Pseudospin and Deformation-Induced Gauge Field in Graphene

The electronic properties of a single layer of graphite, graphene1)–4) have attracted much attention due to the “relativistic” character of π-electrons near the Fermi level. The energy band structure of graphene exhibits a linear energy dispersion relation around the two inequivalent, hexagonal corners of the first Brillouin zone in the k-space (the K and K′ points).5),6) The wavefunction (Hamiltonian) of π-electrons has two component (a 2 × 2 matrix) form due to the fact that the unit cell of graphene consists of two carbon atoms (A and B atoms). The effective-mass Hamiltonian of π-electrons around the K point or the K′ point is given by linear momentum operator, which is relevant to the linear energy dispersion relation of graphene. The effective-mass equation is similar to the massless Dirac equation or the Weyl equation.7) The original Dirac equation for an electron has the form