# Visualizing topological transport

## TL;DR

This paper introduces a simple visualization method for understanding the dynamics of quantized charge transport in topological insulators, clarifying how topological invariants govern charge flow in quantum Hall systems.

## Contribution

It provides a straightforward visualization technique for topological transport, making the complex dynamics more accessible and understandable.

## Key findings

- Visualizes real-space charge evolution during topological pumping
- Demonstrates charge quantization linked to topological invariants
- Clarifies charge flow between edges in quantum Hall systems

## 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. It 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.