There has been increasing interest in phenomena emerging from relativistic electrons in a solid, which have a potential impact on spintronics and magnetoelectrics. One example is the Rashba effect, which lifts the electron-spin degeneracy as a consequence of spin-orbit interaction under broken inversion symmetry. A high-energy-scale Rashba spin splitting is highly desirable for enhancing the coupling between electron spins and electricity relevant for spintronic functions. Here we describe the finding of a huge spin-orbit interaction effect in a polar semiconductor composed of heavy elements, BiTeI, where the bulk carriers are ruled by large Rashba-like spin splitting. The band splitting and its spin polarization obtained by spin- and angle-resolved photoemission spectroscopy are well in accord with relativistic first-principles calculations, confirming that the spin splitting is indeed derived from bulk atomic configurations. Together with the feasibility of carrier-doping control, the giant-Rashba semiconductor BiTeI possesses excellent potential for application to various spin-dependent electronic functions.

The valley degree of freedom of electrons is attracting growing interest as a carrier of information in various materials, including graphene, diamond and monolayer transition-metal dichalcogenides. The monolayer transition-metal dichalcogenides are semiconducting and are unique due to the coupling between the spin and valley degrees of freedom originating from the relativistic spin-orbit interaction. Here, we report the direct observation of valley-dependent out-of-plane spin polarization in an archetypal transition-metal dichalcogenide--MoS2--using spin- and angle-resolved photoemission spectroscopy. The result is in fair agreement with a first-principles theoretical prediction. This was made possible by choosing a 3R polytype crystal, which has a non-centrosymmetric structure, rather than the conventional centrosymmetric 2H form. We also confirm robust valley polarization in the 3R form by means of circularly polarized photoluminescence spectroscopy. Non-centrosymmetric transition-metal dichalcogenide crystals may provide a firm basis for the development of magnetic and electric manipulation of spin/valley degrees of freedom.

A hexagonal deformation of the Fermi surface of Bi 2 Se 3 has been for the first time observed by angleresolved photoemission spectroscopy. This is in contrast to the general belief that Bi 2 Se 3 possesses an ideal Dirac cone. The hexagonal shape is found to disappear near the Dirac node, which would protect the surface state electrons from backscattering. It is also demonstrated that the Fermi energy of naturally electron-doped Bi 2 Se 3 can be tuned by 1% Mg doping in order to realize the quantum topological transport. DOI: 10.1103/PhysRevLett.105.076802 PACS numbers: 73.20.Àr, 79.60.Ài After the theoretical prediction and experimental realization of two-dimensional topological insulators in the HgTe=CdTe quantum well [1-4], a spectroscopic discovery of a three-dimensional topological insulator by probing the odd number of massless Dirac cones has generated a great interest in this new state of quantum matter [5][6][7][8][9]. Unlike the conventional Dirac fermions as found in graphene, this novel electronic state possesses helical spin textures protected by time-reversal symmetry, which could realize the quantum spin transport without heat dissipation. This new state of matter has been predicted to exist in a number of materials, for example, in Bi 1Àx Sb x , Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 [10]. Among them, stoichiometric Bi 2 Se 3 is theoretically predicted to be a 3D topological insulator with a single Dirac cone within a substantial bulk energy gap (0.3 eV), which makes it the most suitable candidate for the high-temperature spintronics application [10]. However, in the actual situation, the bulk conduction band is energetically lowered and crosses the Fermi energy through natural electron doping from vacancies or antisite defects, which allows bulk electron conduction. In order to avoid the bulk electron conduction and realize the quantum spin Hall phase, the Fermi energy must be tuned by additional doping [11,12].In ideal topological insulators with perfect linear dispersion, the surface state electrons should be protected from backscattering by nonmagnetic impurities between timereversal partners with opposite momenta because of their opposite spin configurations. However, recent scanning tunneling microscopy experiments for the Bi 2 Te 3 surface show a clear quasiparticle interference pattern as a result of backscattering nearby the step edge or at the point defect on the surface [13,14]. Theoretically, it is pointed out that the hexagonal Fermi surface warping would also induce the quasiparticle interference pattern [15]. It is generally believed that, owing to a large band gap (0.35 eV), which exceeds the thermal excitation energy at room temperature, Bi 2 Se 3 features a nearly ideal Dirac cone, in contrast to Bi 2 Te 3 [16,17]. In the present Letter, we show by a precise angle-resolved photoemission spectroscopy (ARPES) measurement that the Fermi surface of naturally electrondoped Bi 2 Se 3 is hexagonally deformed, while the constant energy contour is circular-shaped near the Dirac point...

