Magnetic and topological transitions in three-dimensional topological Kondo insulator

Using an extended slave-boson method,we draw a global phase diagram summarizing both magnetic phases and paramagnetic(PM) topological insulators(TIs) in a three-dimensional topological Kondo insulator(TKI). By including electron hopping(EH) up to the third neighbors, we identify four strong TI(STI) phases and two weak TI(WTI) phases. Then, the PM phase diagrams characterizing topological transitions between these TIs are depicted as functions of EH,f-electron energy level,and hybridization constant. We also find an insulator-metal transition from an STI phase that has surface Fermi rings and spin textures in qualitative agreement with the TKI candidate SmBs. In the weak hybridization regime, antiferromagnetic(AF) order naturally arises in the phase diagrams. Depending on how the magnetic boundary crosses the PM topological transition lines,AF phases are classified into the AF topological insulator(AFTI) and the non-topological AF insulator, according to their Z_2 indices. In two small regions of parameter space, two distinct topological transition processes between AF phases occur, leading to two types of AFTIs showing distinguishable surface dispersions around their Dirac points.     

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.     

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.     

Spin-resolved edge states transport in a normal/ferromagnetic/normal topological insulator junction: The role of interface

The spin-resolved edge states transport in a normal/ferromagnetic/normal topological insulator (TI) junction is investigated numerically. It is shown that the transport properties of the hybrid junction strongly depend on the interface shape. For the junction with two sharp interfaces, a nonzero spin conductance can be generated besides the spin-split energy windows. Moreover, the axial symmetries of the in-plane spin conductance amplitude are broken. The underlying physics is attributed to the sharp-interface-induced quantum interference effect. However, for the hybrid junction with two smooth interfaces, a non-zero spin conductance can only be achieved in the spin-split energy windows. Further, the axial symmetries of the in-plane spin conductance amplitude recover. These findings may not only benefit to further apprehend the spin-dependent edge states transport in the hybrid TI junctions but also provide some theoretical bases to the application of the topological spintronics devices.     

Surface state charge dynamics of a high-mobility three-dimensional topological insulator

We present a magneto-optical study of the three-dimensional topological insulator, strained HgTe, using a technique which capitalizes on advantages of time-domain spectroscopy to amplify the signal from the surface states. This measurement delivers valuable and precise information regarding the surface-state dispersion within <1 meV of the Fermi level. The technique is highly suitable for the pursuit of the topological magnetoelectric effect and axion electrodynamics.     

Interface-induced states at the boundary between a 3D topological insulator and a normal insulator

We show that, when a three-dimensional (3D) narrow-gap semiconductor with inverted band gap (“topological insulator,” TI) is attached to a 3D wide-gap semiconductor with non-inverted band gap (“normal insulator,” NI), two types of bound electron states having different spatial distributions and spin textures arise at the TI/NI interface. Namely, the gapless (“topological”) bound state can be accompanied by the emergence of the gapped (“ordinary”) bound state. We describe these states in the framework of the envelope function method using a variational approach for the energy functional; their existence hinges on the ambivalent character of the constraint for the envelope functions that correspond to the “open” or “natural” boundary conditions at the interface. The properties of the ordinary state strongly depend on the effective interface potential, while the topological state is insensitive to the interface potential variation.     

Anomalous Aharonov-Bohm conductance oscillations from topological insulator surface states

We study Aharonov-Bohm (AB) conductance oscillations arising from the surface states of a topological insulator nanowire, when a magnetic field is applied along its length. With strong surface disorder, these oscillations are predicted to have a component with anomalous period Φ(0)=hc/e, twice the conventional period. The conductance maxima are achieved at odd multiples of 1/2Φ(0), implying that a π AB phase for electrons strengthens the metallic nature of surface states. This effect is special to topological insulators, and serves as a defining transport property. A key ingredient, the surface curvature induced Berry phase, is emphasized here. We discuss similarities and differences from recent experiments on Bi2Se3 nanoribbons, and optimal conditions for observing this effect.     

Spectrum of Andreev bound states in Josephson junctions with a ferromagnetic insulator

Ferromagnetic-insulator (FI) based Josephson junctions are promising candidates for a coherent superconducting quantum bit as well as a classical superconducting logic circuit. Recently the appearance of an intriguing atomic-scale 0–π$0–\pi$ transition has been theoretically predicted. In order to uncover the mechanism of this phenomena, we numerically calculate the spectrum of Andreev bound states in a FI barrier by diagonalizing the Bogoliubov–de Gennes equation. We show that Andreev spectrum drastically depends on the parity of the FI-layer number L   and accordingly the π(0)$\pi (0)$ state is always more stable than the 0 (π$\pi$) state if L is odd (even).     

Weak antilocalization in a three-dimensional topological insulator based on a high-mobility HgTe film

The up-conversion luminescence of Er³⁺ from the ²H_11/2, ⁴S_3/2, and ⁴F_9/2 levels in nanocrystals of Y_0.95(1?x)Yb_0.95xEr_0.05PO₄ (x = 0, 0.3, 0.5, 0.7, 1) orthophosphates activated with Er³⁺ ions has been studied under the excitation of Yb³⁺ ions to the ²F_5/2 level by 972-nm cw laser radiation. Broadband radiation in the wavelength range of 370–900 nm has been observed at certain power densities of exciting laser radiation; this broadband radiation is absent in the case of excitation of the powders under study by pulsed laser radiation with a wavelength of 972 nm at a pulse repetition frequency of 10 Hz and a duration of a pulse of 15 ns. Experimental data indicating that this radiation is thermal in nature have been presented.     

