Signatures of surface states in bismuth at high magnetic fields

Magnetoresistance and valley degree of freedom in bulk bismuth

In this paper, we first review fundamental aspects of magnetoresistance in multi-valley systems based on the semiclassical theory. Then we will review experimental evidence and theoretical understanding of magnetoresistance in an archetypal multi-valley system, where the electric conductivity is set by the sum of the contributions of different valleys. Bulk bismuth has three valleys with an extremely anisotropic effective mass. As a consequence the magnetoconductivity in each valley is extremely sensitive to the orientation of the magnetic field. Therefore, a rotating magnetic field plays the role of a valley valve tuning the contribution of each valley to the total conductivity. In addition to this simple semiclassical effect, other phenomena arise in the high-field limit as a consequence of an intricate Landau spectrum. In the vicinity of the quantum limit, the orientation of magnetic field significantly affects the distribution of carriers in each valley, namely, the valley polarization is induced by the magnetic field. Moreover, experiment has found that well beyond the quantum limit, one or two valleys become totally empty. This is the only case in condensed matter physics where a Fermi sea is completely dried up by a magnetic field without a metal-insulator transition. There have been two long-standing problems on bismuth near the quantum limit: the large anisotropic Zeeman splitting of holes, and the extra peaks in quantum oscillations, which cannot be assigned to any known Landau levels. These problems are solved by taking into account the interband effect due to the spin-orbit couplings for the former, and the contributions from the twinned crystal for the latter. Up to here, the whole spectrum can be interpreted within the one-particle theory. Finally, we will discuss transport and thermodynamic signatures of breaking of the valley symmetry in this system. By this term, we refer to the observed spontaneous loss of threefold symmetry at high magnetic field and low temperature. Its theoretical understanding is still missing. We will discuss possible explanations.

Large-Area Dry Transfer of Single-Crystalline Epitaxial Bismuth Thin Films

We report the first direct dry transfer of a single-crystalline thin film grown by molecular beam epitaxy. A double cantilever beam fracture technique was used to transfer epitaxial bismuth thin films grown on silicon (111) to silicon strips coated with epoxy. The transferred bismuth films retained electrical, optical, and structural properties comparable to the as-grown epitaxial films. Additionally, we isolated the bismuth thin films on freestanding flexible cured-epoxy post-transfer. The adhesion energy at the bismuth/silicon interface was measured to be ∼1 J/m², comparable to that of exfoliated and wet transferred graphene. This low adhesion energy and ease of transfer is unexpected for an epitaxially grown film and may enable the study of bismuth's unique electronic and spintronic properties on arbitrary substrates. Moreover, this method suggests a route to integrate other group-V epitaxial films (i.e., phosphorus) with arbitrary substrates, as well as potentially to isolate bismuthene, the atomic thin-film limit of bismuth.

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

The development of next-generation electronics is much dependent on the discovery of materials with exceptional surface-state spin and valley properties. Because of that, bismuth has attracted a renewed interest in recent years. However, despite extensive studies, the intrinsic electronic transport properties of Bi surfaces are largely undetermined due to the strong interference from the bulk. Here we report the unambiguous determination of the surface-state Landau levels in Bi (111) ultrathin films using scanning tunnelling microscopy under magnetic fields perpendicular to the surface. The Landau levels of the electron-like and the hole-like carriers are accurately characterized and well described by the band structure of the Bi (111) surface from density functional theory calculations. Some specific surface spin states with a large g-factor are identified. Our findings shed light on the exploiting surface-state properties of Bi for their applications in spintronics and valleytronics.

Robust surface state transport in thin bismuth nanoribbons

While a two-dimensional (2D) metallic surface state in bismuth has been proposed, experimental 2D evidence of quantum transport, e.g., angular dependent Shubnikov-de Haas (SdH) oscillations is still lacking. Here, we report the angular-dependent magnetoresistance measurements in single-crystal Bi nanoribbons, and found that both the low-field weak antilocalization behavior and the high-field angle-dependent SdH oscillations follow exactly the 2D character, indicative of the 2D metallic surface states which dominate the transport properties of thin Bi nanoribbons. Moreover, by controllable exposing the ribbons to ambient environment (1 atm and room temperature), the metallic surface states were found to be robust to the oxidation although the carrier density in the surface states are modified after the exposures. These results suggest that the metallic surface states in Bi nanoribbons should be topologically protected which can provide key information in understanding the surface properties of Bi in nanometer scale.

In situ magnetotransport measurements in ultrathin Bi films: evidence for surface-bulk coherent transport

We performed in situ magnetotransport measurements on ultrathin Bi(111) films [4-30 bilayers (BLs), 16-120 Å thick] to elucidate the role of bulk or surface states in the transport phenomena. We found that the temperature dependence of the film conductivity shows no thickness dependence for the 6-16 BL films and is affected by the electron-electron scattering, suggesting surface-state dominant contribution. In contrast, the weak antilocalization effect observed by applying a magnetic field shows clear thickness dependence, indicating bulk transport. This apparent inconsistency is explained by a coherent bulk-surface coupling that produces a single channel transport. For the films thicker than 20 BLs, the behavior changes drastically which can likely be interpreted as a bulk dominant conduction.

Evidence of topological two-dimensional metallic surface states in thin bismuth nanoribbons

Understanding the exotic quantum phenomena in bulk bismuth beyond its ultraquantum limit remains controversial and gives rise to renewed interest. The focus of the issues is whether these quantum properties have a conventional bulk nature or just the surface effect due to the significant spin-orbital interaction and in relation to the Bi-based topological insulators. Here, we present angular-dependent magnetoresistance (AMR) measurements on single-crystal bismuth nanoribbons of different thicknesses with magnetic fields up to 31 T. In thin nanoribbons with thickness of ∼40 nm, a two-fold rational symmetry of the low field AMR spectra and two sets of 1/2-shifted (i.e., γ = 1/2) Shubnikov-de Haas (SdH) quantum oscillations with exact two- dimensional (2D) character were obtained. However, when the thickness of the ribbon increases, a 3D bulk-like SdH oscillations with γ = 0 and a four-fold rotational symmetry of the AMR spectra appear. These results provided unambiguous transport evidence of the topological 2D metallic surface states in thinner nanoribbons with an insulating bulk. Our observations provide a promising pathway to understand the quantum phenomena in Bi arising from the surface states.

Landau spectrum and twin boundaries of bismuth in the extreme quantum limit

The Landau spectrum of bismuth is complex and includes many angle-dependent lines in the extreme quantum limit. The adequacy of single-particle theory to describe this spectrum in detail has been an open issue. Here, we present a study of angle-resolved Nernst effect in bismuth, which maps the angle-resolved Landau spectrum for the entire solid angle up to 28 T. The experimental map is in good agreement with the results of a theoretical model with parabolic dispersion for holes and an extended Dirac Hamiltonian for electrons. The angular dependence of additional lines in the Landau spectrum allows us to uncover the mystery of their origin. They correspond to the lines expected for the hole Landau levels in a secondary crystal tilted by 108°, the angle between twinned crystals in bismuth. According to our results, the electron reservoirs of the two identical tilted crystals have different chemical potentials, and carriers across the twin boundary have different concentrations. An exceptional feature of this junction is that it separates two electron-hole compensated reservoirs. The link between this edge singularity and the states wrapping a three-dimensional electron gas in the quantum limit emerges as an outstanding open question.