Chapter 3
Optical Properties of Armchair Graphene Nanoribbons

Armchair graphene nanoribbons (AGNRs) have recently attracted much interest as they are recognized as promising building blocks for nanoelectronic devices  [38]. AGNRs, a type of graphene nanoribbons (GNRs) with armchair edges, introduce a tunable band-gap which is suitable for electrical and optical applications  [70].

Single-layer hexagonal boron nitride (h-BN) and boron nitride nanoribbons (BNNRs), which are regarded as the III-V analogs of graphene and GNRs, respectively, have been synthesized and studied in recent years  [129–132]. Theoretical and experimental results have shown that the sp2 bonding in the BN lattice gains an ionic character due to different electronegativity of B and N, that causes the optical and electronic properties of BN and BNNRs to be substantially different from that of graphene and GNRs  [131]. Unlike graphene, which is a zero-gap material, h-BN has a wide bandgap of approximately 5.9eV and shows good insulating behavior  [133].

BNNRs are expected to be produced using a single-layer h-BN as the starting material  [131]. The similarity of the crystal structures of BN and graphene gives rise to thermodynamically stable two-dimensional structures containing isolated regions of graphene and BN  [132,134]. It has been shown that AGNRs embedded in BN sheets (AGNRs/BN) are semiconductors  [132]. Due to the relatively large ionicities of boron and nitrogen, BN-confined AGNRs exhibit a generally larger bandgap compared to H-passivated AGNRs  [135,136]. These hybrid C-BN structures can be synthesized by approaches such as thermal catalytic CVD methods  [134].

A relatively large bandgap of graphene nanoribbons incorporated in a BN lattice renders them as suitable candidates for opto-electronic applications. Structures composed of GNRs and BNNRs introduce more flexibility for electronic and opto-electronic applications. In this chapter, we investigate for the first time a theoretical study of the optical properties of graphene and graphene/BN nanoribbons.

 3.1 Models
  3.1.1 First Principle Calculations
  3.1.2 Tight-Binding Model
  3.1.3 Non-Equilibrium Green’s Function
 3.2 Optical Matrix Elements
 3.3 Dielectric Response
 3.4 Conclusions