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.     

Photoinduced Weyl semimetal phase and anomalous Hall effect in a three-dimensional topological insulator

Motivated by the fact that Weyl fermions can emerge in a three-dimensional topological insulator on breaking either time-reversal or inversion symmetries, we propose that a topological quantum phase transition to a Weyl semimetal phase occurs under the off-resonant circularly polarized light, in a three-dimensional topological insulator, when the intensity of the incident light exceeds a critical value. The circularly polarized light effectively generates a Zeeman exchange field and a renormalized Dirac mass, which are highly controllable. The phase transition can be exactly characterized by the first Chern number. A tunable anomalous Hall conductivity emerges, which is fully determined by the location of the Weyl nodes in momentum space, even in the doping regime. Our predictions are experimentally realizable through pump-probe angle-resolved photoemission spectroscopy and raise a new way for realizing Weyl semimetals and quantum anomalous Hall effects.     

Magnetically confined states and transport property on the surface of a topological insulator

We study the electronic structure and transport for a quasi-one-dimensional channel constructed via two ferromagnetic (FM) stripes on the surface of a three-dimensional (3D) topological insulator (TI) in parallel (P) or antiparallel (AP) magnetization configuration along the vertical z$z$-direction. We demonstrate that the confined states which are localized inside the channel always exist due to the magnetic potential confinement. Interestingly, the channel is metallic because of the existence of a topologically protected gapless chiral edge mode in the case of AP configuration. The asymmetric spatial-distribution of both electron probability density and in-plane spin polarization for the confined states implies that in the case of P configuration there exists a chiral state near the channel edge owing to the Hamiltonian inversion symmetry broken in real space, while the distributions in AP case are always symmetry since the inversion symmetry is still kept. Furthermore, the transmission probability and the spatial-dependent distributions of charge and spin along a narrow–wide–narrow channel on the surface with P configuration confinement are also calculated, from which a fully in-plane spin-polarized electron output is achieved. Along with the mathematical analysis we provide an intuitive, topological understanding of these effects.     

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.     

Field-effect modulation of anomalous Hall effect in diluted ferromagnetic topological insulator epitaxial films

High quality chromium(Cr) doped three-dimensional topological insulator(TI) Sb_2Te_3 films are grown via molecular beam epitaxy on heat-treated insulating SrTiO_3(111) substrates. We report that the Dirac surface states are insensitive to Cr doping, and a perfect robust long-range ferromagnetic order is unveiled in epitaxial Sb_(2–x)Cr_xTe_3 films. The anomalous Hall effect is modulated by applying a bottom gate, contrary to the ferromagnetism in conventional diluted magnetic semiconductors(DMSs), here the coercivity field is not significantly changed with decreasing carrier density. Carrier-independent ferromagnetism heralds Sb_(2–x)Cr_xTe_3 films as the base candidate TI material to realize the quantum anomalous Hall(QAH) effect. These results also indicate the potential of controlling anomalous Hall voltage in future TI-based magneto-electronics and spintronics.     

Electrically controllable conductance and tunneling magnetoresistance through a topological insulator quantum well coupled to ferromagnetic electrodes

We theoretically investigate the electrically controllable conductance and tunneling magnetoresistance (TMR) through a two-dimensional topological insulator (TI) quantum well sandwiched between ferromagnetic (FM) electrodes in the method of nonequilibrium Green’s function (GF). It is demonstrated that the inter-edge tunnelings modulated conductance for spin-up and spin-down carriers presents an opposite tend with the polarization of the FM electrodes. The system TMR from the spin-valve effect is observed to be up to 65,000 %, as can be significantly suppressed and enhanced by the backscattering and spin-dephasing effect of the inter-edge spin-conserving and spin-flipping tunneling, respectively, other than the quite different energy-dependent oscillation behavior. The obtained results may provide a deeper understanding of the TI edge states and be used to design a dissipationless spintronic device based on TIs.     

Quench dynamics of edge states in 2-D topological insulator ribbons

We study the dynamics of edge states of the two dimensional BHZ Hamiltonian in a ribbon geometry following a sudden quench to the quantum critical point separating the topological insulator phase from the trivial insulator phase. The effective edge state Hamiltonian is a collection of decoupled qubit-like two-level systems which get coupled to bulk states following the quench. We notice a pronounced collapse and revival of the Lochschmidt echo for low-energy edge states illustrating the oscillation of the state between the two edges. We also observe a similar collapse and revival in the spin Hall current carried by these edge states, leading to a persistence of its time-averaged value.     

Bound states of topological defects in parametrically excited capillary waves

Bound states of topological defects arising in a tetragonal lattice formed by two orthogonal standing parametrically excited capillary surface waves are investigated. Such bound states are shown to consist either of two topological charges of one sign (type 1) or of topological charges having opposite signs (type 2). It was found that bound states of type 1 move primarily along wave fronts, and type 2 bound states move at an angle of 45^○ to the wave fronts forming a tetragonal lattice. A system of four coupled Ginzburg–Landau equations is proposed to model bound states. Numerical modeling of this system gave solutions corresponding to type 1 bound states observed in experiment.     

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.     

Engineering near-surface electron states in three-dimensional topological insulators

Using the continual model of a semi-infinite three dimensional (3D) topological insulator (TI) we study the effect of the surface potential (SP) on the formation of helical topological states near the surface. The results reveal that spatial profile and spectrum of these states strongly depend on the SP type and strength. We pay special attention to the 3D TI substrate/non-magnetic insulating overlayer system to illustrate the principles of the topological near-surface states engineering.