I am confused about the quantum Hall state and topological insulating states. Following are the points (according to my naive understanding of this field) which confuse me:
Topological insulator has insulating bulk and conducting edge states which are protected by time reversal symmetry.
The quantum Hall state has conducting edge states and insulating bulk (Landau levels). And to achieve this Hall state we have to apply a strong magnetic field which breaks time-reversal symmetry.
Is not quantum Hall state a topological insulating state? it has insulating bulk and conducting edges. If yes, then how can we have topological insulator with broken time reversal symmetry? If no, why is it not a topological insulating state?