Confined states and spin polarization on a topological insulator thin film modulated by an electric potential

We study the electronic structure and spin polarization of the surface states of a three-dimensional topological insulator thin film modulated by an electrical potential well. By routinely solving the low-energy surface Dirac equation for the system, we demonstrate that confined surface states exist, in which the electron density is almost localized inside the well and exponentially decayed outside in real space, and that their subband dispersions are quasilinear with respect to the propagating wavevector. Interestingly, the top and bottom surface confined states with the same density distribution have opposite spin polarizations due to the hybridization between the two surfaces. Along with the mathematical analysis, we provide an intuitive, topological understanding of the effect.     

Magnetic ratchet effects in a two-dimensional electron gas

The effect of the magnetic field on the generation of an electric current in a two-dimensional electronic ratchet is theoretically studied. Mechanisms of the formation of magnetically induced photocurrent are proposed for a structure with a two-dimensional electron gas (quantum well, graphene, or topological insulator) with a lateral asymmetric superlattice consisting of metallic strips on the external surface of the structure. The ratchet with the spatially oscillating magnetic field generated by the ferromagnetic lattice, as well as the nonmagnetic ratchet placed in the uniform magnetic field both classically weak and strong quantizing, is considered. It is established that the ratio of the amplitude of the magnetic oscillations of photocurrent to the ratchet photocurrent in zero field can exceed two orders of magnitude.     

Electronic structure and transport on the surface of topological insulator attached to an electromagnetic superlattice

We study the electronic structure and transport for Dirac electron on the surface of a three-dimensional (3D) topological insulator attached to an electromagnetic superlattice. It is found that, by means of the transfer-matrix method, the number of electronic tunneling channels for magnetic barriers in antiparallel alignment is larger than that in parallel alignment, which stems to the energy band structures. Interestingly, a remarkable semiconducting transport behavior appears in this system with a strong magnetic barrier due to low energy band nearly paralleling to the Fermi level. Consequently, there is only small incident angle transport in the higher energy region when the system is modulated mainly by the higher electric barriers. We further find that the spatial distribution of the spin polarization oscillates periodically in the incoming region, but it is almost in-plane with a fixed direction in the transmitting region. The results may provide a further understanding of the nature of 3D TI surface states, and may be useful in the design of topological insulator-based electronic devices such as collimating electron beam.     

Electrodynamic response of charge carriers in doubly periodic semiconductor <Emphasis Type="Italic">n</Emphasis>-type superlattices in a permanent homogeneous magnetic field

The electromagnetic response of the two-dimensional electron gas of a surface superlattice placed in a perpendicular permanent homogeneous magnetic field is studied. The magneto–optic Kerr and Faraday effects are calculated. The conditions of transparency of model semiconductor structures in the terahertz frequency region are found and the field-induced spin density of the electronic states is calculated. The features of the frequency dependences of complex Kerr and Faraday angles are connected with the symmetry of the spinor states of the charge carriers in a superlattice.     

Characterization of topological phase of superlattices in superconducting circuits

The recent experimental observation of topological magnon insulator states in a superconducting circuit chain marks a breakthrough for topological physics with qubits, in which a dimerized qubit chain has been realized. Here, we extend such a dimer lattice to superlattice with arbitrary number of qubits in each unit cell in superconducting circuits, which exhibits rich topological properties. Specifically, by considering a quadrimeric superlattice, we show that the topological invariant (winding number) can be effectively characterized by the dynamics of the single-excitation quantum state through time-dependent quantities. Moreover, we explore the appearance and detection of the topological protected edge states in such a multiband qubit system. Finally, we also demonstrate the stable Bloch-like-oscillation of multiple interface states induced by the interference of them. Our proposal can be readily realized in experiment and may pave the way towards the investigation of topological quantum phases and topologically protected quantum information processing.     

Electronic states and spin-filter effect in three-dimensional topological insulator Bi_2Se_3 nanoribbons

We study the electronic band structure, density distribution, and transport of a Bi_2Se_3 nanoribbon. We find that the density distribution of the surface states is dependent on not only the shape and size of the transverse cross section of the nanoribbon, but also the energy of the electron. We demonstrate that a transverse electric field can eliminate the coupling between surface states on the walls of the nanoribbon, remove the gap of the surface states, and restore the quantum spin Hall effects. In addition, we study the spin-dependent transport property of the surface states transmitting from top and bottom surfaces(x-y plane) to the side surfaces(z-x plane) of a Bi_2Se_3 nanoribbon. We find that transverse electric fields can open two surface channels for spin-up and-down Dirac electrons, and then switch off one channel for the spin-up Dirac electron. Our results may provide a simple way for the design of a spin filter based on topological insulator nanostructures.     

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.     

