Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Quantum Hall effect of Weyl fermions in n-type semiconducting tellurene

Abstract

Dirac and Weyl nodal materials can host low-energy relativistic quasiparticles. Under strong magnetic fields, the topological properties of Dirac/Weyl materials can directly be observed through quantum Hall states. However, most Dirac/Weyl nodes generically exist in semimetals without exploitable band gaps due to their accidental band-crossing origin. Here, we report the first experimental observation of Weyl fermions in a semiconductor. Tellurene, the two-dimensional form of tellurium, possesses a chiral crystal structure which induces unconventional Weyl nodes with a hedgehog-like radial spin texture near the conduction band edge. We synthesize high-quality n-type tellurene by a hydrothermal method with subsequent dielectric doping and detect a topologically non-trivial π Berry phase in quantum Hall sequences. Our work expands the spectrum of Weyl matter into semiconductors and offers a new platform to design novel quantum devices by marrying the advantages of topological materials to versatile semiconductors.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Crystal structure of Te and n-type ALD doped tellurene devices.
Fig. 2: Quantum Hall effect in tellurene 2D electron gas.
Fig. 3: Shubnikov–de Haas oscillation analysis of two layers of electrons in a Te wide quantum well.
Fig. 4: Weyl nodes and Berry phase near Te conduction band edge.
Fig. 5: Temperature-dependent SdH oscillations and effective mass of Weyl fermions.

Data availability

The data that supports the argument and generates the plots in this paper are available from the corresponding author upon reasonable request.

References

  1. 1.

    Geim, A. K. & Novoselov, K. S. The rise of graphene. Nat. Mater. 6, 183–191 (2007).

    CAS  Google Scholar 

  2. 2.

    Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    CAS  Google Scholar 

  3. 3.

    Zhang, Y. B., Tan, Y. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

    CAS  Google Scholar 

  4. 4.

    Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).

    CAS  Google Scholar 

  5. 5.

    Hasan, M. Z., Xu, S. Y., Belopolski, I. & Huang, S. M. Discovery of Weyl fermion semimetals and topological Fermi arc states. Annu. Rev. Condens. Matter Phys. 8, 289–309 (2017).

    CAS  Google Scholar 

  6. 6.

    Hirayama, M., Okugawa, R., Ishibashi, S., Murakami, S. & Miyake, T. Weyl node and spin texture in trigonal tellurium and selenium. Phys. Rev. Lett. 114, 206401 (2015).

    Google Scholar 

  7. 7.

    Nakayama, K. et al. Band splitting and Weyl nodes in trigonal tellurium studied by angle-resolved photoemission spectroscopy and density functional theory. Phys. Rev. B 95, 125204 (2017).

    Google Scholar 

  8. 8.

    Tsirkin, S. S., Puente, P. A. & Souza, I. Gyrotropic effects in trigonal tellurium studied from first principles. Phys. Rev. B 97, 035158 (2018).

    CAS  Google Scholar 

  9. 9.

    Agapito, L. A., Kioussis, N., Goddard, W. A. & Ong, N. P. Novel family of chiral-based topological insulators: elemental tellurium under strain. Phys. Rev. Lett. 110, 176401 (2013).

    Google Scholar 

  10. 10.

    Şahin, C., Rou, J., Ma, J. & Pesin, D. A. Pancharatnam-Berry phase and kinetic magnetoelectric effect in trigonal tellurium. Phys. Rev. B 97, 205206 (2018).

    Google Scholar 

  11. 11.

    Chang, G. et al. Topological quantum properties of chiral crystals. Nat. Mater. 17, 978 (2018).

    CAS  Article  Google Scholar 

  12. 12.

    Rao, Z. et al. Observation of unconventional chiral fermions with long Fermi arcs in CoSi. Nature 567, 496–499 (2019).

    CAS  Google Scholar 

  13. 13.

    Sanchez, D. S. et al. Topological chiral crystals with helicoid-arc quantum states. Nature 567, 500–505 (2019).