Topological insulators and semimetals as well as unconventional iron-based superconductors have attracted major recent attention in condensed matter physics. Previously, however, little overlap has been identified between these two vibrant fields, even though the principal combination of topological bands and superconductivity promises exotic unprecedented avenues of superconducting states and Majorana bound states (MBSs), the central building block for topological quantum computation. Along with progressing laser-based spin-resolved and angle-resolved photoemission spectroscopy (ARPES) towards high energy and momentum resolution, we have resolved topological insulator (TI) and topological Dirac semimetal (TDS) bands near the Fermi level (E F ) in the iron-based superconductors Li(Fe,Co)As and Fe(Te,Se), respectively. The TI and TDS bands can be individually tuned to locate close to E F by carrier doping, allowing to potentially access a plethora of different superconducting topological states in the same material. Our results reveal the generic coexistence of superconductivity and multiple topological states in iron-based superconductors, rendering these materials a promising platform for high-T c topological superconductivity.High-T c iron-based superconductors feature multiple bands near E F , which enhances the difficulty in understanding the details of unconventional pairing 1-3 . It, however, also allows for a wealth of, possibly topologically non-trivial, electronic bands, of which a recent example is the TI states discovered in the ironbased superconductor Fe(Te,Se) 4 , hinting at a promising direction to realize topological superconductivity and MBSs 5-9 . In view of Fe(Te,Se), a pressing subsequent question is to which extent this marks a generic phe-nomenon in different classes of iron-based high-T c superconductors. In this work, we find that the emergence of non-trivial topological bands near the Fermi level is indeed a common feature of various iron-based superconductors. Our first-principles calculations reveal that BaFe 2 As 2 , LiFeAs and Fe(Te,Se) all exhibit band inversions along k z . To confirm these calculations, the band structures of Li(Fe,Co)As and Fe(Te,Se) were investigated by laser-based high-resolution ARPES. Firstly, we observe that TI bands reminiscent of Fe(Te,Se) exist in Li(Fe,Co)As as well, supporting the generic existence of non-trivial topology in iron-based superconductors. Secondly and more interestingly, we predict and observe TDS bands in Li(Fe,Co)As and Fe(Te,Se), which we investigate via high-resolution ARPES, spin-resolved ARPES (SARPES), and magnetoresistance (MR) measurements. Finally, we discuss the phase diagram of these topological high-T c compounds as a function of Fermi level (doping). The combination of topological states and superconductivity may produce not only surface topological superconductivity deriving from the TI edge states, but also bulk topological superconductivity from the TDS bands.Normal insulator (NI), TI, and TDS constitute topologically disti...

The electronic structure of ultrathin Bi͑001͒ films on Si͑111͒-7 ϫ 7 was studied by spin and angle-resolved photoemission spectroscopy. We directly observed a clear momentum-dependent spin splitting and polarization of the surface-state bands. The spin structure was antisymmetric with respect to the ⌫ point as predicted by theory, and the obtained in-plane spin polarization was as high as ±0.5. The qualitative features of the observed spin polarization are discussed in comparison with the spin-polarized band structure obtained by first-principles calculations. DOI: 10.1103/PhysRevB.76.153305 PACS number͑s͒: 79.60.Bm, 68.35.Ϫp, 73.20.Ϫr, 85.75.Ϫd Spintronics, which aims at the utilization of the spin degree of freedom, has attracted wide interest due to its potential in realizing new functionalities in electronic devices. 1Spin manipulation is the key factor in spintronics, and the conventional style was to develop novel ferromagnetic materials.2 Recently, on the other hand, it was found that spin-split two-dimensional electron gases can be formed in asymmetric quantum wells controlled by an electric field even for nonmagnetic materials.3 This is called the Rashba effect, which is a combined effect of the spin-orbit interaction and structural inversion asymmetry ͑SIA͒. 4At the crystal surface, the same effect occurs and spinorbit split band structures have been found for Au͑111͒ ͑Refs. 5 and 6͒ and W͑110͒-H ͑Ref. 7͒ surfaces. This splitting is caused by the spin-orbit coupling Hamiltonian, H soc = ͑ប /4m e 2 c 2 ͒ ជ · ٌ͑V ϫ p ជ͒, where ជ is the spin of electrons, V the one-electron potential, and p ជ the momentum. 8 Usually in the bulk, the time-reversal symmetry ͓E͑k ជ , ↑ ͒ = E͑−k ជ , ↓ ͔͒ and the space-inversion symmetry ͓E͑k ជ , ↑ ͒ = E͑−k ជ , ↑ ͔͒ lead to the Kramers degeneracy. However, at the crystal surface, due to the SIA in the surface-normal direction, the degeneracy will be lifted. The spin orientation of such states is perpendicular both to the momentum p ជ and to the electric field ٌV, meaning an in-plane spin polarization antisymmetric about k ជ = 0, as the electric field is perpendicular to the surface. 8Bismuth ͑Bi͒ is a very heavy element and its electronic structure is highly influenced by the spin-orbit interaction.9 It was recently shown from angle-resolved photoemission spectroscopy ͑ARPES͒ measurements that the surface states of Bi crystals are highly metallic in contrast to the semimetallic nature of bulk Bi ͑Fig. 1͒. [10][11][12][13] Additionally, it was suggested by ab initio calculations that they will show large Rashba splitting due to the significant spin-orbit coupling.12,13 Furthermore, in a recent theoretical study, 14 two-dimensional Bi bilayers were predicted to show the quantum spin Hall ͑QSH͒ effect, and it was said that these surface states may have some relations with the edge modes that characterize the QSH phase. The spin property of the highly metallic surface states of semimetallic Bi films also has importance in application to spintronics. However, although some insi...