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.     

Persistence of Spin Edge Currents in Disordered Quantum Spin Hall Systems

For a disordered two-dimensional model of a topological insulator (such as a Kane-Mele model with disordered potential) with small coupling of spin invariance and time-reversal symmetry breaking terms (such as a Rashba spin-orbit coupling and a Zeeman term), it is proved that the spin edge currents persist provided there is a spectral gap and the spin Chern numbers are well-defined and non-trivial. These are sufficient conditions for being in the quantum spin Hall phase. The result materializes the general philosophy that topological insulators are topologically non-trivial bulk systems with persistent edge or surface currents.     

Observation of a warped helical spin texture in Bi2Se3 from circular dichroism angle-resolved photoemission spectroscopy

A differential coupling of topological surface states to left- versus right-circularly polarized light is the basis of many optospintronics applications of topological insulators. Here we report direct evidence of circular dichroism from the surface states of Bi(2)Se(3) using laser-based time-of-flight angle-resolved photoemission spectroscopy. By employing a novel sample rotational analysis, we resolve unusual modulations in the circular dichroism photoemission pattern as a function of both energy and momentum, which perfectly mimic the predicted but hitherto unobserved three-dimensional warped spin texture of the surface states. By developing a microscopic theory of photoemission from topological surface states, we show that this correlation is a natural consequence of spin-orbit coupling. These results suggest that our technique may be a powerful probe of the spin texture of spin-orbit coupled materials in general.     

Dephasing effects in topological insulators

Topological insulators, a class of typical topological materials in both two dimensions and three dimensions,are insulating in bulk and metallic at surface. The spin-momentum locked surface states and peculiar transport properties exhibit promising potential applications on quantum devices, which generate extensive interest in the last decade. Dephasing is the process of the loss of phase coherence, which inevitably exists in a realistic sample. In this review, we focus on recent progress in dephasing effects on the topological insulators. In general, there are two types of dephasing processes: normal dephasing and spin dephasing. In two-dimensional topological insulators, the phenomenologically numerical investigation shows that the longitudinal resistance plateaus is robust against normal dephasing but fragile with spin dephasing. Several microscopic mechanisms of spin dephasing are then discussed. In three-dimensional topological insulators, the helical surface states exhibit a helical spin texture due to the spin-momentum locking mechanism. Thus, normal dephasing has close connection to spin dephasing in this case, and gives rise to anomalous “gap-like” feature. Dephasing effects on properties of helical surface states are investigated.     

Topological magnetic insulators with corundum structure

Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap are protected by time-reversal symmetry. When a proper kind of antiferromagnetic long-range order is established in a topological insulator, the system supports axionic excitations. In this Letter, we study theoretically the electronic states in a transition metal oxide of corundum structure, in which both spin-orbit interaction and electron-electron interaction play crucial roles. A tight-binding model analysis predicts that materials with this structure can be strong topological insulators. Because of the electron correlation, an antiferromagnetic order may develop, giving rise to a topological magnetic insulator phase with axionic excitations.     

Topological insulator: Spintronics and quantum computations

Topological insulators are emergent states of quantum matter that are gapped in the bulk with timereversal symmetry-preserved gapless edge/surface states, adiabatically distinct from conventional materials. By proximity to various magnets and superconductors, topological insulators show novel physics at the interfaces, which give rise to two new areas named topological spintronics and topological quantum computation. Effects in the former such as the spin torques, spin-charge conversion, topological antiferromagnetic spintronics, and skyrmions realized in topological systems will be addressed. In the latter, a superconducting pairing gap leads to a state that supports Majorana fermions states, which may provide a new path for realizing topological quantum computation. Various signatures of Majorana zero modes/edge mode in topological superconductors will be discussed. The review ends by outlooks and potential applications of topological insulators. Topological superconductors that are fabricated using topological insulators with superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.     

Chiral topological phases and fractional domain wall excitations in one-dimensional chains and wires

According to the general classification of topological insulators, there exist one-dimensional chirally (sublattice) symmetric systems that can support any number of topological phases. We introduce a zigzag fermion chain with spin-orbit coupling in magnetic field and identify three distinct topological phases. Zero-mode excitations, localized at the phase boundaries, are fractionalized: two of the phase boundaries support ±e/2 charge states while one of the boundaries support ±e and neutral excitations. In addition, a finite chain exhibits ±e/2 edge states for two of the three phases. We explain how the studied system generalizes the Peierls-distorted polyacetylene model and discuss possible realizations in atomic chains and quantum spin Hall wires.     

Studies on the electronic structures of three-dimensional topological insulators by angle resolved photoemission spectroscopy

Three-dimensional (3D) topological insulators represent a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. The unusual surface states of topological insulators rise from the nontrivial topology of their electronic structures as a result of strong spin-orbital coupling. In this review, we will briefly introduce the concept of topological insulators and the experimental method that can directly probe their unique electronic structure: angle resolved photoemission spectroscopy (ARPES). A few examples are then presented to demonstrate the unique band structures of different families of topological insulators and the unusual properties of the topological surface states. Finally, we will briefly discuss the future development of topological quantum materials.     

