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Tuning the Chern number in quantum anomalous Hall insulators

Abstract

A quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has a quantized Hall resistance of h/(Ce2) and vanishing longitudinal resistance under zero magnetic field (where h is the Planck constant, e is the elementary charge, and the Chern number C is an integer)1,2. The QAH effect has been realized in magnetic topological insulators3,4,5,6,7,8,9 and magic-angle twisted bilayer graphene10,11. However, the QAH effect at zero magnetic field has so far been realized only for C = 1. Here we realize a well quantized QAH effect with tunable Chern number (up to C = 5) in multilayer structures consisting of alternating magnetic and undoped topological insulator layers, fabricated using molecular beam epitaxy. The Chern number of these QAH insulators is determined by the number of undoped topological insulator layers in the multilayer structure. Moreover, we demonstrate that the Chern number of a given multilayer structure can be tuned by varying either the magnetic doping concentration in the magnetic topological insulator layers or the thickness of the interior magnetic topological insulator layer. We develop a theoretical model to explain our experimental observations and establish phase diagrams for QAH insulators with high, tunable Chern number. The realization of such insulators facilitates the application of dissipationless chiral edge currents in energy-efficient electronic devices, and opens up opportunities for developing multi-channel quantum computing and higher-capacity chiral circuit interconnects.

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Fig. 1: The high-C QAH effect in magnetic–undoped topological insulator multilayer structures.
Fig. 2: Observations of the high-C QAH effect in magnetic–undoped topological insulator multilayer structures.
Fig. 3: Demonstration of high-C QAH states in magnetic–undoped topological insulator multilayer structures.
Fig. 4: Tunable Chern number in QAH insulators.

Data availability

The datasets generated and/or analysed during this study are available from the corresponding authors on reasonable request.

Code availability

The codes used in theoretical simulations and calculations are available from the corresponding authors on reasonable request.

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Acknowledgements

We are grateful to Y. T. Cui, J. Jain, W. D. Wu, D. Xiao and X. D. Xu for discussion. This work was primarily supported by a DOE grant (DE-SC0019064), including sample synthesis, transport measurements and theoretical calculations. The sample characterization was partially supported by an ARO Young Investigator Program Award (W911NF1810198), an NSF-CAREER award (DMR-1847811) and the Gordon and Betty Moore Foundation’s EPiQS Initiative (GBMF9063 to C.Z.C.). Part of the measurements at dilution-refrigerator temperature is supported by NSF grant DMR-1707340. N.S. and R.X. acknowledge support from DOE EFRC grant DE-SC0019331.

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Authors

Contributions

C.-Z.C. conceived and designed the experiment. Y.-F.Z., L.-J.Z. and Y.-Q.Z. grew the magnetic TI/TI multilayer samples and carried out the PPMS transport measurements, with help from C.-Z.C. K.W. performed the TEM measurements. R.Z., L.-J.Z. and Y.-Q.Z. carried out the dilution transport measurements, with help from M.H.W.C. and C.-Z.C. R.M., J.Y. and C.-X.L. did all calculations and provided theoretical support. Y.-F.Z., R.Z., R.M., C.-X.L. and C.-Z.C. analysed the data and wrote the manuscript, with input from all authors.

Corresponding authors

Correspondence to Chao-Xing Liu or Cui-Zu Chang.

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The authors declare no competing interests.

Additional information

Peer review information Nature thanks Xianhui Chen, Sanfeng Wu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Characterization of magnetic TI/TI multilayer samples.

a, RHEED patterns of the heat-treated SrTiO3(111) substrate. The reconstruction pattern indicates its atomic flat surface, which is crucial for the MBE growth of the high-quality TI films. b, RHEED patterns of the [3QL Cr-doped (Bi,Sb)2Te3–4QL (Bi,Sb)2Te3]2–3QL Cr-doped (Bi,Sb)2Te3 sample. The sharp and streaky 1 × 1 patterns indicate the high quality of our magnetic TI/TI multilayer samples. c, d, STEM images of the m = 2 (c) and m = 3 (d) magnetic TI/TI multilayer samples grown on SrTiO3 substrate (left), accompanied by the energy-dispersive spectroscopy maps of Cr distribution (right).

Extended Data Fig. 2 Transport results for the C = 1 sample.

a, Dependence of ρyx(0) (blue squares) and ρxx(0) (red circles) on T. All measurements were taken at μ0H = 0 T after magnetic training. b, c, Dependence of ρyx (b) and ρxx (c) on μ0H, measured at different temperatures and Vg = Vg,0. dg, Dependence of ρyx (d, e) and ρxx (f, g) on μ0H, measured at different gate voltages (d, f, Vg < Vg,0; e, g, Vg ≥ Vg,0) and T = 25 mK. When Vg is tuned away from Vg,0, ρyx and ρxx show additional transition features once the external magnetic field changes the polarity. We speculate that these features are probably a result of the heating generated in the dilution fridge and/or the indium contacts used in our samples.

