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...

We report the first observation of a topological surface state on the (111) surface of the ternary chalcogenide TlBiSe 2 by angle-resolved photoemission spectroscopy. By tuning the synchrotron radiation energy we reveal that it features an almost ideal Dirac cone with the Dirac point well isolated from bulk continuum states. This suggests that TlBiSe 2 is a promising material for realizing quantum topological transport. DOI: 10.1103/PhysRevLett.105.146801 PACS numbers: 73.20.Àr, 79.60.Ài Three-dimensional topological insulators, which harbor massless helical Dirac fermions in a bulk energy gap [1][2][3][4], provide fertile ground to realize new phenomena in condensed matter physics, such as a magnetic monopole arising from the topological magnetoelectric effect and Majorana fermions hosted by hybrids with superconductors [5,6]. All of them can hardly be achieved with trivial 2D electron gas of the semiconductor heterostructures or graphene. The topological insulator phase has been predicted to exist in a number of materials, such as Bi 1Àx Sb x , Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 [4]. The experimental realization of the 1st and 2nd generation of the 3D topological insulators has opened a way for applications of the quantum matter [7][8][9][10][11][12].In particular, Bi 2 Se 3 has been regarded as the most promising candidate because of its single and less-warping Dirac cone than in Bi 2 Te 3 . However, recent magnetotransport measurements showed that the bulk conductance dominates even in low carrier samples [13][14][15], which raises the question of possible scattering channels responsible for the reduced surface mobility. Band-structure calculations [9,16] predict that the Dirac point (DP) of the surface state in Bi 2 Se 3 is close to the bulk valence band (BVB) maximum. As a consequence, the electron scattering channel from surface states to bulk continuum states opens, and the topological transport regime collapses. Thus, it is important to extend the search for 3D topological insulators with an ideal and isolated helical Dirac cone to a wider range of materials. Recent first principles studies suggested a variety of candidates with nontrivial electronic states ranging from oxide materials, in which the electron correlation plays a role in addition to the spin-orbit coupling [17], to Heusler-type alloys with an uniaxial strain [18,19].Recently, thallium-based ternary compounds have been proposed as a new family of 3D topological insulators [20][21][22]. In contrast to the layered binary chalcogenides, with their inert surface due to the weak bonding between the layers, in the ternary compounds the broken bonds may give rise to trivial surface states. The theoretical studies [21,22] have indeed revealed the presence of such surface states in addition to the topological ones. This calls for an angle-resolved photoemission spectroscopy (ARPES) experiment with broadly tunable photon energy, which allows us to unambiguously separate out two-dimensional electron states in this new class of ternary compound...

We present a method to microscopically derive a small-size k·p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three-and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true Z2 topological invariant. We consider bulk crystals and thin films of Bi2Se3, Bi2Te3, and Sb2Te3. It turns out that the effective continuous k·p models with open boundary conditions often incorrectly predict the topological character of thin films.PACS numbers: 71.18.+y, 71.70.Ej, Electronic structure of topological insulators (TIs) has been in focus of theoretical research regarding linear response, transport properties, Hall conductance, and motion of Dirac fermions in external fields [1,2]. These problems call for a physically justified model Hamiltonian of small dimension. As in semiconductors, it is thought sufficient that the model accurately reproduces the TI band structure near the inverted band gap [3]. The desired Hamiltonian is derived either from the theory of invariants [4] or within the k·p perturbation theory using the symmetry properties of the basis states [5].In Ref.[3], along with the pioneering prediction of the topological nature of Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 , a 4-band Hamiltonian was first constructed from the theory of invariants, which is presently widely used to analyze the properties of bulk TIs as well as their surfaces and thin films [6][7][8][9][10][11][12][13][14]. The Hamiltonian parameters in Ref. [3] were obtained by fitting ab initio band dispersion curves. Later, an attempt was made [15] to recover the Hamiltonian of Ref.[3] by a k·p perturbation theory with symmetry arguments and to derive its parameters from the ab initio wave functions of the bulk crystals. Furthermore, in Ref. To analyze how the properties of thin films are inherited from the bulk TI features, effective continuous models have been developed: they are based on the substitution k z → −i∂ z (originally introduced for slowly varying perturbations [16]) in the Hamiltonian of Ref.[3] and on the imposition of the open boundary conditions [15,[17][18][19]. These models predict a variety of intriguing phenomena at surfaces, interfaces, and thin films of TIs [20][21][22][23]. A fundamental issue here is the topological phase transition between an ordinary 2D insulator and a quantum spin Hall insulator (QSHI). Apart from the theoretical prediction, the model parameters are fitted to the measured band dispersion to deduce the topological phase from the experiment [24,25]. By analyzing the signs and relative values of the parameters of the empirically obtained effective model a judgement is made on whether the edge states would exist in a given TI film, the logic being similar to that of Ref. [26]: The valence band should have a positive and conduction band a negative effective mass.In order to avoid any ambiguity in deriving the model Hamiltonian and to treat 3D and 2D s...

