Dual Interpretation of the Pseudo-Spin and Moment of Electrons in Graphene

The electrons in graphene can be described by a two-dimensional Dirac theory. The Dirac formalism (DF) transforms an injected spinless electron into an electron with a (pseudo) spin and magnetic moment (for finite mass m). According to Dirac's formalism the (z component of the) angular momentum is only conserved in combination with the spin. In this consistent description the pseudo spin and magnetic moment of an electron in graphene are real. On the other hand the origin of the pseudo spin and moment can be traced in graphene to distorted magnetic Landau energies. For example the n=0 Landau term has zero kinetic energy because only one of the two sub-lattices A and B is occupied. The solid state system graphene offers an insight into the microscopic working of Dirac's theory. For graphene it shows that spin and moment are an illusion.