Interaction-driven topological and nematic phases on the Lieb lattice
  We show that topological states are often developed in two dimensional semimetals with quadratic band crossing points (BCPs) by electron-electron interactions. To illustrate this, we construct a concrete model with the BCP on an extended Lieb lattice and investigate the interaction-driven topological instabilities. We find that the BCP is marginally unstable against infinitesimal repulsions. Depending on the interaction strengths, topological quantum anomalous/spin Hall, charge nematic, and nematic-spin-nematic phases, develop separately. Possible physical realizations of quadratic BCPs are provided. 
Wei-Feng Tsai, Chen Fang, Hong Yao, and JiangPing Hu
cond-mat.str-el cond-mat.mes-hall