Graphene and topological insulators: Teaching electrons new tricks


The periodic potential imposed by the crystal lattice allows new effective Hamiltonians for electrons to be generated which may be qualitatively different than the Schrodinger equation for a free electron at low energies. I will discuss two striking recent examples. In graphene, the basis of two identical atoms in the honeycomb lattice leads to a massless Dirac Hamiltonian with an emergent spin-1/2 “pseudospin” spinor coupled to momentum. In the three-dimensional topological insulators, strong spin-orbit coupling leads to a Hamiltonian which is topologically distinct from the free-electron case, which gives rise to emergent metallic states at the boundaries (surfaces) of the material. These surface states also have a Dirac effective Hamiltonian, but with momentum coupled to the intrinsic electron spin. I will discuss how these materials are made, and how they are used to enable the study of Dirac electrons in the laboratory.