Hall effects are investigated for three-dimensional Dirac electrons as a model of bismuth alloys. It is found that there is unconventional contributions to the Hall conductivity $σ_{xy}$ generated by the interband effects of a magnetic field. This phenomena is remarkable near the band-edge. The Hall coefficient exhibits two unexpected properties; a sharp peak at around the band-edges, and a drastic sign change in the band gap region. Implications of the present results to bismuth alloys are discussed.
We present a systematical study of thermal Hall effect on a bismuth single crystal by measuring resistivity, Hall coefficient, and thermal conductivity under magnetic field, which shows a large thermal Hall coefficient comparable to the largest one in a semiconductor HgSe. We discuss that this is mainly due to a large mobility and a low thermal conductivity comparing theoretical calculations, which will give a route for controlling heat current in electronic devices.
Bismuth Selenide (Bi2Se3) is a topological insulator exhibiting helical spin polarization and strong spin-orbit coupling. The spin-orbit coupling links the charge current to spin current via the spin Hall effect (SHE). We demonstrate a Bi2Se3 spin detector by injecting the pure spin current from a magnetic permalloy layer to a Bi2Se3 thin film and detect the inverse SHE in Bi2Se3. The spin Hall angle of Bi2Se3 is found to be 0.0093 and the spin diffusion length in Bi2Se3 to be 6.2 nm at room temperature. Our results suggest that topological insulators with strong spin-orbit coupling can be use…
The discovery of quantum spin Hall effect has ignited the field of topological physics with vast variety of exotic properties. Here, we present the emergence of doubled quantum spin Hall effect in two dimensions characterized with a high spin Chern number of ${\mathcal C_S}=2$ and two pairs of helical edge states. Although is overlooked and invisible in topological quantum chemistry and symmetry indicator theory, the already experimentally synthesized $α$-antimonene and $α$-bismuthene are revealed as realistic material candidates of predicted topological states with band inversions emerging at…
We implement the molecular beam epitaxy method to embed the black-phosphorus-like bismuth nanosheets into the bulk ferromagnet Cr$_2$Te$_3$. As a typical surfactant, bismuth lowers the surface tensions and mediates the layer-by-layer growth of Cr$_2$Te$_3$. Meanwhile, the bismuth atoms precipitate into black-phosphorus-like nanosheets with the lateral size of several tens of nanometers. In Cr$_2$Te$_3$ embedded with Bi-nanosheets, we observe simultaneously a large topological Hall effect together with the magnetic susceptibility plateau and magnetoresistivity anomaly. As a control experiment, …
Bismuth chalcogenides are the most studied 3D topological insulators. As a rule, at low temperatures thin films of these materials demonstrate positive magnetoresistance due to weak antilocalization. Weak antilocalization should lead to resistivity decrease at low temperatures; in experiments, however, resistivity grows as temperature decreases. From transport measurements for several thin films (with various carrier density, thickness, and carrier mobility), and by using purely phenomenological approach, with no microscopic theory, we show that the low temperature growth of the resistivity is…
We demonstrate that a giant spin Hall effect (SHE) can be induced by introducing a small amount of Bi impurities in Cu. Our analysis based on a new 3-dimensional finite element treatment of spin transport shows that the sign of the SHE induced by the Bi impurities is negative and its spin Hall (SH) angle amounts to -0.24. Such a negative large SH angle in CuBi alloys can be explained by applying the resonant scattering model proposed by Fert and Levy [Phys. Rev. Lett. 106, 157208 (2011)] to 6p impurities.
