanotubes
• Choice of the unit cell, selection rules, and optical matrix elements: a tight-binding study of graphene nanoribbons
• Electron transmission through step- and barrier-like potentials in graphene ribbons
• Electronic and transport properties of rectangular graphene macromolecules and zigzag carbon nanotubes of finite length
• Spatial Current Patterns, Dephasing and Current Imaging in Graphene Nanoribbons
• Wave functions and edge states in rectangular honeycomb lattices revisited: nanoflakes, armchair and zigzag nanoribbons and nanotubes
• Interplay of relativistic and nonrelativistic transport in atomically precise segmented graphene nanoribbons
• Robust conductance zeroes in graphene quantum dots and other bipartite systems
• Current vortices in hexagonal graphene quantum dots
• Conductance of graphene flakes contacted at their corners
• Influence of chirality on the electron transmission through step-like potential in zigzag, armchair, and (2m,m) carbon nanotubes
• Topological Interface States and Nonlinear Thermoelectric Performance in Armchair Graphene Nanoribbon Heterostructures
• Topological edge states of the hexagonal linear chain
• Effects of zigzag edge states on the thermoelectric properties of finite graphene nanoribbons