Pseudo spin torque induced by strain field of Dirac fermions in graphene

In contrast to recent description [Phys. Rev. Lett. 106 (2011)116803], we show that pseudo spin in graphene is not completely a real angular momentum. The pseudo spin only in the direction perpendicular to graphene sheet is real angular momentum, while the pseudo spin parallel to graphene plane is still not real angular momentum. Interestingly, it is also shown that the Newtonian-like force and pseudo spin torque of massive Dirac electrons in graphene under strain field mimic gravitomagnetic force and gravitomagnetic spin torque, respectively. This is due to the equivalence of pseudo spin and velocity operators of 2+1 dimensional massive electrons in graphene, different from that in real 3+1 dimensional Dirac fields. This work reveals new physical property of graphene as a pseudo gravitomagnetic material.