Spin texture and circular dichroism in photoelectron spectroscopy from the topological insulator bi_{2}te_{3}: first-principles photoemission calculations

By relativistic first-principles photoemission calculations for the topological insulator Bi_{2}Te_{3}, we study how the spin texture of the Dirac state manifests itself in circular dichroism. On one hand, there are significant modifications of the initial state's spin texture, which are explained by final-state effects and the symmetry of the photoemission setup. On the other hand, a highly symmetric setup allows us to draw conclusions about the detailed Dirac state's spin texture. Our study supports that circular dichroism in angular distribution successfully complements spin- and angle-resolved photoelectron spectroscopy from topological insulators.     

Chiral orbital-angular momentum in the surface states of Bi2Se3

We performed angle-resolved photoemission (ARPES) experiments with circularly polarized light and first-principles density functional calculation with spin-orbit coupling to study surface states of a topological insulator Bi2Se3. We observed circular dichroism (CD) as large as 30% in the ARPES data with upper and lower Dirac cones showing opposite signs in CD. The observed CD is attributed to the existence of local orbital-angular momentum (OAM). First-principles calculation shows that OAM in the surface states is significant and is locked to the electron momentum in the opposite direction to the spin, forming chiral OAM states. Our finding opens a new possibility for strong light-induced spin-polarized current in surface states. We also provide a proof for local OAM origin of the CD in ARPES.     

Spin-orbit hybridization points in the face-centered-cubic cobalt band structure

Linear magnetic dichroism is observed in spin-, time-, and energy-resolved two-photon photoemission from valence bands of epitaxial fcc cobalt on Cu(001). With image-potential states as spectator states we identify initial bulk and surface states with minority spin character as the source for dichroic intensities and apparent dichroic lifetimes. Excellent agreement with ab initio fully relativistic calculations of the cobalt fcc band structure allows us to precisely determine spin-orbit hybridization points close to the Fermi level. These spin hot spots enhance spin-flip scattering by several orders of magnitude and are therefore assumed to be crucial in ultrafast demagnetization.     

Selective probing of photoinduced charge and spin dynamics in the bulk and surface of a topological insulator

Topological insulators possess completely different spin-orbit coupled bulk and surface electronic spectra that are each predicted to exhibit exotic responses to light. Here we report time-resolved fundamental and second harmonic optical pump-probe measurements on the topological insulator Bi(2)Se(3) to independently measure its photoinduced charge and spin dynamics with bulk and surface selectivity. Our results show that a transient net spin density can be optically induced in both the bulk and surface, which may drive spin transport in topological insulators. By utilizing a novel rotational anisotropy analysis we are able to separately resolve the spin depolarization, intraband cooling, and interband recombination processes following photoexcitation, which reveal that spin and charge degrees of freedom relax on very different time scales owing to strong spin-orbit coupling.     

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number C_s for energy-bands of trilayer graphene having the essence of intrinsic spin–orbit coupling is analytically calculated. We find that for each valley and spin, C_s is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states,consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin–orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin–orbit(RSO) interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin–orbit coupling, while the other two layers have zero intrinsic spin–orbit coupling.Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.     

Spin-resolved photoemission of surface states of W(110)-(1 x 1)H

The surface electronic states of W(110)-(1 x 1)H have been measured using spin- and angle-resolved photoemission. We directly demonstrate that the surface bands are both split and spin-polarized by the spin-orbit interaction in association with the loss of inversion symmetry near a surface. We observe 100% spin polarization of the surface states, with the spins aligned in the plane of the surface and oriented in a circular fashion relative to the Smacr; symmetry point. In contrast, no measurable polarization of nearby bulk states is observed.     

Can spin-polarized photoemission measure spin properties in condensed matter?

Photoemitted electrons move in a vacuum; their quantum state can be completely characterized in terms of energy, momentum and spin polarization by spin-polarized photoemission experiments. A review article in this issue by Heinzmann and Dil (2012 J. Phys.: Condens. Matter 24 173001) considers whether the measured spin properties, i.e. the magnitude and direction of the spin polarization vector, can be traced back to the quantum state from which these electrons originate. The careful conclusion is that they can, which is highly relevant in view of the current interest in these experiments and their application to topological insulators, where the spin-orbit interaction produces spin-polarized surface states.     

