Possibilities for novel phases in strongly correlated band insulators

While experimental and theoretical studies of strongly correlated band metals (i.e., systems that should be metals according to band theory) have occupied center-stage in condensed matter physics in recent decades, not that much attention has been paid to strong correlation effects in band insulators (i.e., systems that should be insulating as per band theory). Presented is a broad overview that will drive home the message that there are interesting possibilities here as well. Discussed are the possibilities for novel phases in strongly correlated band insulators by considering simple models of such materials, for example, the Ionic Hubbard Model with a strong onsite Coulomb repulsion energy, using simple approximations such as Hartree-Fock approximation, Dynamical Mean-Field Theory, slave-particle mean filed theories, etc. Specifically, in the paramagnetic regime which can persist down to low temperatures in models with frustration, a metallic phase is induced by strong correlations! In the magnetically ordered regimes, an antiferromagnetically ordered phase with different band gaps for the up and down spins ensues, including region ins parameter space where one of the spin gaps vanish, giving rise to a half-metallic antiferromagnet or ferromagnet. Doping the band insulator in such regimes would considerably enhance the possibilities for obtaining a half-metallic ferromagnet. Possibilities exist for superconducting phases as well, and more exotic possibilities have been suggested for strongly correlated topological insulators. These developments and their experimental realizability are reviewed