Thin bismuth crystals with enhanced quantum oscillations

In a recent journal article Natural productsThe researchers proposed a synthesis approach in which thin bismuth crystals with excellent electronic transport and quantum oscillations are grown on an atomically flat van der Waals (vdW) material-defined nanoscale mold.

Research: Synthesis of thin bismuth crystals with enhanced quantum oscillations. Image credit: Declan Hillman/


Confining materials to two-dimensional (2D) shapes changes electron behavior and enables new device development. However, forming thin, uniform crystals from most materials is challenging. Although the study of isolated ultrathin vdW materials using mechanical exfoliation has significantly improved the understanding of 2D electronic physics, this approach cannot be applied to other materials. In a few cases, 2D growth of non-vdW materials has been realized using deposition techniques such as molecular beam epitaxy.

However, the approach often resulted in undesirable substrate interactions or disordered surfaces. An alternative approach to 2D synthesis can be considered where crystals are grown in a defined space between layers of a vdW material. An axis primarily defines the geometry of the crystal in finite growth.

However, in this approach any surface roughness in the mold may be imprinted on the crystal, adversely affecting the electronic properties. Recent studies have shown that vdW materials can define ultra-thin/nano-scale thick, atomically smooth channels that cannot be easily realized using other techniques, reducing the risk of defects.

The proposed approach

In this study, the researchers demonstrated the finite growth of ultra-flat bismuth between layers of hexagonal boron nitride (hBN). Bismuth plays an important role in the development of quantum electronic physics because of its small effective mass, ability to grow ultra-pure bulk crystals, and low carrier density.

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Recently, bismuth boundaries have received significant attention due to spin momentum locking in one-dimensional (1D) helical edge modes and 2D Rashpa surface states. Boundary modes were investigated using ARPES and STM, which revealed a variety of phenomena.

However, limited transport studies have been performed due to disorder within thin crystals, where the blockage caused disturbances in bulk transport. The vdW-printing technique used in this study allows for the formation of crystals that aid intrinsic transport studies of thin bismuth and its surface states.

In a vdW-in-mold crystal-growing process, standard vdW transfer techniques were initially used to incorporate micron-sized bismuth flakes into thin hBN layers. Then, the bismuth-HPN stack was compressed between two substrates and continuously heated and cooled to melt and resolidify the bismuth.

During melting, the liquid bismuth diffused rapidly between the hBN layers, and its thickness was reduced due to the applied pressure. This viscous form of bismuth was retained while releasing the pressure and cooling into the solid phase, leading to a thin bismuth crystal embedded within the hBN.

During melt-growth, pressing bismuth reduced the thickness of the flakes from 250–500 nm to 5–30 nm/ultra-thin crystals. In addition, Hall-bar-shaped devices were fabricated and measured in a variable-temperature cryostat to electrostatically characterize vdW-patterned bismuth.

Study results

Ultra-flat bismuth crystals with a thickness of less than 10 nm were successfully grown by compressing and heating bismuth on an hBN mold. All three measurements, including transmission electron microscopy (TEM), electron backscatter diffraction (EBSD) and Raman spectroscopy, are consistent with the typical rhombohedral structure of bismuth.

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Metallic behavior at low temperatures with a positive slope of resistance versus temperature was observed in all vdW-cast bismuth devices. In particular, the slope decreased with increasing temperature, unlike the linear-t dependence of bulk bismuth, indicating confinement effects in vdW-cast bismuth.

The vdW-patterned devices showed strong metal bias, suggesting that surface-derived states may dominate room-temperature conduction. This led to large residual resistance ratios (RRR) of 5.4 and 12 for flat 13 nm and 8 nm devices, respectively.

vdW-patterned bismuth demonstrated exceptional electronic transport, enabling observation of Shubnikov–de Haas quantum oscillations originating from the (111) surface state Landau states. In particular, vdW-cast bismuth showed significantly improved transport properties compared to molecular beam epitaxy-grown thin films.

In the vdW-patterned devices, quantum oscillations in the magnetosphere emerged at high fields, and oscillations occurred in 11 devices with thicknesses of 8 to 107 nm with starting fields of 3 to 4 T. Additionally, the dominant oscillations were 13–20 times larger compared to bulk bismuth and are consistent with ARPES and STM studies.

By measuring the gate-dependent magnetization, the researchers observed multi-carrier quantum oscillations and Landau level splitting. The quantum oscillations were strongly dispersed with the backgate voltage, leading to Landau fan features.

Overall, the findings of this study demonstrated the feasibility of using the proposed vdW mold growth technique to synthesize flat and ultrathin bismuth crystals within a nanoscale vdW mold. Beyond bismuth, this approach provides an inexpensive way to synthesize other ultra-thin crystals directly into a vdW heterostructure.

Journal Note

Chen, L. and many others (2024) Exceptional electronic transport and quantum oscillations in thin bismuth crystals grown in van der Waals materials. Natural products1-6.,

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