Angular momentum and pseudospin in graphene

Any quantum mechanical problem with two levels can be treated by analogy with the spin 1/2 system. For instance, treating the proton and neutron as `up' and `down' states of the same particle leads to the fruitful concept of nuclear isospin. Because the honeycomb structure of graphene has two inequivalent atoms per unit cell, a pseudospin variable arises in the solution of the graphene Hamiltonian. This variable is commonly thought to be analogous to a spin 1/2 angular momentum. Unlike isospin, however, pseudospin is intimately connected to rotations in real space. Furthermore, graphene electrons couple to the electromagnetic field through their pseudospin: the pseudospin flip seen in electron-hole recombination creates a spin-1 photon. The natural conclusion is that the pseudospin is a real angular momentum. Implications of this identification for condensed matter and particle physics will be discussed.