Derived from the tight-binding Hamiltonian of graphene, the band structure of graphene is composed by two...

Transcribed Image Text:

Derived from the tight-binding Hamiltonian of graphene, the band structure of graphene is composed by two branches: Yo f(kr, ky)| 1 - sof(kx, ky)| and -Yo f(kx, ky)| 1 + $0 |f (kx, ky)' where so 0.129 and E+ (ke, ky) = |f(kx, ky): = 1+ 4 cos E_(ka, ky) = kya √3k₂ a) con (12₂²) 2 +1 cos² (¹₂²). 4 2 Plot the band structure of graphene by matplotlib. 1. Define the dimensionless quantities: E = E+ /70, Ẽ_ = E_ / Yo, k = k₂a and ky = kŋa. Rewrite the above equations by Ẽ, E, K, and ky. In the new equations, Yo and a are eliminated. So, we don't need to know the values of Yo and a. 2. Plot E+ (ka, Ky) and E_(ka, ky) by plot_surface() in the same figure. Derived from the tight-binding Hamiltonian of graphene, the band structure of graphene is composed by two branches: Yo f(kr, ky)| 1 - sof(kx, ky)| and -Yo f(kx, ky)| 1 + $0 |f (kx, ky)' where so 0.129 and E+ (ke, ky) = |f(kx, ky): = 1+ 4 cos E_(ka, ky) = kya √3k₂ a) con (12₂²) 2 +1 cos² (¹₂²). 4 2 Plot the band structure of graphene by matplotlib. 1. Define the dimensionless quantities: E = E+ /70, Ẽ_ = E_ / Yo, k = k₂a and ky = kŋa. Rewrite the above equations by Ẽ, E, K, and ky. In the new equations, Yo and a are eliminated. So, we don't need to know the values of Yo and a. 2. Plot E+ (ka, Ky) and E_(ka, ky) by plot_surface() in the same figure.