Pseudospin, velocity and Berry phase in a bilayer graphene
  Hamiltonian and eigenstate problem is formulated for a bilayer graphene in terms of Clifford's geometric algebra \textit{Cl}$_{3,1}$. It is shown that such approach allows to perform analytical calculations in a simple way if geometrical algebra rotors are used. The measured quantities are express through spectrum and rotation half-angle of the pseudospin that appears in geometric algebra rotors. Properties of free charge carriers -- pseudospin, velocity and Berry phase -- in a bilayer graphene are investigated in the presence of the external voltage applied between the two layers. 
Adolfas Dargys, Arturas Acus
cond-mat.mes-hall