Professor Jorg Schmalian
Department of Physics and Astronomy
and DOE Ames Laboratory
Iowa State University

Quantum critical transport in clean graphene

We study the role of the electron-electron Coulomb interaction in clean graphene. Key for an understanding of this interaction is the fact that clean, undoped graphene at T=0 and for zero external magnetic field is quantum critical with a marginally irrelevant effective ′fine structure constant′. Using standard crossover arguments, we derive scaling laws, valid near this quantum critical point, that dictate the nontrivial magnetic and charge response of interacting graphene. Our analysis yields numerous predictions for how the Coulomb interaction will be manifested in experimental observables such as the diamagnetic response and electronic compressibility. The most dramatic consequence of this analysis is the electrical transport in ideal single-layer graphene at zero applied bias. There is a crossover from collisionless transport at larger frequencies to collision-dominated, hydrodynamic transport at lower frequencies. The d.c. conductivity of clean graphene, computed by the solution of a quantum Boltzmann equation, is then shown to diverge for decreasing temperature (as the inverse square of the logarithm of T) making this material a quantum critical metal.