The search for new large band gap quantum spin Hall (QSH) and quantum anomalous Hall (QAH) insulators is critical for their realistic applications at room temperature. Here we predict, based on first principles calculations, that the band gap of QSH and QAH states can be as large as 1.01 eV and 0.35 eV in an H-decorated Bi(111) film. The origin of this giant band gap lies both in the large spin-orbit interaction of Bi and the H-mediated exceptional electronic and structural properties. Moreover, we find that the QAH state also possesses the properties of quantum valley Hall state, thus intrins…
Spin-Hall conductivity (SHC) of fully relativistic (4x4 matrix) Dirac electrons is studied based on the Kubo formula aiming at possible application to bismuth and bismuth-antimony alloys. It is found that there are two distinct contributions to SHC, one only from the states near the Fermi energy and the other from all the occupied states. The latter remains even in the insulating state, i.e., when the chemical potential lies in the band-gap, and turns to have the same dependences on the chemical potential as the orbital susceptibility (diamagnetism), a surprising fact. These results are applie…
Recent advancement in laser technology has opened the path toward the manipulation of functionalities in quantum materials by intense coherent light. Here, we study three-dimensional (3D) Dirac electrons driven by circularly polarized light (CPL), when the photon energy lies within the Dirac bands. As an experimental realization of this setup, we irradiate a thin film sample of elemental bismuth, which is a well-known semimetal hosting 3D Dirac electrons, with mid-infrared CPL. We successfully observe the emergence of the anomalous Hall effect (AHE) via terahertz Faraday rotation that is both …
Direct visualizations of spin accumulation due to the enhanced spin Hall effect (SHE) in bismuth (Bi) - doped silicon (Si) at room temperature are realized by using helicity-dependent photovoltage (HDP) measurements. Under application of a dc current to the Bi-doped Si, clear helicity-dependent photovoltages are detected at the edges of the Si channel, indicating a perpendicular spin accumulation due to the SHE. In contrast, the HDP signals are negligibly small for phosphorus-doped Si. Compared to a platinum channel, which has a large spin Hall angle, more than two-orders of magnitude larger H…
Bismuth is an archetypal semimetal with gigantic spin-orbit coupling and it has been a major source material for the discovery of seminal phenomena in solid state physics for more than a century. In recent years, spin current transports in bismuth have also attracted considerable attention. In this paper, we theoretically study both spin Hall effect (SHE) and spin Nernst effect (SNE) in bismuth, based on relativistic band structure calculations. First, we find that there are three independent tensor elements of spin Hall conductivity (SHC) and spin Nernst conductivity (SNC), namely, $Z_{yx}^z$…
Bismuth crystal is known for its remarkable properties resulting from particular electronic states, e. g., the Shubnikov-de Haas effect and the de Haas-van Alphen effect. Above all, the large diamagnetism of bismuth had been a long-standing puzzle soon after the establishment of quantum mechanics, which had been resolved eventually in 1970 based on the effective Hamiltonian derived by Wolff as due to the interband effects of a magnetic field in the presence of a large spin-orbit interaction. This Hamiltonian is essentially the same as the Dirac Hamiltonian, but with spatial anisotropy and an e…
Spin- and Angle-resolved Photoelectron Spectroscopy Study of the Quantum Spin Hall Insulator Bismuthene and its Precursor Phase
Chemnitz University of Technology（开姆尼茨工业大学）；Research Center for Materials, Architectures and Integration of Nanomembranes (MAIN)（纳米膜材料、架构与集成研究中心）；MAX IV Laboratory（MAX IV 实验室）；Lund University（隆德大学）
By means of first-principles calculations, we predict a new 2D QSH insulator in the porous allotrope of Bismuth monolayer, bismuthylene, its dynamics stability being confirmed by phonon spectrum and molecular dynamics simulations. The analyses of electronic structures reveal that it is a native QSH state with a gap much as large as 0.29 eV at the Γ point, which is larger than the buckled (0.2 eV) and flattened (0.2 eV) bismuth, Bi4Br4 (0.18 eV), as well as stanene (0.1 eV), also more stable energetically than these systems. Interestingly, the bismuthylene has tunable band gaps and nontrivial b…
