Visualizing topological transport

Abstract

We present a mathematically simple procedure for explaining and visualizing the dynamics of quantized transport in topological insulators. The procedure serves to illustrate and clarify the dynamics of topological transport in general, but for the sake of concreteness, it is phrased here in terms of electron transport in a charge-ordered chain, which may be mapped exactly onto transport between edge channels in the Integer Quantum Hall Effect. This approach has the advantage that it allows a direct visualization of the real-space and real-time evolution of the electronic charges throughout the topological pumping cycle, thus demystifying how charge flows between remote edges separated by an insulating bulk, why the amount of transported charge is given by a topological invariant, and how continuous driving yields a discrete, quantized amount of transported charge.