The electronic transport property conductivity of a graphene nanoribbon is strongly influenced by its width, as well as its edge structure. According to density functional theory DFT calculations, the change in conductivity as the width of the ribbon is varied can be explained as follows:1. Bandgap: Graphene nanoribbons exhibit a bandgap, which is the energy difference between the valence band and the conduction band. This bandgap is inversely proportional to the width of the nanoribbon. As the width of the ribbon increases, the bandgap decreases, leading to an increase in conductivity. Conversely, as the width decreases, the bandgap increases, resulting in reduced conductivity.2. Edge structure: Graphene nanoribbons can have either armchair or zigzag edges. The electronic properties of these two edge structures are different, leading to variations in conductivity. Armchair nanoribbons exhibit a semiconducting behavior, with a bandgap that depends on the ribbon's width. Zigzag nanoribbons, on the other hand, can exhibit either metallic or semiconducting behavior, depending on the ribbon's width.3. Quantum confinement: As the width of the graphene nanoribbon decreases, the electrons are confined to a smaller space, leading to quantization of the energy levels. This quantum confinement effect can result in an increase in the bandgap, which in turn reduces the conductivity of the nanoribbon.In summary, the conductivity of a graphene nanoribbon is highly dependent on its width and edge structure. As the width of the ribbon is varied, the bandgap and quantum confinement effects play a significant role in determining the electronic transport properties. Density functional theory DFT calculations can help predict these changes and provide valuable insights into the design and optimization of graphene nanoribbons for various applications.