Tunable topological quantum states in three- and two-dimensional materials

We review our theoretical advances in tunable topological quantum states in three- and twodimensional materials with strong spin–orbital couplings. In three-dimensional systems, we propose a new tunable topological insulator, bismuth-based skutterudites in which topological insulating states can be induced by external strains. The orbitals involved in the topological band-inversion process are the d- and p-orbitals, unlike typical topological insulators such as Bi₂Se₃and BiTeI, where only the p-orbitals are involved in the band-inversion process. Owing to the presence of large d-electronic states, the electronic interaction in our proposed topological insulator is much stronger than that in other conventional topological insulators. In two-dimensional systems, we investigated 3d-transition-metal-doped silicene. Using both an analytical model and first-principles Wannier interpolation, we demonstrate that silicene decorated with certain 3d transition metals such as vanadium can sustain a stable quantum anomalous Hall effect. We also predict that the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition-metal-doped silicenes where the energy band inversion occurs. These findings provide realistic materials in which topological states could be arbitrarily controlled.     

Spin current in an electron waveguide tunnel-coupled to a topological insulator

We show that electron tunneling from edge states in a two-dimensional topological insulator into a parallel electron waveguide leads to the appearance of spin-polarized current in the waveguide. The spin polarization P can be very close to unity and the electron current passing through the tunnel contact splits in the waveguide into two branches flowing from the contact. The polarization essentially depends on the electron scattering by the contact and the electron-electron interaction in the one-dimensional edge states. The electron-electron interaction is treated within the Luttinger liquid model. The main effect of the interaction stems from the renormalization of the electron velocity, due to which the polarization increases with the interaction strength. Electron scattering by the contact leads to a decrease in P. A specific effect occurs when the bottom of the subbands in the waveguide crosses the Dirac point of the spectrum of edge states when changing the voltage or chemical potential. This leads to changing the direction of the spin current.     

Resonance reflection of light from two-dimensional superlattice structures

The exciton Bloch states in a quantum well with a two-dimensional periodic potential are studied theoretically. Expressions are derived for the light reflection coefficient and the exciton oscillator strength for a structure with this type of lateral superlattice. The redistribution of the oscillator strength between exciton states with varying period and depth of the potential is analyzed. The limiting cases where the nearly free exciton and tight-binding approximations are applicable are considered.     

Structural instabilities of a two-dimensional Wigner crystal in a lateral superlattice

We consider the instability of a two-dimensional Wigner crystal in a short-period lateral superlattice. To find instabilities, we calculate the phonon spectrum of the electron lattice deformed by a periodic potential. We show that one of the transverse modes of the deformed electron crystal becomes soft when the electron density exceeds a critical value. This can result in a phase transition with the formation of a charge-density wave.     

Spin Hall conductivity in three-dimensional topological insulator/normal insulator heterostructures

In the framework of an effective functional approach based on the k · p method, we study the combined effect of an interface potential and a thickness of a three-dimensional (3D) topological insulator (TI) thin film on the spin Hall conductivity in layered heterostructures comprising TI and normal insulator (NI) materials. We derive an effective two-dimensional (2D) Hamiltonian of a 3D TI thin film sandwiched between two NI slabs and define the applicability limits of approximations used. The energy gap and mass dispersion in the 2D Hamiltonian, originated from the hybridization between TI/NI interfacial bound electron states at the opposite boundaries of a TI film, are demonstrated to change sign with the TI film thickness and the interface potential strength. Finally, we argue that the spin Hall conductivity can efficiently be tuned varying the interface potential characteristics and TI film thickness.     

Proximity effects in topological insulator heterostructures

Topological insulators （Tls） are bulk insulators that possess robust helical conducting states along their interfaces with conventional insulators. A tremendous research effort has recently been devoted to TI-based heterostructures, in which con- ventional proximity effects give rise to a series of exotic physical phenomena. This paper reviews our recent studies on the potential existence of topological proximity effects at the interface between a topological insulator and a normal insu- lator or other topologically trivial systems. Using first-principles approaches, we have realized the tunability of the vertical location of the topological helical state via intriguing dual-proximity effects. To further elucidate the control parameters of this effect, we have used the graphene-based heterostructures as prototypical systems to reveal a more complete phase diagram. On the application side of the topological helical states, we have presented a catalysis example, where the topo- logical helical state plays an essential role in facilitating surface reactions by serving as an effective electron bath, These discoveries lay the foundation for accurate manipulation of the real space properties of the topological helical state in TI- based heterostructures and pave the way for realization of the salient functionality of topological insulators in future device applications.     

Semimetal behavior of bilayer stanene

Stanene is a two-dimensional (2D) buckled honeycomb structure which has been studied recently owing to its promising electronic properties for potential electronic and spintronic applications in nanodevices. In this article we present a first-principles study of electronic properties of fluorinated bilayer stanene. The effect of tensile strain, intrinsic spin-orbit and van der Waals interactions are considered within the framework of density functional theory. The electronic band structure shows a very small overlap between valence and conduction bands at the Γ point which is a characteristic of semimetal in fluorinated bilayer stanene. A relatively high value of tensile strain is needed to open an energy band gap in the electronic band structure and the parity analysis reveals that the strained nanostructure is a trivial insulator. According to our results, despite the monolayer fluorinated stanene, the bilayer one is not an appropriate candidate for topological insulator.     

