  We analyze the eigenstates of a two-dimensional lattice with additional
harmonic confinement in the presence of an artificial magnetic field. While the
softness of the confinement makes a distinction between bulk and edge states
difficult, the interplay of harmonic potential and lattice leads to a different
classification of states in three energy regions: In the low-energy regime,
where lattice effects are small, all states are transporting topologically
non-trivial states. For large energies above a certain critical value, the
periodic lattice causes localization of all states through a mechanism similar
to Wannier-Stark localization. In the intermediate energy regime transporting,
topologically non- trivial states coexist with topologically trivial
counter-transporting chaotic states. The character of the eigenstates, in
particular their transport properties are studied numerically and are explained
using a semiclassical analysis.