    CAS  Google Scholar 

  14. 14.

    Zhang, C. L. et al. Ultraquantum magnetoresistance in the Kramers–Weyl semimetal candidate β-Ag2Se. Phys. Rev. B 96, 1–10 (2017).

    Google Scholar 

  15. 15.

    von Klitzing, K. & Landwehr, G. Surface quantum states in tellurium. Solid State Commun. 9, 2201–2205 (1971).

    Google Scholar 

  16. 16.

    Silbermann, R. & Landwehr, G. Surface quantum oscillations in accumulation and inversion layers on tellurium. Solid State Commun. 16, 6–9 (1975).

    Google Scholar 

  17. 17.

    von Klitzing, K. Magnetophonon oscillations in tellurium under hot carrier conditions. Solid State Commun. 15, 1721–1725 (1974).

    Google Scholar 

  18. 18.

    Wang, Y. et al. Field-effect transistors made from solution-grown two-dimensional tellurene. Nat. Electron. 1, 228–236 (2018).

    Google Scholar 

  19. 19.

    Du, Y. et al. One-dimensional van der Waals material tellurium: Raman spectroscopy under strain and magneto-transport. Nano Lett. 17, 3965–3973 (2017).

    CAS  Google Scholar 

  20. 20.

    Wu, W., Qiu, G., Wang, Y., Wang, R. & Ye, P. Tellurene: its physical properties, scalable nanomanufacturing, and device applications. Chem. Soc. Rev. 47, 7203–7212 (2018).

    CAS  Google Scholar 

  21. 21.

    Qiu, G. et al. Quantum transport and band structure evolution under high magnetic field in few-layer tellurene. Nano Lett. 18, 5760–5767 (2018).

    CAS  Google Scholar 

  22. 22.

    Gusynin, V. P. & Sharapov, S. G. Unconventional integer quantum Hall effect in graphene. Phys. Rev. Lett. 95, 146801 (2005).

    CAS  Google Scholar 

  23. 23.

    Li, L. et al. Quantum oscillations in a two-dimensional electron gas in black phosphorus thin films. Nat. Nanotechnol. 10, 608–613 (2015).

    CAS  Google Scholar 

  24. 24.

    Li, L. et al. Quantum hall effect in black phosphorus two-dimensional electron system. Nat. Nanotechnol. 11, 593–597 (2016).

    CAS  Google Scholar 

  25. 25.

    Yang, J. et al. Integer and fractional quantum Hall effect in ultra-high quality few-layer black phosphorus transistors. Nano Lett. 18, 229–234 (2018).

    CAS  Google Scholar 

  26. 26.

    Bandurin, D. A. et al. High electron mobility, quantum Hall effect and anomalous optical response in atomically thin Inse. Nat. Nanotechnol. 12, 223–227 (2017).

    CAS  Google Scholar 

  27. 27.

    Fallahazad, B. et al. Shubnikov-de Haas oscillations of high-mobility holes in monolayer and bilayer WSe2: Landau level degeneracy, effective mass, and negative compressibility. Phys. Rev. Lett. 116, 1–5 (2016).

    Google Scholar 

  28. 28.

    Movva, H. C. P. et al. Density-dependent quantum Hall states and Zeeman splitting in monolayer and bilayer WSe2. Phys. Rev. Lett. 118, 247701 (2017).

    Google Scholar 

  29. 29.

    Wu, Z. et al. Even-odd layer-dependent magnetotransport of high-mobility Q-valley electrons in transition metal disulfides. Nat. Commun. 7, 12955 (2016).

    CAS  Google Scholar 

  30. 30.

    Pisoni, R. et al. Interactions and magnetotransport through spin-valley coupled Landau levels in monolayer MoS2. Phys. Rev. Lett. 121, 247701 (2018).

    CAS  Google Scholar 

  31. 31.

