Spectrum of pi electrons in bilayer graphene nanoribbons and nanotubes: an analytical approach

TL;DR

This paper provides an exact analytical method to describe pi electron spectra in finite bilayer graphene nanoribbons and nanotubes with armchair and zigzag edges, analyzing their electronic properties.

Contribution

It introduces an analytical approach to determine the electronic spectrum of finite bilayer graphene structures with specific geometries and edge types.

Findings

Exact analytical spectra for zigzag and armchair bilayer graphene nanoribbons and nanotubes.

Analysis of dispersion relations, density of states, and conductance quantization.

Insights into electronic properties of finite bilayer graphene structures.

Abstract

We present an analytical description of pi electrons of a finite size bilayer graphene within a framework of the tight-binding model. The bilayered structures considered here are characterized by a rectangular geometry and have a finite size in one or both directions with armchair- and zigzag-shaped edges. We provide an exact analytical description of the spectrum of pi electrons in the zigzag and armchair bilayer graphene nanoribbons and nanotubes. We analyze the dispersion relations, the density of states, and the conductance quantization.