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.
Subscribe to Journal
Get full journal access for 1 year
only $4.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The data that supports the argument and generates the plots in this paper are available from the corresponding author upon reasonable request.
Geim, A. K. & Novoselov, K. S. The rise of graphene. Nat. Mater. 6, 183–191 (2007).
Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).
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).
Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).
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).
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).
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).
Tsirkin, S. S., Puente, P. A. & Souza, I. Gyrotropic effects in trigonal tellurium studied from first principles. Phys. Rev. B 97, 035158 (2018).
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).
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).
Chang, G. et al. Topological quantum properties of chiral crystals. Nat. Mater. 17, 978 (2018).
Rao, Z. et al. Observation of unconventional chiral fermions with long Fermi arcs in CoSi. Nature 567, 496–499 (2019).
Sanchez, D. S. et al. Topological chiral crystals with helicoid-arc quantum states. Nature 567, 500–505 (2019).
Zhang, C. L. et al. Ultraquantum magnetoresistance in the Kramers–Weyl semimetal candidate β-Ag2Se. Phys. Rev. B 96, 1–10 (2017).
von Klitzing, K. & Landwehr, G. Surface quantum states in tellurium. Solid State Commun. 9, 2201–2205 (1971).
Silbermann, R. & Landwehr, G. Surface quantum oscillations in accumulation and inversion layers on tellurium. Solid State Commun. 16, 6–9 (1975).
von Klitzing, K. Magnetophonon oscillations in tellurium under hot carrier conditions. Solid State Commun. 15, 1721–1725 (1974).
Wang, Y. et al. Field-effect transistors made from solution-grown two-dimensional tellurene. Nat. Electron. 1, 228–236 (2018).
Du, Y. et al. One-dimensional van der Waals material tellurium: Raman spectroscopy under strain and magneto-transport. Nano Lett. 17, 3965–3973 (2017).
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).
Qiu, G. et al. Quantum transport and band structure evolution under high magnetic field in few-layer tellurene. Nano Lett. 18, 5760–5767 (2018).
Gusynin, V. P. & Sharapov, S. G. Unconventional integer quantum Hall effect in graphene. Phys. Rev. Lett. 95, 146801 (2005).
Li, L. et al. Quantum oscillations in a two-dimensional electron gas in black phosphorus thin films. Nat. Nanotechnol. 10, 608–613 (2015).
Li, L. et al. Quantum hall effect in black phosphorus two-dimensional electron system. Nat. Nanotechnol. 11, 593–597 (2016).
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).
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).
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).
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).
Wu, Z. et al. Even-odd layer-dependent magnetotransport of high-mobility Q-valley electrons in transition metal disulfides. Nat. Commun. 7, 12955 (2016).
Pisoni, R. et al. Interactions and magnetotransport through spin-valley coupled Landau levels in monolayer MoS2. Phys. Rev. Lett. 121, 247701 (2018).
Ren, X. et al. Gate-tuned insulator-metal transition in electrolyte-gated transistors based on tellurene. Nano Lett. 19, 4738–4744 (2019).
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).
Berweger, S. et al. Imaging carrier inhomogeneities in ambipolar tellurene field effect transistors. Nano Lett. 19, 1289–1294 (2019).
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).
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).
Wang, C. H. et al. Unipolar n-type black phosphorus transistors with low work function contacts. Nano Lett. 18, 2822–2827 (2018).
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).
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).
Zhang, N. et al. Evidence for Weyl fermions in the elemental semiconductor tellurium. arXiv Prepr. arXiv1906.06071 (2019).
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).
Ando, Y. Topological insulator materials. J. Phys. Soc. Jpn. 82, 102001 (2013).
Xiong, J. et al. Quantum oscillations in a topological insulator Bi2Te2Se with large bulk resistivity (6Ω∙cm). Phys. E 44, 917–920 (2012).
Yu, W. et al. Quantum oscillations at integer and fractional Landau level indices in single-crystalline ZrTe5. Sci. Rep. 6, 35357 (2016).
Hu, J. et al. π Berry phase and Zeeman splitting of Weyl semimetal TaP. Sci. Rep. 6, 18674 (2016).
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).
Roth, L. Semiclassical theory of magnetic energy levels and magnetic susceptibility of Bloch electrons. Phys. Rev. 145, 434 (1966).
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).
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).
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).
Niu, C. et al. Gate-tunable Strong Spin-orbit Interaction in Two-dimensional Tellurium Probed by Weak-antilocalization. arXiv Prepr. arXiv1909.06659 (2019).
Rotenberg, E. Topological insulators: The dirt on topology. Nat. Phys. 7, 8–10 (2011).
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).
Shinno, H., Yoshizaki, R., Tanaka, S., Doi, T. & Kamimura, H. Conduction band structure of tellurium. J. Phys. Soc. Jpn. 35, 525–533 (1973).
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).
Zasadzinski, J. A., Viswanathan, R., Madsen, L., Garnaes, J. & Schwartz, D. K. Langmuir-Blodgett films. Science 263, 1726–1733 (1994).
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.
The authors declare no competing interests.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Longitudinal (Rxx, red) and transverse (Rxy, blue) resistance measured under magnetic field up to 31.4 T at 1.7 K.
The curves are separated by 80 Ω offset for clarity. No evidence of coincidence effect is observed, suggesting a small effective g-factor.
Extracting Berry phase using SdH oscillation phase offset from eight more devices.
About this article
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
Journal of the Physical Society of Japan (2021)
Study of the Growth Mechanism of Solution‐Synthesized Symmetric Tellurium Nanoflakes at Atomic Resolution
Patterning of type-II Dirac semimetal PtTe2 for optimized interface of tellurene optoelectronic device
Nano Energy (2021)
A high performance self-powered photodetector based on a 1D Te–2D WS2 mixed-dimensional heterostructure
Nanoscale Advances (2021)
Physica E: Low-dimensional Systems and Nanostructures (2021)