Surface Landau levels and spin states in bismuth (111) ultrathin films

Exceptional electronic transport and quantum oscillations in thin bismuth crystals grown inside van der Waals materials

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 modes1-3. Beyond bismuth, the vdW-moulding approach provides a low-cost way to synthesize ultrathin crystals and directly integrate them into a vdW heterostructure.

Structural properties of Bi/Au(110)

Atomically thin bismuth films (2D Bi) are becoming a promising research area due to their unique properties and their wide variety of applications in spintronics, electronic and optoelectronic devices. We report on the structural properties of Bi on Au(110), explored by low-energy electron diffraction (LEED), scanning tunneling microscopy (STM) and density functional theory (DFT) calculations. At a Bi coverage lower than one monolayer (1 ML) various reconstructions are observed, we focus on Bi/Au(110)-c(2 × 2) reconstruction (at 0.5 ML) and Bi/Au(110)-(3 × 3) structure (at 0.66 ML). We propose models for both structures based on STM measurements and further confirm by DFT calculations.

Dynamic Nuclear Spin Polarization Induced by the Edelstein Effect at Bi(111) Surfaces

Nuclear spin polarization induced by hyperfine interaction and mainly the Edelstein effect due to strong spin-orbit interaction, is investigated by quantum transport in Bi(111) thin film samples. The Bi(111) films are deposited on mica by van der Waals epitaxial growth. The Bi(111) films show micrometer-sized triangular islands with 0.39 nm step height, corresponding to the Bi(111) bilayer height. At low temperatures a high current density is applied to generate a nonequilibrium carrier spin polarization by mainly the Edelstein effect at the Bi(111) surface, which then induces dynamic nuclear polarization by hyperfine interaction. Comparative quantum magnetotransport antilocalization measurements indicate a suppression of antilocalization by the in-plane Overhauser field from the nuclear polarization and allow a quantification of the Overhauser field. Hence nuclear polarization was both achieved and quantified by a purely electronic transport-based approach.

Observation of backscattering induced by magnetism in a topological edge state

The boundary modes of topological insulators are protected by the symmetries of the nontrivial bulk electronic states. Unless these symmetries are broken, they can give rise to novel phenomena, such as the quantum spin Hall effect in one-dimensional (1D) topological edge states, where quasiparticle backscattering is suppressed by time-reversal symmetry (TRS). Here, we investigate the properties of the 1D topological edge state of bismuth in the absence of TRS, where backscattering is predicted to occur. Using spectroscopic imaging and spin-polarized measurements with a scanning tunneling microscope, we compared quasiparticle interference (QPI) occurring in the edge state of a pristine bismuth bilayer with that occurring in the edge state of a bilayer, which is terminated by ferromagnetic iron clusters that break TRS. Our experiments on the decorated bilayer edge reveal an additional QPI branch, which can be associated with spin-flip scattering across the Brioullin zone center between time-reversal band partners. The observed QPI characteristics exactly match with theoretical expectations for a topological edge state, having one Kramer's pair of bands. Together, our results provide further evidence for the nontrivial nature of bismuth and in particular, demonstrate backscattering inside a helical topological edge state induced by broken TRS through local magnetism.

Scanning tunneling spectroscopy studies of topological materials

Topological materials have become promising materials for next-generation devices by utilizing their exotic electronic states. Their exotic states caused by spin-orbital coupling usually locate on the surfaces or at the edges. Scanning tunneling spectroscopy (STS) is a powerful tool to reveal the local electronic structures of condensed matters. Therefore, STS provides us with an almost perfect method to access the exotic states of topological materials. In this topical review, we report the current investigations by several methods based on the STS technique for layered topological material from transition metal dichalcogenide Weyl semimetals (WTe₂ and MoTe₂) to two dimensional topological insulators (layered bismuth and silicene). The electronic characteristics of these layered topological materials are experimentally identified.

Surface-state Coulomb repulsion accelerates a metal-insulator transition in topological semimetal nanofilms

The emergence of quantization at the nanoscale, the quantum size effect (QSE), allows flexible control of matter and is a rich source of advanced functionalities. A QSE-induced transition into an insulating phase in semimetallic nanofilms was predicted for bismuth a half-century ago and has regained new interest with regard to its surface states exhibiting nontrivial electronic topology. Here, we reveal an unexpected mechanism of the transition by high-resolution angle-resolved photoelectron spectroscopy combined with theoretical calculations. Anomalous evolution and degeneracy of quantized energy levels indicate that increased Coulomb repulsion from the surface states deforms a quantum confinement potential with decreasing thickness. The potential deformation strongly modulates spatial distributions of quantized wave functions, which leads to acceleration of the transition beyond the original QSE picture. This discovery establishes a complete picture of the long-discussed transition and highlights a new class of size effects dominating nanoscale transport in systems with metallic surface states.

Unusual Electronic States and Superconducting Proximity Effect of Bi Films Modulated by a NbSe2 Substrate

Heterostructures of two-dimensional layered materials can be functionalized with exotic phenomena that are unpresented with each constituting component. The interface effect plays a key role in determining the electronic properties of the heterostructure, whose characterization requires a correlation with the morphology with atomic-scale precision. Here, we report an investigation on the electronic properties of few-layer Bi(110) films mediated by a NbSe₂ substrate. By utilizing scanning tunneling microscopy and spectroscopy, we show a significant variation of the density of states at different Bi film thicknesses, resulting in an unusual superconducting proximity effect that deviates from the conventional monotonous decay behavior. Moreover, the electronic states of the Bi films are also prominently modulated by the Moiré pattern spatially. With first-principles calculations, we illuminate these findings as the results of covalent-like quasi-bonds formed at the Bi/NbSe₂ interface, which profoundly alter the charge distributions in the Bi films. Our study indicates a viable way of modulating the electronic properties of ultrathin films by quasi-covalent interfacial couplings beyond conventional van der Waals interactions.