Attosecond time-resolved photoemission spectroscopy reveals that photoemission from solids is not yet fully understood. The relative emission delays between four photoemission channels measured for the van der Waals crystal tungsten diselenide (WSe) can only be explained by accounting for both propagation and intra-atomic delays. The intra-atomic delay depends on the angular momentum of the initial localized state and is determined by intra-atomic interactions. For the studied case of WSe, the photoemission events are time ordered with rising initial-state angular momentum. Including intra-atomic electron-electron interaction and angular momentum of the initial localized state yields excellent agreement between theory and experiment. This has required a revision of existing models for solid-state photoemission, and thus, attosecond time-resolved photoemission from solids provides important benchmarks for improved future photoemission models.

We have performed scanning tunneling microscopy and differential tunneling conductance (dI/dV) mapping for the surface of the three-dimensional topological insulator Bi(2)Se(3). The fast Fourier transformation applied to the dI/dV image shows an electron interference pattern near Dirac node despite the general belief that the backscattering is well suppressed in the bulk energy gap region. The comparison of the present experimental result with theoretical surface and bulk band structures shows that the electron interference occurs through the scattering between the surface states near the Dirac node and the bulk continuum states.

Strong spin polarization of the photocurrent from bulk continuum states of Bi (111) is experimentally observed. On the basis of ab initio one-step photoemission theory the effect is shown to originate from the strong polarization of the initial states at the surface and to be the result of the surface sensitivity of photoemission. Final state effects cause deviations of the k k dependence of polarization from strictly antisymmetric relative to " À. Spin-split energy-band structures induced by a broken space inversion symmetry with a strong spin-orbit coupling play an important role in spin injection, spin accumulation, and the generation of spin current, which would be key properties in the next generation of spintronics devices [1][2][3]. Rashba-type spin-orbit splitting of surface states on low index surfaces has been directly studied by angle-resolved photoemission spectroscopy (ARPES) for Au [4,5], Bi [6-9], Sb [10], and surface alloys [11][12][13]. The spin polarization of the surface states on Au(111) [5] and Bi(111) [14] was confirmed by spin-resolved (SR) ARPES. In general, the experimental effort in SRARPES on nonmagnetic solids has concentrated on low-dimensional systems [15]. Spin-orbit coupling is known to cause a spindependent photoemission also from bulk continuum states, and the cases hitherto observed are explained either by a final state effect (spin-dependent transmission of the photoelectron through the surface) [16,17] or by special symmetry properties of initial states at a surface of reduced symmetry [18]. In the latter case, for s-polarized light or for nonpolarized light at non-normal incidence [19], the spin polarization of photoelectrons can occur in normal emission, which was experimentally verified in Refs. [20,21]. This is different from the Rashba effect, which is caused by the potential gradient in the surface perpendicular direction, and which occurs even at a surface of arbitrarily high symmetry but can be seen only in offnormal emission. In spite of its basic and general nature, such an effect in the continuum spectrum has not been reported yet.This work presents the observation of a Rashba-type polarization of photocurrent from continuum spectrum states of Bi(111). The ARPES on Bi(111) was pioneered by Jezequel et al. [6] followed by the work by Tanaka et al.[7] with a higher energy resolution. Ast and Höchst resolved two surface states at the Fermi level [8] that were later identified as Rashba-split states by Koroteev et al. [9]. Both quantum-well and surface states were studied on thin films [22], and the spin character of the surface states at the Fermi energy was measured by SRARPES in Refs. [14,23].The polarization of the bulk emission observed in the present work is similar to the Rashba effect for surface states: it is zero at normal emission k k ¼ 0, and at k k Þ 0 it may occur even at high-symmetry surfaces, in contrast to the Tamura-Piepke-Feder case [18]. Our theoretical analysis shows that the effect comes from the polarization of initial states at the surface due ...

The spin transport and spin-to-charge current conversion properties of bismuth are investigated using permalloy/copper/bismuth (Py/Cu/Bi) lateral spin valve structures. The spin current is strongly absorbed at the surface of Bi, leading to ultrashort spin-diffusion lengths. A spin-to-charge current conversion is measured, which is attributed to the inverse Rashba-Edelstein effect at the Cu/Bi interface. The spin-current-induced charge current is found to change direction with increasing temperature. A theoretical analysis relates this behavior to the complex spin structure and dispersion of the surface states at the Fermi energy. The understanding of this phenomenon opens novel possibilities to exploit spin-orbit coupling to create, manipulate, and detect spin currents in two-dimensional systems.

The development of materials that are non-magnetic in the bulk but exhibit two-dimensional (2D) magnetism at the surface is at the core of spintronics applications. Here, we present the valence-fluctuating material EuIr 2 Si 2 , where in contrast to its nonmagnetic bulk, the Si-terminated surface reveals controllable 2D ferromagnetism. Close to the surface the Eu ions prefer a magnetic divalent configuration and their large 4f moments order below 48 K. The emerging exchange interaction modifies the spin polarization of the 2D surface electrons originally induced by the strong Rashba effect. The temperature-dependent mixed valence of the bulk allows to tune the energy and momentum size of the projected band gaps to which the 2D electrons are confined. This gives an additional degree of freedom to handle spin-polarized electrons at the surface. Our findings disclose valence-fluctuating rare-earth based materials as a very promising basis for the development of systems with controllable 2D magnetic properties which is of interest both for fundamental science and applications.