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The surface state of a three-dimensional topological insulator forms atwo-dimensional massless Dirac electron system. In Dirac electron systems,Coulomb interaction is not screened due to the small density of states at theFermi energy and thus the long-range Coulomb interaction (LRCI) plays a crucialrole. In this paper, we investigate the surface state with chemical potential$\mu=0$ in the presence of the LRCI using the Wilsonian renormalization group.We first check the Fermi velocity enhancement in the surface Dirac system,which also occurs in a usual Dirac electron system. The most remarkable featureof the surface Dirac system is that the Dirac Hamiltonian contains not pseudospin but real spin Pauli matrices. Because of this feature, we find theg-factor enhancement, which is a unique property of the surface Dirac system.We also investigate the explicit form of the spin susceptibility and find thatthe spin susceptibility is enhanced in the presence of the LRCI.

Long-range Coulomb interaction effects on the surface Dirac electron system of a three-dimensional topological insulator