Extended Data Fig. 3 Transport results for the C = 2 sample.

As in Extended Data Fig. 2, but for the C = 2 sample.

Extended Data Fig. 4 Transport results for the C = 3 sample.

As in Extended Data Fig. 2, but for the C = 3 sample.

Extended Data Fig. 5 Transport results of the C = 4 sample.

As in Extended Data Fig. 2, but for the C = 4 sample.

Extended Data Fig. 6 Transport results of the C = 5 sample.

As in Extended Data Fig. 2, but for the C = 5 sample.

Extended Data Fig. 7 Hall and longitudinal conductance results for the C = 1–5 samples.

ae, Dependence of the longitudinal conductance σxx (red) and Hall conductance σxy (blue) on μ0H for the C = 1–5 samples. All measurements were taken at the charge-neutral point (Vg = Vg,0) and T = 25 mK. fj, Dependence of σxy(0) (blue squares) and σxx(0) (red circles) on gate voltage (Vg − Vg,0) for the C = 1–5 samples. All measurements were taken at T = 25 mK and μ0H = 0 T after magnetic training.

Extended Data Fig. 8 The high-C QAH effect observed in another group of magnetic TI/TI multilayer samples.

ad, Dependence of ρxx (red) and ρyx (blue) on μ0H, measured at the charge-neutral point (Vg = Vg,0) and T = 25 mK. ρyx(0) displays the quantized values of 0.494h/e2, 0.307h/e2, 0.231h/e2 and 0.169h/e2 for the samples with C = 2, 3, 4 and 5, respectively. The corresponding ρxx(0) values are 0.010h/e2, 0.050h/e2, 0.039h/e2 and 0.087h/e2. Vg,0 values for the four samples are +15 V (C = 2), −3 V (C = 3), −15 V (C = 4) and +5 V (C = 5). eh, Dependence of ρyx(0) (blue squares) and ρxx(0) (red circles) on gate voltage (Vg − Vg,0) for the C = 2–5 samples. All measurements were taken at T = 25 mK and μ0H = 0 T after magnetic training.

Extended Data Fig. 9 Chern number tuned by varying the Cr doping level in magnetic TI layers.

ad, Dependence of ρxx (red) and ρyx (blue) on μ0H for the m = 2 sample, with different Cr doping levels x. All measurements were taken at the charge-neutral point (Vg = Vg,0) and T = 25 mK. ρyx(0) displays the quantized values of 0.969h/e2, 0.994h/e2, 0.498h/e2 and 0.497h/e2 for the samples with x = 0.13, 0.15, 0.24 and 0.35, respectively. The corresponding ρxx(0) value are 0.078h/e2, 0.002h/e2, 0.008h/e2 and 0.010h/e2. eh, Dependence of ρyx(0) (blue squares) and ρxx(0) (red circles) on gate voltage (Vg − Vg,0) for x = 0.13, 0.15, 0.24 and 0.35. All measurements were taken at T = 25 mK and μ0H = 0 T after magnetic training.

Extended Data Fig. 10 Chern number tuned by controlling the thickness of the middle magnetic TI layer.

ad, Dependence of ρxx (red) and ρyx (blue) on μ0H for the m = 2 sample, with different middle magnetic TI layer thicknesses d. All measurements were taken at the charge-neutral point (Vg = Vg,0) and T = 25 mK. ρyx(0) displays the quantized values of 0.995h/e2, 0.996h/e2, 0.469h/e2, 0.498h/e2 and 0.490h/e2 for the samples with d = 0, 1, 2, 3 and 4, respectively. The corresponding ρxx(0) values are 0.0001h/e2, 0.0009h/e2, 0.089h/e2, 0.008h/e2 and 0.024h/e2. eh, Dependence of ρyx(0) (blue squares) and ρxx(0) (red circles) on gate voltage (Vg − Vg,0) for d = 0, 1, 2, 3 and 4. All measurements were taken at T = 25 mK and μ0H = 0 T after magnetic training. Because the d = 2 sample is near the topological phase transition regime and therefore has a smaller hybridization gap (Fig. 4d), it has a larger ρxx. For the d = 4 sample, the larger ρxx is probably induced by the enhanced dissipative quasi-helical side surface states and/or residual bulk carriers with increasing sample thickness.

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Zhao, YF., Zhang, R., Mei, R. et al. Tuning the Chern number in quantum anomalous Hall insulators. Nature 588, 419–423 (2020). https://doi.org/10.1038/s41586-020-3020-3

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