Spin-orbit lateral superlattices: Energy bands and spin polarization in 2DEG

The Bloch spinors, energy spectrum, and spin density in energy bands are studied for a two-dimensional electron gas (2DEG) with Rashba spin-orbit (SO) interaction subject to the one-dimensional (1D) periodic electrostatic potential of a lateral superlattice. The space symmetry of the Bloch spinors with spin parity is studied. It is shown that the Bloch spinors at fixed quasi-momentum describe the standing spin waves with the wavelength equal to the superlattice period. The spin projections in these states have components both parallel and transverse to the 2DEG plane. The anticrossing of the energy dispersion curves due to the interplay between the SO and periodic terms is observed, thus, leading to the spin flip. The relation between the spin parity and the interband optical selection rules is discussed, and the effect of magnetization of the SO superlattice in the presence of an external electric field is predicted. The text was submitted by the authors in English.     

新型高分辨率电子能量损失谱仪与表面元激发研究

高分辨率电子能量损失谱仪利用单色平行电子束入射样品表面,与表面吸附基团的化学键振动、表面声子、电子及其集体激发模式等相互作用而被散射,通过分析散射电子的能量和动量,可以测量表面化学键、晶格动力学、电子态占据以及表面等离激元等的精确信息,是表面科学研究的有力工具.最近,能够对电子能量、动量做二维成像探测分析的半球形电子能量分析器被引入电子能量损失谱仪,实现了高能量、动量分辨率的高效率测量.在对FeSe/SrTiO_3界面超导增强物理机制的研究中,不同厚度的FeSe膜表面的电子能量损失谱表明衬底光学声子产生的偶极电场能够穿透到薄膜内部,诱导较强的电子-声子耦合作用,从而增强薄膜中电子的配对作用,进而使超导转变温度显著提高.三维拓扑绝缘体Bi_2Se_3表面大动量范围的电子能量损失谱还显示出一支奇异的电子集体激发模式,其色散特征不受晶格周期性的限制,而且其寿命和强度几乎不随动量的增加而衰减.这说明在拓扑绝缘体表面,不仅是狄拉克电子态本身,其集体激发也受到拓扑保护.充分发挥新型电子能量损失谱仪观测表面元激发分辨率高、动态范围大的优势,将有力地推动表面界面凝聚态物理问题研究的深入和发展.     

Spin-filtered edge states in graphene

Spin–orbit coupling changes graphene, in principle, into a two-dimensional topological insulator, also known as quantum spin Hall insulator. One of the expected consequences is the existence of spin-filtered edge states that carry dissipationless spin currents and undergo no backscattering in the presence of non-magnetic disorder, leading to quantization of conductance. Whereas, due to the small size of spin–orbit coupling in graphene, the experimental observation of these remarkable predictions is unlikely, the theoretical understanding of these spin-filtered states is shedding light on the electronic properties of edge states in other two-dimensional quantum spin Hall insulators. Here we review the effect of a variety of perturbations, like curvature, disorder, edge reconstruction, edge crystallographic orientation, and Coulomb interactions on the electronic properties of these spin filtered states.     

Electronic band structure of GaAs/AlxGa1−xAs superlattice in an intense laser field

We perform theoretical calculations for the band structure of semiconductor superlattice under intense high-frequency laser field. In the frame of the non-perturbative approach, the laser effects are included via laser-dressed potential. Results reveal that an intense laser field creates an additional geometric confinement on the electronic states. Numerical results show that when tuning the strength of the laser field significant changes come in the electronic energy levels and density of states.     

Nonlocal transport properties of topological insulator F/I/SC/I/F junction with perpendicular magnetization

We investigate theoretically the nonlocal transport properties in a ferromagnet/insulator/superconductor/insulator/ferromagnet (F/I/SC/I/F) junction with perpendicular magnetization formed on a topological insulator. The nonlocal conductance through the junction depends strongly on whether the perpendicular magnetizations of the two ferromagnets are in a parallel or an antiparallel alignment. This stems from the fact that on the surface of three dimensional topological insulator the exchange field acts as vector potential and from spin-momentum locking property of the topological insulator surface states. It is found that the nonlocal conductance as a function of barrier strength of the I regions exhibits a quantum switch on-off property.     

Lateral surface magnetoplasma modes of type II semiconductor superlattices

The recently developed theory of superlattice lateral surface magnetoplasmon is extended to type II superlattices consisting of alternating two-dimensional planes of electrons and holes. The magnetoplasmon dispersion relation is calculated by transforming the two coupled integral equations for the a.c. potential into a composite matrix equation. This method can be generalized to study charge density collective excitations in an arbitrary multi-component superlattice.