  We present a general analysis of two-dimensional optical lattice models that
give rise to topologically non-trivial insulating states. We identify the main
ingredients of the lattice models that are responsible for the non-trivial
topological character and argue that such states can be realized within a large
family of realistic optical lattice Hamiltonians with cold atoms. We focus our
quantitative analysis on the properties of topological states with broken
time-reversal symmetry specific to cold-atom settings. In particular, we
analyze finite-size effects, multi-orbital phenomena that give rise to a
variety of distinct topological states and transitions between them, the
dependence on the trap geometry, and most importantly, the behavior of the edge
states for different types of soft and hard boundaries. Furthermore, we
demonstrate the possibility of experimentally detecting the topological states
through light Bragg scattering of the edge and bulk states.

Quantum Gases;Mesoscale and Nanoscale Physics;Quantum Physics