    Ren, X. et al. Gate-tuned insulator-metal transition in electrolyte-gated transistors based on tellurene. Nano Lett. 19, 4738–4744 (2019).

    CAS  Google Scholar 

  32. 32.

    Qiu, G. et al. High-performance few-layer tellurium CMOS devices enabled by atomic layer deposited dielectric doping technique. In 2018 76th Device Research Conference (DRC) 1–2 (IEEE, 2018).

  33. 33.

    Berweger, S. et al. Imaging carrier inhomogeneities in ambipolar tellurene field effect transistors. Nano Lett. 19, 1289–1294 (2019).

    Google Scholar 

  34. 34.

    Liu, H., Neal, A. T., Si, M., Du, Y. & Ye, P. D. The effect of dielectric capping on few-layer phosphorene transistors: Tuning the Schottky barrier heights. IEEE Electron Device Lett. 35, 795–797 (2014).

    Google Scholar 

  35. 35.

    Perello, D. J., Chae, S. H., Song, S. & Lee, Y. H. High-performance n-type black phosphorus transistors with type control via thickness and contact-metal engineering. Nat. Commun. 6, 7809 (2015).

    CAS  Google Scholar 

  36. 36.

    Wang, C. H. et al. Unipolar n-type black phosphorus transistors with low work function contacts. Nano Lett. 18, 2822–2827 (2018).

    CAS  Google Scholar 

  37. 37.

    Coss, B. E. et al. Near band edge Schottky barrier height modulation using high-κ dielectric dipole tuning mechanism. Appl. Phys. Lett. 95, 222105 (2009).

    Google Scholar 

  38. 38.

    Klitzing, K. V., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980).

    Google Scholar 

  39. 39.

    Zhang, N. et al. Evidence for Weyl fermions in the elemental semiconductor tellurium. arXiv Prepr. arXiv1906.06071 (2019).

  40. 40.

    Ren, Z., Taskin, A. A., Sasaki, S., Segawa, K. & Ando, Y. Large bulk resistivity and surface quantum oscillations in the topological insulator Bi2Te2Se. Phys. Rev. B 82, 241306 (2010).

    Google Scholar 

  41. 41.

    Ando, Y. Topological insulator materials. J. Phys. Soc. Jpn. 82, 102001 (2013).

    Google Scholar 

  42. 42.

    Xiong, J. et al. Quantum oscillations in a topological insulator Bi2Te2Se with large bulk resistivity (6Ω∙cm). Phys. E 44, 917–920 (2012).

    CAS  Google Scholar 

  43. 43.

    Yu, W. et al. Quantum oscillations at integer and fractional Landau level indices in single-crystalline ZrTe5. Sci. Rep. 6, 35357 (2016).

    CAS  Google Scholar 

  44. 44.

    Hu, J. et al. π Berry phase and Zeeman splitting of Weyl semimetal TaP. Sci. Rep. 6, 18674 (2016).

    CAS  Google Scholar 

  45. 45.

    Zhao, Y. et al. Anisotropic Fermi surface and quantum limit transport in high mobility three-dimensional dirac semimetal Cd3As2. Phys. Rev. X 5, 031037 (2015).

    Google Scholar 

  46. 46.

    Roth, L. Semiclassical theory of magnetic energy levels and magnetic susceptibility of Bloch electrons. Phys. Rev. 145, 434 (1966).

    CAS  Google Scholar 

  47. 47.

    Dhillon, J. S. & Shoenberg, D. The de Haas-van alphen effect III. Experiments at fields up to 32 KG. Philos. Trans. R. Soc. A 248, 1–21 (1955).

    Google Scholar 

  48. 48.

    Alexandradinata, A., Wang, C., Duan, W. & Glazman, L. Revealing the topology of Fermi-surface wave functions from magnetic quantum oscillations. Phys. Rev. X 8, 11027 (2018).

    CAS  Google Scholar 

  49. 49.

