Interactions and doping effects in a topological insulator

We investigate the effect of repulsive and attractive onsite interactions on a Quantum Spin Hall Insulator (QSHI). For repulsive interactions, we show that the topological phase is stable up to quite large interactions $U\sim t$ before the system reaches a magnetically ordered phase\,[1]. For attractive interactions, we discuss superconductivity in a doped QSHI and compare it with a doped trivial band insulator. We also consider the effect of spin orbit coupling to zero--mode bound states at vortex cores.\\[10pt] [1] S.Rachel and K.Le Hur, Phys.\,Rev.\,B 82, 075106 (2010).