The virial theorem in graphene and other Dirac materials

摘要

The virial theorem is applied to graphene and other Dirac Materials for systems close to the Dirac points where the dispersion relation is linear. From this, we find the exact form for the total energy given by E = B/r_s where r_sa_0 is the mean radius of the d-dimensional sphere containing one particle, with a_0 the Bohr radius, and B is a constant independent of r_s. This result implies that, given a linear dispersion and a Coulombic interaction, there is no Wigncr crystallization and that calculating B or measuring at any value of r_s determines the energy and compressibility for all r_s. In addition to the total energy, we calculate the exact forms of the chemical potential, pressure and inverse compressibility in arbitrary dimension.