Theory of a quantum critical phenomenon in a topological insulator: (3+1)-dimensional quantum electrodynamics in solids

摘要

We study theoretically the quantum critical phenomenon of the phasetransition between the trivial insulator and the topological insulator in (3+1)dimensions, which is described by a Dirac fermion coupled to theelectromagnetic field. The renormalization group (RG) equations for the runningcoupling constant \alpha, the speed of light c and electron v are derived. Thealmost exact analytic solutions to these RG equations are obtained to revealthat (i) c and v approach to the common value with combination c^2v beingalmost unrenormalized, (ii) the RG flow of \alpha is the same as that of usualQED with c^3 being replaced by c^2v, and (iii) there are two crossovermomentum/energy scales separating three regions of different scaling behaviors.The dielectric and magnetic susceptibilities, angle-resolved photoemissionspectroscopy (ARPES), and the behavior of the gap are discussed from thisviewpoint.