Since 2017, epitaxial graphene has been the base material for the US national standard for resistance. A future avenue of research within electrical metrology is to remove the need for strong magnetic fields, as is currently the case for devices exhibiting the quantum Hall effect. The quantum Hall effect is just one of many research endeavours that revolve around recent quantum physical phenomena like composite fermions, charge density waves, and topological properties [1-2]. New materials, like magnetically doped topological insulators (MTIs), offer access to the quantum anomalous Hall effect…
Field theory arguments suggest the possibility of $\mathbb{Z}$-classification of quantum spin Hall effect with magnetic flux tubes, that cause separation of spin and charge degrees of freedom, and pumping of spin or Kramers pair. However, the \emph{proof of principle} demonstration of spin-charge separation is yet to be accomplished for realistic, \emph{ab initio} band structures of spin-orbit-coupled materials, lacking spin-conservation law. In this work, we perform thought experiments with magnetic flux tubes on $β$-bismuthene to demonstrate spin-charge separation, and quantized pumping of s…
The semiclassical transport theory is especially powerful for investigating galvanomagnetic effects. Generally, the semiclassical theory is applicable only in weak fields because it does not consider Landau quantization. Herein, we extend the conventional semiclassical theory by considering Landau quantization through the field dependence of carrier density in semimetals. The extended semiclassical theory is applicable even in strong fields, where Landau quantization is noticeable. Using this new approach, we explain the qualitative change in the angular dependence of transverse magnetoresista…
In this paper, we report on the investigation of (1) the transport properties of multi-carriers in semi-metal Bi and (2) the spin conversion physics in this semimetal system in a ferrimagnetic insulator, yttrium-iron-garnet. Hall measurements reveal that electrons and holes co-exist in the Bi, with electrons being the dominant carrier. The results of a spin conversion experiment corroborate the results of the Hall measurement; in addition, the inverse spin Hall effect governs the spin conversion in the semimetal/insulator system. This study provides further insights into spin conversion physic…
Quantum Spin Hall (QSH) insulators with a large topologically nontrivial bulk gap are crucial for future applications of the QSH effect. Among these, group III-V monolayers and their halides with chair structure (regular hexagonal framework, RHF) were widely studied. Using first-principles calculations, we propose a new structure model for the functionalized group III-V monolayers, which consist of rectangular GaBi-X2 (X=I, Br, Cl) monolayers with a distorted hexagonal framework (DHF). These structures have a much lower energy than the GaBi-X2 monolayers with chair structure. Remarkably, the D…
Topological insulators (TIs) exhibit novel physics with great promise for new devices, but considerable challenges remain to identify TIs with high structural stability and large nontrivial band gap suitable for practical applications. Here we predict by first-principles calculations a two-dimensional (2D) TI, also known as a quantum spin Hall (QSH) insulator, in a tetragonal bismuth bilayer (TB-Bi) structure that is dynamically and thermally stable based on phonon calculations and finite-temperature molecular dynamics simulations. Density functional theory and tight-binding calculations revea…
Temperature dependence of charge-to-spin conversion in rhombohedral (110) bismuth thin film
Kyoto University（京都大学）；The Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Kobe University（神户大学）；Saitama University（埼玉大学）；Center for Spintronics Research Network (CSRN), Kyoto University（京都大学自旋电子学研究网络中心）；Osaka Metropolitan University（大阪公立大学）
Quantum spin Hall (QSH) materials promise revolutionary device applications based on dissipationless propagation of spin currents. They are two-dimensional (2D) representatives of the family of topological insulators, which exhibit conduction channels at their edges inherently protected against scattering. Initially predicted for graphene, and eventually realized in HgTe quantum wells, in the QSH systems realized so far, the decisive bottleneck preventing applications is the small bulk energy gap of less than 30 meV, requiring cryogenic operation temperatures in order to suppress detrimental b…
Quantum spin Hall (QSH) insulators have gapless topological edge states inside the bulk band gap, which can serve as dissipationless spin current channels protected by the time-reversal symmetry. The major challenge currently is to find suitable materials for this topological state. Here, we predict a new large-gap QSH insulator with bulk direct band gap of $\sim$0.18 eV, in single-layer Bi$_{4}$Br$_{4}$, which could be exfoliated from its three-dimensional bulk material due to the weakly-bonded layered structure. The band gap of single-layer Bi$_{4}$Br$_{4}$ is tunable via strain engineering,…
