Meandering conduction channels and the tunable nature of quantized charge transport

Our work addresses the question: “Where does the, famously quantized, charge current flow in a Chern insulator”. This received considerable attention in the quantum Hall effect, but the progress there was hampered by the lack of local probes, and no consensus has emerged. The fundamental problem is: topological protection is excellent at hiding local information (such as the spatial distribution of the current) – a phenomenon we call topological censorship. Two recent experiments, using local probes to determine the spatial current distribution in Chern insulator heterostructures (Bi,Sb)2Te3, have remedied the dearth of experimental data in the case of the anomalous quantum Hall effect. These experiments reached unexpected, albeit very different, conclusions. Here, we provide the theory explaining one of them.

The discovery of the quantum Hall effect has established the foundation of the field of topological condensed matter physics. An amazingly accurate quantization of the Hall conductance, now enshrined in quantum metrology, is stable against any reasonable perturbation due to its topological protection. Conversely, the latter implies a form of censorship by concealing any local information from the observer. The spatial distribution of the current in a quantum Hall system is such a piece of information, which, thanks to spectacular recent advances, has now become accessible to experimental probes. It is an old question whether the original and intuitively compelling theoretical picture of the current, flowing in a narrow channel along the sample edge, is the physically correct one. Motivated by recent experiments locally imaging quantized current in a Chern insulator (Bi, Sb)${}_2$Te${}_3$ heterostructure [Rosen et al., Phys. Rev. Lett. 129, 246602 (2022); Ferguson et al., Nat. Mater. 22, 1100–1105 (2023)], we theoretically demonstrate the possibility of a broad “edge state” generically meandering away from the sample boundary deep into the bulk. Further, we show that by varying experimental parameters one can continuously tune between the regimes with narrow edge states and meandering channels, all the way to the charge transport occurring primarily within the bulk. This accounts for various features observed in, and differing between, experiments. Overall, our findings underscore the robustness of topological condensed matter physics, but also unveil the phenomenological richness, hidden until recently by the topological censorship—most of which, we believe, remains to be discovered.