where W ( k ) is the energy function, k = ( k x , k y ) is the crystal momentum, and E 0 is an empirical parameter. The magnetic field B = ∇ ∇ × × A , where A the magnetic vector potential, can be taken into account by using Peierls substitution, replacing the crystal momentum with the canonical momentum ℏ ℏ k → → p − − q A , where p = ( p x , p y ) is the particle momentum operator and q is the charge of the particle ( q = − − e for the electron, e is the elementary charge). For convenience we choose the gauge A = ( 0 , B x , 0 ) .