Magnetic and topological transitions in three-dimensional topological Kondo insulator

Using an extended slave-boson method,we draw a global phase diagram summarizing both magnetic phases and paramagnetic（PM） topological insulators（TIs） in a three-dimensional topological Kondo insulator（TKI）. By including electron hopping（EH） up to the third neighbors, we identify four strong TI（STI） phases and two weak TI（WTI） phases. Then, the PM phase diagrams characterizing topological transitions between these TIs are depicted as functions of EH,f-electron energy level,and hybridization constant. We also find an insulator-metal transition from an STI phase that has surface Fermi rings and spin textures in qualitative agreement with the TKI candidate SmBs. In the weak hybridization regime, antiferromagnetic（AF） order naturally arises in the phase diagrams. Depending on how the magnetic boundary crosses the PM topological transition lines,AF phases are classified into the AF topological insulator（AFTI） and the non-topological AF insulator, according to their Z2 indices. In two small regions of parameter space, two distinct topological transition processes between AF phases occur, leading to two types of AFTIs showing distinguishable surface dispersions around their Dirac points.