For decades, two-dimensional electron gases (2DEG) have allowed important experimental discoveries1,2 and conceptual developments in condensed-matter physics3. When combined with the unique electronic properties of two-dimensional crystals, they allow rich physical phenomena to be probed at the quantum level4,5. Here, we create a 2DEG in black phosphorus—a recently added member of the two-dimensional atomic crystal family6,7,8—using a gate electric field. The black phosphorus film hosting the 2DEG is placed on a hexagonal boron nitride substrate. The resulting high carrier mobility in the 2DEG allows the observation of quantum oscillations. The temperature and magnetic field dependence of these oscillations yields crucial information about the system, such as cyclotron mass and lifetime of its charge carriers. Our results, coupled with the fact that black phosphorus possesses anisotropic energy bands with a tunable, direct bandgap6,7,8,9,10,11,12,13,14,15, distinguish black phosphorus 2DEG as a system with unique electronic and optoelectronic properties.
This is a preview of subscription content
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Sarma, S. D. & Pinczuk, A. Perspectives in Quantum Hall Effects (Wiley, 2004).
Ando, T., Fowler, A. B. & Stern, F. Electronic properties of two-dimensional systems. Rev. Mod. Phys. 54, 437–672 (1982).
Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).
Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).
Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nature Phys. 10, 343–350 (2014).
Li, L. et al. Black phosphorus field-effect transistors. Nature Nanotech. 9, 372–377 (2014).
Liu, H. et al. Phosphorene: an unexplored 2D semiconductor with a high hole mobility. ACS Nano 8, 4033–4041 (2014).
Koenig, S. P., Doganov, R. A., Schmidt, H., Neto, A. H. C. & Özyilmaz, B. Electric field effect in ultrathin black phosphorus. Appl. Phys. Lett. 104, 103106 (2014).
Takao, Y. & Morita, A. Electronic structure of black phosphorus: tight binding approach. Physica B+C 105, 93–98 (1981).
Tran, V., Soklaski, R., Liang, Y. & Yang, L. Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus. Phys. Rev. B 89, 235319 (2014).
Castellanos-Gomez, A. et al. Isolation and characterization of few-layer black phosphorus. 2D Mater. 1, 025001 (2014).
Das, S. et al. Tunable transport gap in phosphorene. Nano Lett. 14, 5733–5739 (2014).
Yuan, H. et al. Broadband linear-dichroic photodetector in a black phosphorus vertical p–n junction. Preprint at http://arxiv.org/abs/1409.4729 (2014).
Zhang, S. et al. Extraordinary photoluminescence and strong temperature/angle-dependent Raman responses in few-layer phosphorene. ACS Nano 8, 9590–9596 (2014).
Wang, X. et al. Highly anisotropic and robust excitons in monolayer black phosphorus. Preprint at http://arxiv.org/abs/1411.1695 (2014).
Podzorov, V., Gershenson, M. E., Kloc, C., Zeis, R. & Bucher, E. High-mobility field-effect transistors based on transition metal dichalcogenides. Appl. Phys. Lett. 84, 3301–3303 (2004).
Schwierz, F. & Liou, J. J. Modern Microwave Transistors: Theory, Design, and Performance (Wiley-Interscience, 2003).
Keyes, R. W. The electrical properties of black phosphorus. Phys. Rev. 92, 580–584 (1953).
Warschauer, D. Electrical and optical properties of crystalline black phosphorus. J. Appl. Phys. 34, 1853–1860 (1963).
Maruyama, Y., Suzuki, S., Kobayashi, K. & Tanuma, S. Synthesis and some properties of black phosphorus single crystals. Physica B+C 105, 99–102 (1981).
Akahama, Y., Endo, S. & Narita, S. Electrical properties of black phosphorus single crystals. J. Phys. Soc. Jpn 52, 2148–2155 (1983).
Xia, F., Wang, H. & Jia, Y. Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics. Nature Commun. 5, 4458 (2014).
Wang, H. et al. Black phosphorus radio frequency transistors. Nano Lett. 14, 6424–6429 (2014).
Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nature Nanotech. 5, 722–726 (2010).
Sze, S. M. & Ng, K. K. Physics of Semiconductor Devices (Wiley, 2006).
Datta, S. Electronic Transport in Mesoscopic Systems (Cambridge Univ. Press, 1995).
Ye, J. T. et al. Superconducting dome in a gate-tuned band insulator. Science 338, 1193–1196 (2012).
Shoenberg, D. Magnetic Oscillations in Metals (Cambridge Univ. Press, 1984).
Zhang, Y., 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).
Zhou, X. Y. et al. Landau levels and magneto-transport property of monolayer phosphorene. Preprint at http://arxiv.org/abs/1411.4275 (2014).
Narita, S. et al. Far-infrared cyclotron resonance absorptions in black phosphorus single crystals. J. Phys. Soc. Jpn 52, 3544–3553 (1983).
Fang, F. F. & Stiles, P. J. Effects of a tilted magnetic field on a two-dimensional electron gas. Phys. Rev. 174, 823–828 (1968).
Tayari, V. et al. Two-dimensional magnetotransport in a black phosphorus naked quantum well. Preprint at http://arxiv.org/abs/1412.0259 (2014).
Chen, X. et al. High quality sandwiched black phosphorus heterostructure and its quantum oscillations. Preprint at http://arxiv.org/abs/1412.1357 (2014).
Gillgren, N. et al. Gate tunable quantum oscillations in air-stable and high mobility few-layer phosphorene heterostructures. 2D Mater. 2, 011001 (2015).
Castellanos-Gomez, A. et al. Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping. 2D Mater. 1, 011002 (2014).
The authors thank F. Wang, X. Lin, Y-W. Tan, L. He and Y. Liu for discussions, J. Zhao, Q. Wang and Y. Shen for help with sample preparation and S. Hannahs, T. Murphy, D. Graf, J. Billings, B. Pullum, L. Balicas and B. Zeng for help with measurements in high magnetic fields. 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-1157490, the State of Florida, and the US Department of Energy. Part of the sample fabrication was conducted at Fudan Nano-fabrication Lab. L.L., G.C. and Y.Z. acknowledge financial support from the National Basic Research Program of China (973 Program; grants nos. 2011CB921802 and 2013CB921902) and the NSF of China (grant no. 11034001). L.L. and Y.Z. also acknowledge support from Samsung Global Research Outreach (GRO) Program. G.J.Y. and X.H.C. acknowledge support from the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB04040100) and the National Basic Research Program of China (973 Program; grant no. 2012CB922002). V.T., R.F. and L.Y. are supported by the NSF (DMR-1207141). H.W. and J.W. are supported by the National Basic Research Program of China (grant no. 2013CB934600) and the NSF of China (grant no. 11222434). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan. T.T. also acknowledges support by a Grant-in-Aid for Scientific Research on Innovative Areas, ‘Nano Informatics’ (grants nos. 262480621 and 25106006) from JSPS.
The authors declare no competing financial interests.
About this article
Cite this article
Li, L., Ye, G., Tran, V. et al. Quantum oscillations in a two-dimensional electron gas in black phosphorus thin films. Nature Nanotech 10, 608–613 (2015). https://doi.org/10.1038/nnano.2015.91
Nano-Micro Letters (2022)
Nature Electronics (2021)
Properties and photodetector applications of two-dimensional black arsenic phosphorus and black phosphorus
Science China Information Sciences (2021)
Surface charge transfer doping for two-dimensional semiconductor-based electronic and optoelectronic devices
Nano Research (2021)
Nature Communications (2020)