Meandering conduction channels and the tunable nature of quantized charge transport

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 <i>locally</i> imaging quantized current in a Chern insulator (Bi, Sb)[Formula: see text]Te[Formula: see text] heterostructure [Rosen et al., <i>Phys. Rev. Lett.</i> <b>129</b>, 246602 (2022); Ferguson et al., <i>Nat. Mater.</i> <b>22</b>, 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.