Abstract
Confining materials to two-dimensional forms changes the behaviour of the electrons and enables the creation of new devices. However, most materials are challenging to produce as uniform, thin crystals. Here we present a synthesis approach where thin crystals are grown in a nanoscale mould defined by atomically flat van der Waals (vdW) materials. By heating and compressing bismuth in a vdW mould made of hexagonal boron nitride, we grow ultraflat bismuth crystals less than 10 nm thick. Due to quantum confinement, the bismuth bulk states are gapped, isolating intrinsic Rashba surface states for transport studies. The vdW-moulded bismuth shows exceptional electronic transport, enabling the observation of Shubnikov–de Haas quantum oscillations originating from the (111) surface state Landau levels. By measuring the gate-dependent magnetoresistance, we observe multi-carrier quantum oscillations and Landau level splitting, with features originating from both the top and bottom surfaces. Our vdW mould growth technique establishes a platform for electronic studies and control of bismuth’s Rashba surface states and topological boundary modes1,2,3. Beyond bismuth, the vdW-moulding approach provides a low-cost way to synthesize ultrathin crystals and directly integrate them into a vdW heterostructure.
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Data availability
All of the data that support the findings of this study are available via Zenodo at https://doi.org/10.5281/zenodo.10929346 (ref. 46).
Code availability
The code for the experimental data analysis is available from the corresponding author upon request.
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Acknowledgements
The fabrication and measurement of ultrathin bismuth devices were primarily supported by the Air Force Office of Scientific Research under award numbers FA9550-21-1-0165 and FA9550-23-1-0454 (L.C. and A.X.W.). Materials characterization and technique development were supported by the National Science Foundation (NSF) Materials Research Science and Engineering Center (MRSEC) programme through the University of California (UC) Irvine Center for Complex and Active Materials Seed Program (DMR-2011967, A.X.W.). We acknowledge the use of facilities and instrumentation at the Integrated Nanosystems Research Facility (INRF) in the Samueli School of Engineering at UC Irvine and at the UC Irvine Materials Research Institute (IMRI), which is supported in part by the NSF MRSEC through the UC Irvine Center for Complex and Active Materials. Film deposition work was performed using instrumentation funded by Defense University Research Instrumentation Program (DURIP) award FA2386-14-1-3026. Raman spectroscopy was supported by the Laboratory Directed Research and Development programme of Los Alamos National Laboratory under project number 20210782ER (M.T.P. and M.A.C.). This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the US Department of Energy (DOE) Office of Science. Los Alamos National Laboratory, an affirmative action equal opportunity employer, is managed by Triad National Security, LLC, for the US Department of Energy’s NNSA, under contract 89233218CNA000001. K.W. and T.T. acknowledge support from the Japan Society for the Promotion of Science (JSPS) KAKENHI (Grant Numbers 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan. Another portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative Agreement no. DMR-2128556 and the State of Florida. We thank I. Krivorotov and A. Khan for the assistance and use of their sputtering machine. We thank V. Fatemi, A. F. Young, M. Q. Arguilla and X. Yan for productive discussions and F. Guzman, M. Xu, J. Zheng and Q. Lin for technical assistance.
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J.D.S.-Y. supervised the overall research. L.C., A.X.W., N.T., J.W. and A.J. prepared the samples. L.C. and A.X.W. performed the device measurements and analysed the experimental data. M.A.C. performed the Raman measurements. M.X. and A.X.W. performed and analysed the EBSD measurements. C.A.G. performed TEM measurements. Y.Z. performed the first-principles calculations. H.C. and P.C. developed the molecular dynamics simulations of squeezing models. K.W. and T.T. synthesized the hBN samples. L.A.J., J.D.S.-Y., X.P., M.T.P., R.W. and P.C. discussed the results and commented on the manuscript. L.C., A.X.W. and J.D.S.-Y. wrote the manuscript.