It has been suggested that the enlarged spin susceptibility in topological insulators, described by Van Vleck's formalism, accounts for the ferromagnetism of bismuth-antimony topological chalcogenides doped with transition metal impurities. In contrast, earlier studies of HgTe and related topological systems pointed out that the interband analog of the Ruderman-Kittel-Kasuya-Yosida interaction (the Bloembergen-Rowland mechanism) leads to antiferromagnetic coupling between pairs of localized spins. Here, we critically revisit these two approaches, show their shortcomings, and elucidate why the …
We show that the spin Hall conductivity in insulators is related with a magnetic susceptibility representing the strength of the spin-orbit coupling. We use this relationship as a guiding principle to search real materials showing quantum spin Hall effect. As a result, we theoretically predict that bismuth will show the quantum spin Hall effect, both by calculating the helical edge states, and by showing the non-triviality of the Z_2 topological number, and propose possible experiments.
Two-dimensional quantum spin Hall (QSH) insulators are a promising material class for spintronic applications based on topologically-protected spin currents in their edges. Yet, they have not lived up to their technological potential, as experimental realizations are scarce and limited to cryogenic temperatures. These constraints have also severely restricted characterization of their dynamical properties. Here, we report on the electron dynamics of the novel room-temperature QSH candidate bismuthene after photoexcitation using time- and angle-resolved photoemission spectroscopy. We map the tr…
Giant spin Nernst effect in a two-dimensional antiferromagnet due to magnetoelastic coupling-induced gaps and interband transitions between magnon-like bands
We review our recent theoretical works on the the quantum spin Hall effect. First we compare edge states in various 2D systems, and see whether they are robust or fragile against perturbations. Through the comparisons we see the robust nature of edge states in 2D quantum spin Hall phases. We see how it is protected by the Z_2 topological number, and reveal the nature of the Z_2 topological number by studying the phase transition between the quantum spin Hall and insulator phases. We also review our theoretical proposal of the ultrathin bismuth film as a candidate to the 2D quantum spin Hall sy…
Quantum spin Hall (QSH) systems hold promises of low-power-consuming spintronic devices, yet their practical applications are extremely impeded by the small energy gaps. Fabricating QSH materials with large gaps, especially under the guidance of design principles, is essential for both scientific research and practical applications. Here, we demonstrate that large on-site atomic spin-orbit coupling can be directly exploited via the intriguing substrate-orbital-filtering effect to generate large-gap QSH systems and experimentally realized on the epitaxially synthesized ultraflat bismuthene on A…
A circularly polarized a.c. pump field illuminated near resonance on two-dimensional transition metal dichalcogenides (TMDs) produces an anomalous Hall effect in response to a d.c. bias field. In this work, we develop a theory for this photo-induced anomalous Hall effect in undoped TMDs irradiated by a strong coherent laser field. The strong field renormalizes the equilibrium bands and opens up a dynamical energy gap where single-photon resonance occurs. The resulting photon dressed states, or Floquet states, are treated within the rotating wave approximation. A quantum kinetic equation approa…
We derive and analyze the longitudinal and the anomalous Hall conductivity for a general momentum-block-diagonal two-band model. This model captures a broad spectrum of physically very different systems including Néel antiferromagnetic and spiral spin density waves as well as models that involve spin-orbit interaction and are known to show topological properties. We present a complete microscopic derivation for finite temperature and constant scattering rate $Γ$ that is diagonal and equal, but arbitrarily large for both bands. We identify two criteria that allow for a unique and physically mot…
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…