Topological phases and phase transitions on the honeycomb lattice

We investigate possible phase transitions among the different topological insulators in a honeycomb lattice under the combined influence of spin-orbit couplings and staggered magnetic flux. We observe a series of topological phase transitions when tuning the flux amplitude, and find topologically nontrivial phases with high Chern number or spin-Chern number. Through tuning the exchange field, we also find a new quantum state which exhibits the electronic properties of both the quantum spin Hall state and quantum anomalous Hall state. The topological characterization based on the Chern number and the spin-Chern number are in good agreement with the edge-state picture of various topological phases.     

Topological crystalline insulators

The recent discovery of topological insulators has revived interest in the band topology of insulators. In this Letter, we extend the topological classification of band structures to include certain crystal point group symmetry. We find a class of three-dimensional "topological crystalline insulators" which have metallic surface states with quadratic band degeneracy on high symmetry crystal surfaces. These topological crystalline insulators are the counterpart of topological insulators in materials without spin-orbit coupling. Their band structures are characterized by new topological invariants. We hope this work will enlarge the family of topological phases in band insulators and stimulate the search for them in real materials.     

Interface states in two-dimensional electron systems with spin-orbital interaction

Interface states at a boundary between regions with different spin-orbit interactions (SOIs) in two-dimensional (2D) electron systems are investigated within the one-band effective mass method with generalized boundary conditions for envelope functions. We have found that the interface states unexpectedly exist even if the effective interface potential equals zero. Depending on the system parameters, the energy of these states can lie in either or both forbidden and conduction bands of bulk states. The interface states have chiral spin texture similar to that of the edge states in 2D topological insulators. However, their energy spectrum is more sensitive to the interfacial potential, the largest effect being produced by the spin-dependent component of the interfacial potential. We have also studied the size quantization of the interface states in a strip of 2D electron gas with SOI and found an unusual (non-monotonic) dependence of the quantization energy on the strip width.     

Switching spin and charge between edge states in topological insulator constrictions

We show how the coupling between opposite edge states, which overlap in a constriction made of the topological insulator mercury telluride (HgTe), can be employed both for steering the charge flow into different edge modes and for controlled spin switching. Unlike in a conventional spin transistor, the switching does not rely on a tunable Rashba spin-orbit interaction, but on the energy dependence of the edge state wave functions. Based on this mechanism, and supported by extensive numerical transport calculations, we present two different ways to control spin and charge currents, depending on the local gating of the constriction, resulting in a high fidelity spin transistor.     

拓扑绝缘体Bi_2Se_3中层堆垛效应的第一性原理研究

运用第一性原理方法,研究了拓扑绝缘体Bi_2Se_3块体和薄膜中的层堆垛对其结构、电子态、拓扑态和自旋劈裂的影响.发现不同的堆垛会引起Bi_2Se_3层间的相互作用,改变系统的中心对称性.块体的ABC和AAA堆垛都具有中心对称性和相似的能带结构.ABA堆垛破坏了体系的中心对称性,能带发生很大改变,并且产生了很大的能带自旋劈裂.用能带反转的方法判定体系的拓扑相,在不同堆垛的Bi_2Se_3块体中,考虑自旋轨道耦合时都发生了能带反转,因而具有不同堆垛的Bi2Se3仍是拓扑绝缘体.进一步研究了Bi_2Se_3薄膜中的堆垛效应,发现非中心对称的ABA堆垛在Bi_2Se_3薄膜中引起明显的自旋劈裂,并且提出和验证了用应变调控自旋劈裂的方法.     

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.     

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.     

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.     

Spin-orbit torque from spin-flipping scattering at ferromagnetic metal/topological insulator interface

Recent experiments report large damping-like spin-orbit torque in a magnetic bilayer that consists of a topological insulator (TI) layer and a ferromagnetic metal (FM) layer. Here we examine the bilayer theoretically with particular attention to roles of conduction electrons in FM on the spin-orbit torque in this structure. We use electron scattering approach to address electron spin accumulation at the interface between TI/FM caused by the conduction electrons. While topological surface states are not well defined in this bilayer, we find that large damping-like spin-orbit torque can still arise through spin-flipping scattering of the conduction electrons at the TI-FM interface. The resulting damping-like spin-orbit torque is comparable in magnitude to that of the field-like spin-orbit torque. The ratio between the components of the spin-orbit torque relies on various details of the system. The result is compared with recent experimental results and other theoretical works.     

Robustness of topologically protected surface states in layering of Bi2Te3 thin films

Bulk Bi2Te3 is known to be a topological insulator. We investigate surface states of Bi2Te3(111) thin films of one to six quintuple layers using density-functional theory including spin-orbit coupling. We construct a method to identify topologically protected surface states of thin film topological insulators. Applying this method to Bi2Te3 thin films, we find that the topological nature of the surface states remains robust with the film thickness and that the films of three or more quintuple layers have topologically nontrivial surface states, which agrees with experiments.     

Topological Insulators in α-Graphyne

In this paper, we investigate topological phases of α-graphyne with tight-binding method. By calculating the topological invariant Z2 and the edge states, we identify topological insulators. We present the phase diagrams of α-graphyne with different filling fractions as a function of spin-orbit interaction and the nearest-neighbor hopping energy. We find there exist topological insulators in α-graphyne. We analyze and discuss the characteristics of topological phases of α-graphyne.     

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.