Effects of trigonal deformation on electronic structure and thermoelectric properties of bismuth

First principles calculation and Boltzmann transport theory have been used to reveal the effects of trigonal deformation on electronic structure and thermoelectric properties of bulk bismuth. It is found that the semimetal-semiconductor transition would happen at the critical c/a points of 2.41 and 2.51, and that such a transition should be ascribed to the opposite changes of band edges at T and L points during trigonal deformation. Calculations also reveal that trigonal deformation has an important effect on various temperature-dependent thermoelectric properties, and that carrier density plays a decisive role in determining the magnitude of Seebeck coefficient and figure of merit. The semimetal  →  semiconductor transition as a result of trigonal compression with the decrease of c/a fundamentally induces the best performance of the thermoelectric properties of bismuth at the c/a ratio of 2.45. The present results agree well with experimental observations in the literature, and provide a deep understanding of the intrinsic relationship between trigonal deformation, band structure, and thermoelectric properties of bismuth.

Spiral Modes and the Observation of Quantized Conductance in the Surface Bands of Bismuth Nanowires

When electrons are confined in two-dimensional materials, quantum-mechanical transport phenomena and high mobility can be observed. Few demonstrations of these behaviours in surface spin-orbit bands exist. Here, we report the observation of quantized conductance in the surface bands of 50-nm Bi nanowires. With increasing magnetic fields oriented along the wire axis, the wires exhibit a stepwise increase in conductance and oscillatory thermopower, possibly due to an increased number of high-mobility spiral surface modes based on spin-split bands. Surface high mobility is unexpected since bismuth is not a topological insulator and the surface is not suspended but in contact with the bulk. The oscillations enable us to probe the surface structure. We observe that mobility increases dramatically with magnetic fields because, owing to Lorentz forces, spiral modes orbit decreases in diameter pulling the charge carriers away from the surface. Our mobility estimates at high magnetic fields are comparable, within order of magnitude, to the mobility values reported for suspended graphene. Our findings represent a key step in understanding surface spin-orbit band electronic transport.

Ballistic edge states in Bismuth nanowires revealed by SQUID interferometry

The protection against backscattering provided by topology is a striking property. In two-dimensional insulators, a consequence of this topological protection is the ballistic nature of the one-dimensional helical edge states. One demonstration of ballisticity is the quantized Hall conductance. Here we provide another demonstration of ballistic transport, in the way the edge states carry a supercurrent. The system we have investigated is a micrometre-long monocrystalline bismuth nanowire with topological surfaces, that we connect to two superconducting electrodes. We have measured the relation between the Josephson current flowing through the nanowire and the superconducting phase difference at its ends, the current–phase relation. The sharp sawtooth-shaped phase-modulated current–phase relation we find demonstrates that transport occurs selectively along two ballistic edges of the nanowire. In addition, we show that a magnetic field induces 0–π transitions and φ₀-junction behaviour, providing a way to manipulate the phase of the supercurrent-carrying edge states and generate spin supercurrents.

Demonstration of ballistic conduction and spin polarization of edge state currents in two dimensional topological insulators remains a challenge. Here, Murani et al. report a direct signature of ballistic one dimensional transport along the topological surfaces of a bismuth nanowire connected to superconducting electrodes.

Resolving the one-dimensional singularity edge states of Bi(1 1 1) thin films

We report our investigation on the electronic properties of the step edges on a Bi(1 1 1) surface in epitiaxially grown thin films, using scanning tunneling microscopy and spectroscopy. Our results show three differential conductance peaks including the previously reported peak in the spectra recorded at the step edges. Our analysis indicates that all of the three peaks can be ascribed to the van Hove singularities and thus to the band extrema of the one-dimensional edge bands, according to the quasiparticle interference and the Fourier transform patterns. These edge states show an overall penetration length of about 5 nm, but they also show different spatial distributions perpendicular to the edge. The well-determined band extrema may provide information for establishing a better model to describe the electronic topology of the step edge in the Bi(1 1 1) films.

Controlling the growth of Bi(110) and Bi(111) films on an insulating substrate

We demonstrate the controlled growth of Bi(110) and Bi(111) films on an α-Al₂O₃(0001) substrate by surface x-ray diffraction and x-ray reflectivity using synchrotron radiation. At temperatures as low as 40 K, unanticipated pseudo-cubic Bi(110) films are grown with thicknesses ranging from a few to tens of nanometers. The roughness at the film-vacuum as well as the film-substrate interface, can be reduced by mild heating, where a crystallographic orientation transition of Bi(110) towards Bi(111) is observed at 400 K. From 450 K onwards high quality ultrasmooth Bi(111) films form. Growth around the transition temperature results in the growth of competing Bi(110) and Bi(111) domains.

Proving Nontrivial Topology of Pure Bismuth by Quantum Confinement

The topology of pure Bi is controversial because of its very small (∼10  meV) band gap. Here we perform high-resolution angle-resolved photoelectron spectroscopy measurements systematically on 14-202 bilayer Bi films. Using high-quality films, we succeed in observing quantized bulk bands with energy separations down to ∼10  meV. Detailed analyses on the phase shift of the confined wave functions precisely determine the surface and bulk electronic structures, which unambiguously show nontrivial topology. The present results not only prove the fundamental property of Bi but also introduce a capability of the quantum-confinement approach.