Spin-split Rashba bands have been exploited to efficiently control the spin degree of freedom of moving electrons, which possesses a great potential in frontier applications of designing spintronic devices and processing spin-based information. Given that intrinsic breaking of inversion symmetry and sizeable spin-orbit interaction, two-dimensional (2D) surface alloys formed by heavy metal elements exhibit a pronounced Rashba-type spin splitting of the surface states. Here, we have revealed the essential role of atomic orbital symmetry in the hexagonally warped Rashba spin-split surface state o…
The interface between a solid and vacuum can become electronically distinct from the bulk. This feature, encountered in the case of quantum Hall effect, has a manifestation in insulators with topologically protected metallic surface states. Non-trivial Berry curvature of the Bloch waves or periodically driven perturbation are known to generate it. Here, by studying the angle-dependent magnetoresistance in prismatic bismuth crystals of different shapes, we detect a robust surface contribution to electric conductivity when the magnetic field is aligned parallel to a two-dimensional boundary betw…
We carry out first-principles calculations which demonstrate the importance of the non-spin-conserving part of the spin-orbit interaction for the intrinsic anomalous Hall conductivity of ordered FePt alloys. The impact of this interaction is strongly reduced if Pt is replaced by the lighter isoelectronic element Pd. An analysis of the interband transitions responsible for the anomalous velocity reveals that spin-flip transitions occur not only at avoided band crossings near the Fermi level, but also between well-separated pairs of bands with similar dispersions. We also predict a strong anisot…
Considering finite-temperature screened electron-impurity scattering, we present a kinetic equation approach to investigate transport properties of two-dimensional massive fermions in silicene. We find that the longitudinal conductivity is always nonvanishing when chemical potential lies within the energy gap. This residual conductivity arises from interband correlation and strongly depends on strength of electron-impurity scattering. We also clarify that the electron-impurity interaction makes substantial contributions to the spin- and valley-Hall conductivities, which, however, are almost in…
Stanene was proposed to be a quantum spin hall insulator containing topological edges states and a time reversal invariant topological superconductor hosting helical Majorana edge mode. Recently, experimental evidences of existence of topological edge states have been found in monolayer stanene films and superconductivity has been observed in few-layer stanene films excluding single layer. An integrated system with both topological edge states and superconductivity are higly pursued as a possible platform to realize topological superconductivity. Few-layer stanene show great potential to meet …
Employing a nonequilibrium Green's function approach, we examine the effects of long-range hole-impurity scattering on spin-Hall current in $p$-type bulk semiconductors within the framework of the self-consistent Born approximation. We find that, contrary to the null effect of short-range scattering on spin-Hall current, long-range collisions do produce a nonvanishing contribution to the spin-Hall current, which is independent of impurity density in the diffusive regime and relates only to hole states near the Fermi surface. The sign of this contribution is opposite to that of the previously p…
Spin-Hall conductivity $σ_{{\rm s}xy}$ and orbital susceptibility $χ$ are investigated for the anisotropic Wolff Hamiltonian, which is an effective Hamiltonian common to Dirac electrons in solids. It is found that, both for $σ_{{\rm s}xy}$ and $χ$, the effect of anisotropy appears only in the prefactors, which is given as the Gaussian curvature of the energy dispersion, and their functional forms are equivalent to those of the isotropic Wolff Hamiltonian. As a result, it is revealed that the relationship between the spin Hall conductivity and the orbital susceptibility in the insulating state,…
We analyze the detailed structure of topological edge mode protection occuring in hexagonal quantum spin Hall (QSH) materials. We focus on bismuthene, antimonene, and arsenene on a SiC substrate, which, due to their large bulk gap, may offer new opportunities for room-temperature QSH applications. While time reversal symmetry is responsible for the principal symmetry protected character of QSH states, the hexagonal edge terminations yield further aspects of crystal symmetry which affect the topological protection. We show that armchair QSH edge states remain gapless under an in-plane magnetic …