Direct measurement of the out-of-plane spin texture in the Dirac-cone surface state of a topological insulator

We have performed spin- and angle-resolved photoemission spectroscopy of Bi(2)Te(3) and present the first direct evidence for the existence of the out-of-plane spin component on the surface state of a topological insulator. We found that the magnitude of the out-of-plane spin polarization on a hexagonally deformed Fermi surface of Bi(2)Te(3) reaches maximally 25% of the in-plane counterpart, while such a sizable out-of-plane spin component does not exist in the more circular Fermi surface of TlBiSe(2), indicating that the hexagonal deformation of the Fermi surface is responsible for the deviation from the ideal helical spin texture. The observed out-of-plane polarization is much smaller than that expected from the existing theory, suggesting that an additional ingredient is necessary for correctly understanding the surface spin polarization in Bi(2)Te(3).     

First-principles study of the topological surface states of α-Sn(111)

α-Sn is on the boundary of a couple of distinct topological phases. It will transform into a topological insulator under a suitable strain. However, a clear picture of its topological surface states (TSSs) is still lacking. Here we perform first-principles calculations on the electronic structure of α-Sn(111) surface to identify its TSSs and reveal their properties. The results show that the presence of valence band reorganizes the TSSs in the inverted sp gap into two Dirac cones. The lower one is in the valence band continuum; the upper one resides in the gap between the valence and conduction bands. We also demonstrate the transformation of the surface states by switching on or off of strain and/or spin-orbit coupling. Without spin-orbit coupling, only the TSSs associated with the lower Dirac cone survive, and they are spin unpolarized. The results are useful for understanding and engineering the topological properties of α-Sn.     

Spin and Majorana polarization in topological superconducting wires

We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in the proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local "Majorana polarization" and "Majorana density" and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local Majorana polarization is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement.     

Spin polarization and transport of surface states in the topological insulators Bi2Se3 and Bi2Te3 from first principles

We investigate the band dispersion and the spin texture of topologically protected surface states in the bulk topological insulators Bi2Se3 and Bi2Te3 by first-principles methods. Strong spin-orbit entanglement in these materials reduces the spin polarization of the surface states to ～50% in both cases; this reduction is absent in simple models but of important implications to essentially any spintronic application. We propose a way of controlling the magnitude of spin polarization associated with a charge current in thin films of topological insulators by means of an external electric field. The proposed dual-gate device configuration provides new possibilities for electrical control of spin.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

Fermi surface and anisotropic spin-orbit coupling of Sb(111) studied by angle-resolved photoemission spectroscopy

High-resolution angle-resolved photoemission spectroscopy has been performed on Sb(111) to elucidate the origin of anomalous electronic properties in group-V semimetal surfaces. The surface was found to be metallic despite the semimetallic character of bulk. We clearly observed two surface-derived Fermi surfaces which are likely spin split, demonstrating that the spin-orbit interaction plays a dominant role in characterizing the surface electronic states of group-V semimetals. The universality or dissimilarity of the electronic structure in Bi and Sb is discussed in relation to the granular superconductivity, electron-phonon coupling, and surface charge or spin density wave.     

Band topology and the quantum spin Hall effect in bilayer graphene

We consider bilayer graphene in the presence of spin-orbit coupling, in order to assess its behavior as a topological insulator. The first Chern number n for the energy bands of single-layer graphene and that for the energy bands of bilayer graphene are computed and compared. It is shown that for a given valley and spin, n for a Bernal-stacked bilayer is doubled with respect to that for the monolayer. This implies that this form of bilayer graphene will have twice as many edge states as single-layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bernal-stacked bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. In contrast, we show that AA-stacked bilayer graphene is not a topological insulator unless the spin-orbit coupling is bigger than the interlayer hopping. Finally, we consider an intermediate situation in which only one of the two layers has spin-orbit coupling, and find that although individual valleys have non-trivial Chern numbers for the case of Bernal stacking, the spectrum as a whole is not gapped, so the system is not a topological insulator.     

The family of topological Hall effects for electrons in skyrmion crystals

Hall effects of electrons can be produced by an external magnetic field, spin–orbit coupling or a topologically non-trivial spin texture. The topological Hall effect (THE) – caused by the latter – is commonly observed in magnetic skyrmion crystals. Here, we show analogies of the THE to the conventional Hall effect (HE), the anomalous Hall effect (AHE), and the spin Hall effect (SHE). In the limit of strong coupling between conduction electron spins and the local magnetic texture the THE can be described by means of a fictitious, “emergent” magnetic field. In this sense the THE can be mapped onto the HE caused by an external magnetic field. Due to complete alignment of electron spin and magnetic texture, the transverse charge conductivity is linked to a transverse spin conductivity. They are disconnected for weak coupling of electron spin and magnetic texture; the THE is then related to the AHE. The topological equivalent to the SHE can be found in antiferromagnetic skyrmion crystals. We substantiate our claims by calculations of the edge states for a finite sample. These states reveal in which situation the topological analogue to a quantized HE, quantized AHE, and quantized SHE can be found.     

