  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.
