Topological quantum criticality of the disordered Chern insulator

Mateo, Moreno-Gonzalez,; Johannes, Dieplinger,; Altland, Alexander

doi:10.1016/j.aop.2023.169258

Annals of Physics

2023

DOI: 10.1016/j.aop.2023.169258

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Topological quantum criticality of the disordered Chern insulator

Moreno-Gonzalez, Mateo

Dieplinger, Johannes

Alexander Altland

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2024

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Cited by 3 publications

References 24 publications

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Meandering conduction channels and the tunable nature of quantized charge transport

Douçot,

Kovrizhin,

Moessner

2024

Proc. Natl. Acad. Sci. U.S.A.

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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.

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Meandering conduction channels and the tunable nature of quantized charge transport

Douçot,

Kovrizhin,

Moessner

2024

Proc. Natl. Acad. Sci. U.S.A.

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Quantum Hall criticality in an amorphous Chern insulator

Bera,

Dieplinger,

Nayak

2024

Phys. Rev. B

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Fragility of Surface States in Non-Wigner-Dyson Topological Insulators

Altland,

Brouwer,

Dieplinger

et al. 2024

Phys. Rev. X

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Topological insulators and superconductors support extended surface states protected against the otherwise localizing effects of static disorder. Specifically, in the Wigner-Dyson insulators belonging to the symmetry classes A, AI, and AII, a band of extended surface states is continuously connected to a likewise extended set of bulk states forming a “bridge” between different surfaces via the mechanism of spectral flow. In this work we show that this mechanism is absent in the majority of non-Wigner-Dyson topological superconductors and chiral topological insulators. In these systems, there is precisely one point with granted extended states, the center of the band, E=0. Away from it, states are spatially localized, or can be made so by the addition of spatially local potentials. Considering the three-dimensional insulator in class AIII and winding number ν=1 as a paradigmatic case study, we discuss the physical principles behind this phenomenon, and its methodological and applied consequences. In particular, we show that low-energy Dirac approximations in the description of surface states can be treacherous in that they tend to conceal the localizability phenomenon. We also identify markers defined in terms of Berry curvature as measures for the degree of state localization in lattice models, and back our analytical predictions by extensive numerical simulations. A main conclusion of this work is that the surface phenomenology of non-Wigner-Dyson topological insulators is a lot richer than that of their Wigner-Dyson siblings, extreme limits being spectrumwide quantum critical delocalization of all states versus full localization except at the E=0 critical point. As part of our study we identify possible experimental signatures distinguishing between these different alternatives in transport or tunnel spectroscopy. Published by the American Physical Society 2024

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Topological quantum criticality of the disordered Chern insulator

Cited by 3 publications

References 24 publications

Meandering conduction channels and the tunable nature of quantized charge transport

Meandering conduction channels and the tunable nature of quantized charge transport

Quantum Hall criticality in an amorphous Chern insulator

Fragility of Surface States in Non-Wigner-Dyson Topological Insulators

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