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Magnetic quantum phase transition in Cr-doped Bi2(SexTe1−x)3 driven by the Stark effect

Nature Nanotechnology volume 12, pages 953957 (2017) | Download Citation


The recent experimental observation of the quantum anomalous Hall effect1,2,3,4,5 has cast significant attention on magnetic topological insulators. In these magnetic counterparts of conventional topological insulators such as Bi2Te3, a long-range ferromagnetic state can be established by chemical doping with transition-metal elements6,7,8. However, a much richer electronic phase diagram can emerge and, in the specific case of Cr-doped Bi2(SexTe1−x)3, a magnetic quantum phase transition tuned by the actual chemical composition has been reported8. From an application-oriented perspective, the relevance of these results hinges on the possibility to manipulate magnetism and electronic band topology by external perturbations such as an electric field generated by gate electrodes—similar to what has been achieved in conventional diluted magnetic semiconductors9. Here, we investigate the magneto-transport properties of Cr-doped Bi2(SexTe1−x)3 with different compositions under the effect of a gate voltage. The electric field has a negligible effect on magnetic order for all investigated compositions, with the remarkable exception of the sample close to the topological quantum critical point, where the gate voltage reversibly drives a ferromagnetic-to-paramagnetic phase transition. Theoretical calculations show that a perpendicular electric field causes a shift in the electronic energy levels due to the Stark effect, which induces a topological quantum phase transition and, in turn, a magnetic phase transition.

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  1. 1.

    et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).

  2. 2.

    et al. Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator. Nat. Phys. 10, 731–736 (2014).

  3. 3.

    et al. Scale-invariant quantum anomalous Hall effect in magnetic topological insulators beyond the two-dimensional limit. Phys. Rev. Lett. 113, 137201 (2014).

  4. 4.

    et al. High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator. Nat. Mater. 14, 473–477 (2015).

  5. 5.

    et al. Precise quantization of the anomalous Hall effect near zero magnetic field. Phys. Rev. Lett. 114, 187201 (2015).

  6. 6.

    Transition Metal-Doped Sb2Te3 and Bi2Te3 Diluted Magnetic Semiconductors. PhD thesis, Univ. Michigan (2007).

  7. 7.

    et al. Development of ferromagnetism in the doped topological insulator Bi2−xMnxTe3. Phys. Rev. B 81, 195203 (2010).

  8. 8.

    et al. Topology-driven magnetic quantum phase transition in topological insulators. Science 339, 1582–1586 (2013).

  9. 9.

    & Dilute ferromagnetic semiconductors: physics and spintronic structures. Rev. Mod. Phys. 86, 187–251 (2014).

  10. 10.

    , , , & Dirac-fermion-mediated ferromagnetism in a topological insulator. Nat. Phys. 8, 729–733 (2012).

  11. 11.

    et al. Interplay between different magnetisms in Cr-doped topological insulators. ACS Nano 7, 9205–9212 (2013).

  12. 12.

    et al. Electrically tuned magnetic order and magnetoresistance in a topological insulator. Nat. Commun. 5, 4915 (2014).

  13. 13.

    & Electric field driven quantum phase transition between band insulator and topological insulator. Appl. Phys. Lett. 95, 222110 (2009).

  14. 14.

    , & Effective continuous model for surface states and thin films of three-dimensional topological insulators. New J. Phys. 12, 043048 (2010).

  15. 15.

    , , & Chern number of thin films of the topological insulator Bi2Se3. Phys. Rev. B 82, 165104 (2010).

  16. 16.

    , , & Topological quantum phase transitions driven by external electric fields in Sb2Te3 thin films. Proc. Natl Acad. Sci. USA 109, 671–674 (2012).

  17. 17.

    , , , & Switching a normal insulator into a topological insulator via electric field with application to phosphorene. Nano Lett. 15, 1222–1228 (2015).

  18. 18.

    , & Electrically tunable magnetism in magnetic topological insulators. Phys. Rev. Lett. 115, 036805 (2015).

  19. 19.

    et al. Quantized anomalous Hall effect in magnetic topological insulators. Science 329, 61–64 (2010).

  20. 20.

    et al. Gate-voltage control of chemical potential and weak antilocalization in Bi2Se3. Phys. Rev. Lett. 105, 176602 (2010).

  21. 21.

    Criterion for ferromagnetism from observations of magnetic isotherms. Phys. Rev. 108, 1394–1396 (1957).

  22. 22.

    , , , & Magnetic impurities on the surface of a topological insulator. Phys. Rev. Lett. 102, 156603 (2009).

  23. 23.

    et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nat. Phys. 5, 438–442 (2009).

  24. 24.

    et al. Finite-size and composition-driven topological phase transition in (Bi1–xInx)2Se3 thin films. Nano Lett. 16, 5528–5532 (2016).

  25. 25.

    et al. Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit. Nat. Phys. 6, 584–588 (2010).

  26. 26.

    et al. Creation and control of a two-dimensional electron liquid at the bare SrTiO3 surface. Nat. Mater. 10, 114–118 (2011).

  27. 27.

    et al. Interface charge doping effects on superconductivity of single-unit-cell FeSe films on SrTiO3 substrates. Phys. Rev. B 89, 060506 (2014).

  28. 28.

    et al. Observation of tunable band gap and anisotropic Dirac semimetal state in black phosphorus. Science 349, 723–726 (2015).

  29. 29.

    , , , & Electrically tunable bandgaps in bilayer MoS2. Nano Lett. 15, 8000–8007 (2015).

  30. 30.

    , , , & Observation of the giant Stark effect in boron-nitride nanotubes. Phys. Rev. Lett. 94, 056804 (2005).

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The authors thank P. Tang, J. Li and H. Zhang for discussions. This work was supported by the National Natural Science Foundation of China and the Ministry of Science and Technology of China. This work is supported in part by the Beijing Advanced Innovation Center for Future Chip (ICFC). B.L., J.W. and S.-C.Z. acknowledge support from the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering (contract no. DE-AC02-76SF00515). J.W. acknowledges support from the National Thousand-Young-Talents Program.

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Author notes

    • Zuocheng Zhang
    • , Xiao Feng
    •  & Jing Wang

    These authors contributed equally to this work.


  1. State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China

    • Zuocheng Zhang
    • , Xiao Feng
    • , Jinsong Zhang
    • , Cuizu Chang
    • , Minghua Guo
    • , Yunbo Ou
    • , Yang Feng
    • , Ke He
    • , Xucun Ma
    • , Qi-Kun Xue
    •  & Yayu Wang
  2. State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai 200433, China

    • Jing Wang
  3. Department of Physics, Stanford University, Stanford, California 94305–4045, USA

    • Jing Wang
    • , Biao Lian
    •  & Shou-Cheng Zhang
  4. Collaborative Innovation Center of Quantum Matter, Beijing 100084, China

    • Shou-Cheng Zhang
    • , Ke He
    • , Xucun Ma
    • , Qi-Kun Xue
    •  & Yayu Wang


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Y.W., K.H. and Q.-K.X. conceived and designed the experiments. Z.Z., J.Z., M.G. and Y.F. carried out transport measurements and analysed the data. X.F., C.C., Y.O. and X.C.M. grew magnetic topological insulator thin film and obtained angle-resolved photoemission spectra. J.W., B.L. and S.-C.Z. performed theoretical calculations. Z.Z. and Y.W. wrote the paper, with input from all authors. All authors discussed the results and commented on the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Ke He or Yayu Wang.

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