Abstract

The famous bulk-edge correspondence is one of the striking properties that has strongly motivated enormous interest for topological insulators in the past decades. However, in a rather surprising way, recent experiments imaging the non-equilibrium current pattern in disordered Chern insulators have shown that most of the Hall current happens to flow inside the bulk of the spectrum, and not on narrow edge channels, contrary to the most common expectation. I will present a recent attempt (in a collaboration with D. Kovrizhin and R. Moessner) to account for these striking observations, which relies on two key ingredients: a smooth confining electrostatic potential and quenched disorder. Our main result is the existence of wide meandering conduction channels, that carry the quantized Hall current. I will then present some numerical results for a Chern insulator model, in the presence of on-site disorder and a constant electric field, and fully projected onto a single Chern band. Energy eigenstates exhibit very broad distributions for local observables. We also observe an intriguing coexistence between extended energy eigenstates and sharply localized states, at all energies, for all finite system sizes that we have been able to access so far. Understanding the thermodynamic limit remains a challenge for theory and also for future experimental investigations aiming at probing the behavior of local observables.