Symplectic large-N theory of topological heavy-fermion semiconductors

Abstract

I present a theory of topological heavy-fermion semiconductors based on the large-N symplectic representation for the electron spin. The theory is exact in the limit when the number of spin flavors N=2k is infinite. I find that both weak and strong topological insulating phases exist for k<3. Furthermore, for k>2 the weak topological insulating state fully suppressed while only strong topological and trivial insulator states survive. In addition, using the mean-field theory results, I consider the tunneling into topologically trivial and non-trivial phases of a generic heavy-fermion insulators by calculating the differential tunneling conductance. The implications of the presented results for the existing heavy-fermion semiconductors are discussed.