Effects of edge disorder on thermoelectric performance of graphene nanoribbons (GNRs) were investigated through computational simulations based on the non-equilibrium Green's function method combined with the tight-binding approximation. We found that the thermoelectric power factor PF can be optimized by adjusting the ribbon length, L, of GNRs with edge disorder concentration Cd. For example, at room temperature, PF of zigzag-edged GNRs at the Fermi energy shows a maximum value of 33 mW/(m K2) when Cd = 10% and L = 210 nm. Both the maximum PF and optimum L decrease with increasing Cd. The maximum PF is theoretically explained in terms of the crossover from the ballistic transport regime to the Anderson's localization regime.
The topological aspects in the physics of atomic layers, particularly the valley physics, are briefly reviewed. First, the Berry curvature of band structure is introduced as a basic concept for the k-space topology. The stability of Dirac cones and the valley splitting of Landau levels in gapped graphene are explained topologically. The valley Hall effect in gapped graphene is discussed as a remarkable topological transport phenomenon. The spin-valley correspondence is also mentioned in 2H-MoS2 monolayer with no inversion symmetry.