TaIrTe$_4$ is an example of a candidate Weyl type-II semimetal with a minimal possible number of Weyl nodes. Four nodes are reported to exist a single plane in $k$-space. The existence of a conical dispersion linked to Weyl nodes has yet to be shown experimentally. Here we use optical spectroscopy as a probe of the band structure on a low-energy scale. Studying optical conductivity allows us to probe intraband and interband transitions with zero momentum. In TaIrTe$_4$, we observe a narrow Drude contribution and an interband conductivity that may be consistent with a tilted linear band dispers…
Quantum spin Hall insulators have one-dimensional (1D) spin-momentum locked topological edge states (ES) inside the bulk band gap, which can serve as dissipationless channels for the practical applications in low consumption electronics and high performance spintronics. However, the clean and atomically sharp ES serving as ideal 1D conducting channels are still lack. Here, we report the formation of the quasi-1D Bi4I4 nanoribbons on the surface of Bi(111) with the support of the graphene-terminated 6H-SiC(0001) and the direct observations of the topological ES at the step edge by scanning tunn…
Various nonlinear characteristics of solid states, such as the circular photogalvanic effect of time-reversal symmetric insulators, the quantized photogalvanic effect of Weyl semimetals, and the nonlinear Hall effect of time-reversal symmetric metals, have been associated with the Berry curvature dipole (BCD). Here, we explore the question of whether the Berry curvature dipole and multipoles of time-reversal symmetric insulators can be traced in the nonlinear optical responses. We performed real-time time-dependent density functional theory calculations and examined the second harmonic generat…
Transparent oxides are essential building blocks to many technologies, ranging from components in transparent electronics, transparent conductors, to absorbers and protection layers in photovoltaics and photoelectrochemical devices. However, thus far, it has been difficult to develop p-type oxides with wide band gap and high hole mobility; current state-of-art transparent p-type oxides have hole mobility in the range of < 10 cm$^2$/Vs, much lower than their n-type counterparts. Using high-throughput computational screening to guide the discovery of novel oxides with wide band gap and high hole…
Under broken time reversal symmetry such as in the presence of external magnetic field or internal magnetization, a transverse voltage can be established in materials perpendicular to both longitudinal current and applied magnetic field, known as classical Hall effect. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear anomalous Hall current in time-reversal invariant materials - an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles theory, we demonstrate a rema…
The major breakthroughs in the understanding of topological materials over the past decade were all triggered by the discovery of the Z$_2$ topological insulator (TI). In three dimensions (3D), the TI is classified as either "strong" or "weak", and experimental confirmations of the strong topological insulator (STI) rapidly followed the theoretical predictions. In contrast, the weak topological insulator has so far eluded experimental verification, since the topological surface states emerge only on particular side surfaces which are typically undetectable in real 3D crystals. Here we provide …
Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
Max Planck Institute for Solid State Research（马克斯·普朗克固体的研究研究所）；Technische Universität München（慕尼黑工业大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
A nonequilibrium Green's function approach is employed to investigate the spin-Hall effect in diffusive two-dimensional electron systems with Rashba spin-orbit interaction. Considering a long-range electron-impurity scattering potential in the self-consistent Born approximation, we find that the spin-Hall effect arises from two distinct interband polarizations in helicity basis: a disorder-unrelated polarization directly induced by the electric field and a polarization mediated by electron-impurity scattering. The disorder-unrelated polarization is associated with all electron states below the…
We study the phase diagram of a model quantum spin Hall system as a function of band inversion and band-coupling strength, demonstrating that when band hybridization is weak, an interaction-induced nematic insulator state emerges over a wide range of band inversion. This property is a consequence of the long-range Coulomb interaction, which favors interband phase coherence that is weakly dependent on momentum and therefore frustrated by the single-particle Hamiltonian at the band inversion point. For weak band hybridization, interactions convert the continuous gap closing topological phase tra…