Spin-orbit-induced photoelectron spin polarization in angle-resolved photoemission from both atomic and condensed matter targets

The existence of highly spin polarized photoelectrons emitted from non-magnetic solids as well as from unpolarized atoms and molecules has been found to be very common in many studies over the past 40 years. This so-called Fano effect is based upon the influence of the spin-orbit interaction in the photoionization or the photoemission process. In a non-angle-resolved photoemission experiment, circularly polarized radiation has to be used to create spin polarized photoelectrons, while in angle-resolved photoemission even unpolarized or linearly polarized radiation is sufficient to get a high spin polarization. In past years the Rashba effect has become very important in the angle-resolved photoemission of solid surfaces, also with an observed high photoelectron spin polarization. It is the purpose of the present topical review to cross-compare the spin polarization experimentally found in angle-resolved photoelectron emission spectroscopy of condensed matter with that of free atoms, to compare it with the Rashba effect and topological insulators to describe the influence and the importance of the spin-orbit interaction and to show and disentangle the matrix element and phase shift effects therein.The relationship between the energy dispersion of these phase shifts and the emission delay of photoelectron emission in attosecond-resolved photoemission is also discussed. Furthermore the influence of chiral structures of the photo-effect target on the spin polarization, the interferences of different spin components in coherent superpositions in photoemission and a cross-comparison of spin polarization in photoemission from non-magnetic solids with XMCD on magnetic materials are presented; these are all based upon the influence of the spin-orbit interaction in angle-resolved photoemission.     

Spin- and angle-resolved photoelectron spectroscopy from solid surfaces with circularly polarized light

Spin-polarized photoemission with circularly polarized light represents a relatively new technique in surface science. It became feasible with the increased availability of circularly polarized light in the vacuum ultraviolet and soft X-ray regime, generated in dedicated synchrotron radiation facilities. Another important ingredient was the development of efficient electron spin polarization detectors. Supported by group theoretical considerations, this technique was first employed to study the process of optical spin orientation in single crystalline non-magnetic materials. In these samples, spin-dependent effects arise solely from spin-orbit coupling. The experiments revealed the strong influence of spin-orbit coupling on the details of the electronic band structure, such as the symmetry character of the electronic wave functions, hybridization phenomena, and the behavior of degeneracies. The results opened the way to a detailed understanding of the electronic structure and permit a rigorous test of both state-of-the-art bulk band theories and fully relativistic photoemission calculations. Since 1990, spin-polarized photoemission with circularly polarized light is also used to investigate ferromagnetic systems. These experiments led to the discovery of the counterpart of optical spin orientation in ferromagnets, namely, the magnetic dichroisms. Magnetic dichroism means that the spin-dependent photoexcitation from a ferromagnetically ordered system manifests itself already in the photoelectron intensity distributions. Because of this particular property, techniques based on magnetic dichroisms are currently receiving wide interest in the spectroscopic investigation of magnetic systems and phenomena.

The following article reviews the current status of the field of spin- and angle-resolved photoemission from solids using circularly polarized radiation. We survey the development of this technique over the last 10 years, covering its applications to both non-magnetic and ferromagnetic systems.     

Subband structure of a two-dimensional electron gas formed at the polar surface of the strong spin-orbit perovskite KTaO3

We demonstrate the formation of a two-dimensional electron gas (2DEG) at the (100) surface of the 5d transition-metal oxide KTaO3. From angle-resolved photoemission, we find that quantum confinement lifts the orbital degeneracy of the bulk band structure and leads to a 2DEG composed of ladders of subband states of both light and heavy carriers. Despite the strong spin-orbit coupling, our measurements provide a direct upper bound for the potential Rashba spin splitting of only Δk(parallel)}~0.02 ?(-1) at the Fermi level. The polar nature of the KTaO3(100) surface appears to help mediate the formation of the 2DEG as compared to nonpolar SrTiO3(100).     

Role of spin-orbit splitting and dynamical fluctuations in the Si(557)-Au surface

Our ab initio calculations show that spin-orbit coupling is crucial to understand the electronic structure of the Si(557)-Au surface. The spin-orbit splitting produces the two one-dimensional bands observed in photoemission, which were previously attributed to spin-charge separation in a Luttinger liquid. This spin splitting might have relevance for future device applications. We also show that the apparent Peierls-like transition observed in this surface by scanning tunneling microscopy is a result of the dynamical fluctuations of the step-edge structure which are quenched as the temperature is decreased.