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In three-dimensional topological insulators (TIs), the nontrivial topology intheir electronic bands casts a gapless state on their solid surfaces, usingwhich dissipationless TI edge devices based on the quantum anomalous Hall (QAH)effect and quantum Hall (QH) effect have been demonstrated. Practical TIdevices present a pair of parallel-transport topological surface states (TSSs)on their top and bottom surfaces. However, due to the no-go theorem, the twoTSSs always appear as a pair and are expected to quantize synchronously.Quantized transport of a separate Dirac channel is still desirable, but hasnever been observed in graphene even after intense investigation over a periodof 13 years, with the potential aim of half-QHE. By depositing Co atomicclusters, we achieved stepwise quantization of the top and bottom surfaces inBiSbTeSe2 (BSTS) TI devices. Renormalization group flow diagrams13, 22 (RGFDs)reveal two sets of converging points (CVPs) in the (Gxy, Gxx) space, where thetop surface travels along an anomalous quantization trajectory while the bottomsurface retains 1/2 e2/h. This results from delayed Landau-level (LL)hybridization (DLLH) due to coupling between Co clusters and TSS Fermions.

Stepwise quantized surface states and delayed Landau level hybridization in Co cluster-decorated BiSbTeSe2 topological insulator devices