    Xu, S. et al. Odd-integer quantum hall states and giant spin susceptibility in p-type few-layer WSe2. Phys. Rev. Lett. 118, 067702 (2017).

    Google Scholar 

  50. 50.

    Niu, C. et al. Gate-tunable Strong Spin-orbit Interaction in Two-dimensional Tellurium Probed by Weak-antilocalization. arXiv Prepr. arXiv1909.06659 (2019).

  51. 51.

    Rotenberg, E. Topological insulators: The dirt on topology. Nat. Phys. 7, 8–10 (2011).

    CAS  Google Scholar 

  52. 52.

    Mallet, P. et al. Role of pseudospin in quasiparticle interferences in epitaxial graphene probed by high-resolution scanning tunneling microscopy. Phys. Rev. B 86, 045444 (2012).

    Google Scholar 

  53. 53.

    Shinno, H., Yoshizaki, R., Tanaka, S., Doi, T. & Kamimura, H. Conduction band structure of tellurium. J. Phys. Soc. Jpn. 35, 525–533 (1973).

    CAS  Google Scholar 

  54. 54.

    Liu, Y., Wu, W. & Goddard, W. A. Tellurium: fast electrical and atomic transport along the weak interaction direction. J. Am. Chem. Soc. 140, 550–553 (2018).

    CAS  Google Scholar 

  55. 55.

    Zasadzinski, J. A., Viswanathan, R., Madsen, L., Garnaes, J. & Schwartz, D. K. Langmuir-Blodgett films. Science 263, 1726–1733 (1994).

    CAS  Google Scholar 

Download references

Acknowledgements

P.D.Y. was supported by NSF/AFOSR 2DARE programmes ARO and SRC. W.W. acknowledges the College of Engineering and School of Industrial Engineering at Purdue University for the startup support. W.W. was partially supported by a grant from the Oak Ridge Associated Universities (ORAU) Junior Faculty Enhancement Award Programme. W.W. and P.D.Y. were also supported by NSF under grant no. CMMI-1762698. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative Agreement No. DMR-1644779 and the State of Florida. G.Q. and C.N. acknowledge technical support from National High Magnetic Field Laboratory staff J. Jaroszynski, A. Suslov and W. Coniglio. The authors want to give special thanks to K. von Klitzing, T. Ando, W. Pan, K. Chang, F. Zhang, C. Liu, K. Cho, Y. Nie and J. Hwang for the insightful discussions on electronic structures of Te. The authors also acknowledge A. R. Charnas for editorial assistance.

Author information

Affiliations

Authors

Contributions

P.D.Y. conceived and supervised the project. P.D.Y. and G.Q. designed the experiments. Y.W. synthesized the material under the supervision of W.W. G.Q. and C.N. fabricated the devices. G.Q., C.N. and Z.Z. performed the magneto-transport measurements. G.Q., C.N., M.S. and Z.Z. analysed the data. P.D.Y. and G.Q. wrote the manuscript with input and comments from all the authors.

Corresponding author

Correspondence to Peide D. Ye.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Extended data

Extended Data Fig. 1 Quantum Hall effect of another high mobility sample.

Longitudinal (Rxx, red) and transverse (Rxy, blue) resistance measured under magnetic field up to 31.4 T at 1.7 K.

Extended Data Fig. 2 SdH oscillations in a tilted magnetic field.

The curves are separated by 80 Ω offset for clarity. No evidence of coincidence effect is observed, suggesting a small effective g-factor.

Extended Data Fig. 3

Extracting Berry phase using SdH oscillation phase offset from eight more devices.

Supplementary information

Supplementary Information

Supplementary Notes 1–5, Supplementary Figs. 1–8 and refs. 1–12.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Qiu, G., Niu, C., Wang, Y. et al. Quantum Hall effect of Weyl fermions in n-type semiconducting tellurene. Nat. Nanotechnol. 15, 585–591 (2020). https://doi.org/10.1038/s41565-020-0715-4

Download citation

Further reading

Search

Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research