Meandering conduction channels and the tunable nature of quantized charge transport

TL;DR

This paper demonstrates theoretically that topological edge states can meander into the bulk and be tuned between narrow and broad channels, explaining experimental observations and revealing hidden phenomenological richness in topological systems.

Contribution

It introduces the concept of tunable, meandering conduction channels in topological insulators, expanding understanding of current flow beyond traditional edge state models.

Findings

Edge states can meander into the bulk of the sample.

Experimental parameters allow tuning between narrow edge and bulk transport.

The phenomenological richness of topological systems is greater than previously understood.

Abstract

The discovery of the quantum Hall effect founded the field of topological condensed matter physics. Its amazingly accurate quantisation of the Hall conductance, now enshrined in quantum metrology, is topologically protected: it is stable against any reasonable perturbation. Conversely, topological protection thus implies a form of censorship, as it completely hides any local information from the observer. The spatial distribution of the current in the sample is such a piece of information, which however has now become accessible thanks to spectacular experimental advances. It is an old question whether an original, and intuitively compelling, picture of the current flowing in a narrow channel along the sample edge is the physically correct one. Motivated by recent experiments $\textit{locally}$ imaging the quantized current flow in a Chern insulating (Bi, Sb)$_2$Te$_3$ heterostructure, [Rosen et al., PRL 129, 246602 (2022); Ferguson et.al, Nat. Mater. 22, 1100-1105 (2023)], we theoretically demonstrate the possibility of a broad `edge state' meandering away from the sample boundary deep into the sample bulk. Further, we show that varying experimental parameters permits continuously tuning between narrow edge states and meandering channels all the way to incompressible bulk transport. This accounts for various features observed in, and differing between, experiments. Overall, this underscores the robustness of topological condensed matter physics, but it also unveils a phenomenological richness hidden by topological censorship -- much of which we believe remains to be discovered.