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Here we provide a general methodology to directly measure the topologicalcurrents emerging in the optical lattice implementation of the Haldane model.Alongside the edge currents supported by gapless edge states, transversecurrents can emerge in the bulk of the system whenever the local potential isvaried in space, even if it does not cause a phase transition. In opticallattice implementations the overall harmonic potential that traps the atomsprovides the boundaries of the topological phase that supports the edgecurrents, as well as providing the potential gradient across the topologicalphase that gives rise to the bulk current. Both the edge and bulk currents areresilient to several experimental parameters such as trapping potential,temperature and disorder. We propose to investigate the properties of thesecurrents directly from time-of-flight images with both short-time and long-timeexpansions.

Seeing topological edge and bulk currents in time-of-flight images