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Quantum oscillations in a two-dimensional electron gas in black phosphorus thin films


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.

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Figure 1: Black phosphorus FET and its basic characterization.
Figure 2: SdH oscillations in black phosphorus 2DEG.
Figure 3: Angular dependence of SdH oscillations in black phosphorus 2DEG.
Figure 4: Cyclotron mass, carrier lifetime and Zeeman splitting in black phosphorus 2DEG.


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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.

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Authors and Affiliations



L.L. fabricated the black phosphorus devices, performed transport measurements, and analysed the data. G.J.Y. and X.H.C. grew bulk black phosphorus crystals. V.T., R.F. and L.Y. carried out theoretical calculations. G.C., H.W. and J.W. helped with the transport measurement. K.W. and T.T. grew bulk h-BN. Y.Z. and X.H.C. co-supervised the project. L.L. and Y.Z. wrote the paper with input from all authors.

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Correspondence to Xian Hui Chen or Yuanbo Zhang.

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The authors declare no competing financial interests.

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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).

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