Topological states and quantum phase transitions in spin orbit coupled systems

Solids with strong spin-orbit coupling are being explored in the
context of phases of matter such as topological insulators. With
spontaneous breaking of time-reversal symmetry, obtained by doping
topological insulator films with magnetic atoms, experiments have
shown the realization of analogues of quantum Hall states without a
magnetic field - these are called ``quantum anomalous Hall
insulators'' or ``Chern insulators''. Motivated by these developments,
we have been theoretically exploring oxide materials which can combine
such physics with strong correlations. This talk will present an
overview of this field, and discuss some recent results including how
new and unexpected phases can emerge at certain topological quantum
phase transitions.