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Extended data
Extended Data Fig. 1 Setup used for vdW-molding and process for preparing samples for vdW-molding.
a, Photo of the microsqueezing setup. b, Diagram of the microsqueezing setup with inset of the sample stack. Setup is designed to keep the top and bottom substrates parallel during squeezing while minimizing shear forces. c-e, Diagram and optical sample image of each step to make a bismuth-hBN stack: c, transfer of bottom hBN flake onto substrate, d, transfer of starting bismuth flake on the bottom hBN, e, encapsulating bismuth with top hBN flake.
Extended Data Fig. 2 Optical images of vdW-molded bismuth samples.
For samples M60 and M87 the top hBN flakes have been removed. Scale bar is the same for all the images 10 µm.
Extended Data Fig. 3 AFM scans of the vdW-molded bismuth surfaces showing various flat terrace structures.
All samples have the top hBN removed, except for M92. Clear layered terraces are visible in M92 through the thin hBN layer.
Extended Data Fig. 4 Optical images and EBSD maps for additional samples.
Optical image and X,Y,Z inverse pole figures are in respective order from left to right for each sample. a&c, vdW-molded bismuth encapsulated between hBN. b, vdW-molded bismuth without top hBN. d-e, SiO2-molded bismuth on the edge of a hBN flake. Bismuth thickness for panels a-e are 21 nm, 23 nm, 17 nm, 20 nm − 61 nm, and 30 nm, respectively.
Extended Data Fig. 5 Process for fabricating open-face devices from vdW-molded bismuth crystals.
a-g, Optical image and cross-sectional schematics of the fabrication of the bismuth transport devices.
Extended Data Fig. 6 Temperature-dependent transport measurements of various devices, plotted in designated colors.
a, Sheet resistance as a function of temperature. b, Fitted bulk gap as a function of device thickness, averaged from the minimum and maximum thicknesses of each device. Vertical error bar denotes the standard deviation of the fitted bulk gap. Horizontal error bar denotes the range of the thickness of each device.
Extended Data Fig. 7 Field-dependent transport measurements from various devices.
a, Resistance as a function of magnetic field. b, Quantum oscillations in R(1/B) under 12 T, calculated by subtracting a smoothed background. Sample with a nonuniform thickness is labeled with a range.
Extended Data Fig. 8 Quantum oscillations measured in the rough 13 nm device.
a, Quantum oscillations measured as a function of gate voltage and magnetic field for the rough 13 nm sample (1.1 μm x 2.1 μm) at 1.5 K. Same device as appears in Fig. 3. The amplitude of the quantum oscillation is much smaller in comparison to the flatter sample. b, FFT calculation of the quantum oscillation of the sample. Unlike the flat sample, we observe only one dominant hole oscillation.
Extended Data Fig. 9 DFT calculations of the lattice structure, Fermi surfaces, and band structure for 12-bilayer bismuth.
a, Lattice structure of the bulk bismuth (111) for orientation aligned with the c-axis. The lattice constants are a = 4.57 Å, c = 11.75 Å and the Bi bond length is 3.10 Å. The intra-bilayer height is 1.63 Å and inter-bilayer spacing is 2.29 Å. b, Lattice structure of 12 bilayer bismuth with two (111) surfaces. After relaxation, the average of the intra bilayer height is 1.50 Å and inter bilayer spacing is 2.13 Å. c, The 2D first Brillouin zone of bismuth (111). d, Fermi surface at kz = 0, calculated using WannierTools47 with a dense 201 × 201 × 1 k mesh, based on the tight-binding Hamiltonian obtained by employing maximally localized Wannier functions (MLWFs) method using WANNIER9048 with initial projections to Bi-p orbitals. e, Band structure with Fermi surfaces at 0 eV. This plot is used as the basis of the Fermi surface schematic in Fig. 4f.
Supplementary information
Supplementary Information
Supplementary Figs. 1–11, Tables 1–4 and Discussion.
Supplementary Video 1
Supplementary Video 1 shows the rapid spreading of bismuth during the vdW-moulding process.
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Chen, L., Wu, A.X., Tulu, N. et al. Exceptional electronic transport and quantum oscillations in thin bismuth crystals grown inside van der Waals materials. Nat. Mater. (2024). https://doi.org/10.1038/s41563-024-01894-0
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DOI: https://doi.org/10.1038/s41563-024-01894-0
