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.     

The emergence of bound states in a superconducting gap at the topological insulator edge

We consider the edge of a superconducting topological insulator with the impurity in the presence of the Zeeman field. We analytically prove that in the trivial phase two Andreev bound states (ABSs) arise with energies moving from the superconducting gap edges to zero forming two Majorana-like bound states, as the impurity strength varies from 0 to ±2. When the Zeeman field is locally perturbed, ABSs arise both in the trivial and topological phases, but in the topological phase ABSs with energy near the gap edges cannot transform into Majorana bound states and vice versa.     

Circular photogalvanic effect caused by the transitions between edge and 2D states in a 2D topological insulator

The electron absorption and the edge photocurrent of a 2D topological insulator are studied for transitions between edge states to 2D states. The circular polarized light is found to produce the edge photocurrent, the direction of which is determined by light polarization and edge orientation. It is shown that the edge-state current is found to exceed the 2D current owing to the topological protection of the edge states.     

Emergent Z_2 topological invariant and robust helical edge states in two-dimensional topological metals

In this work, we study the effects of disorder on topological metals that support a pair of helical edge modes deeply embedded inside the gapless bulk states. Strikingly, we predict that a quantum spin Hall(QSH) phase can be obtained from such topological metals without opening a global band gap. To be specific, disorder can lead to a pair of robust helical edge states which is protected by an emergent Z_2 topological invariant, giving rise to a quantized conductance plateau in transport measurements. These results are instructive for solving puzzles in various transport experiments on QSH materials that are intrinsically metallic. This work also will inspire experimental realization of the QSH effect in disordered topological metals.     

Regular and irregular dynamics of spin-polarized wavepackets in a mesoscopic quantum dot at the edge of topological insulator

The dynamics of Dirac–Weyl spin-polarized wavepackets driven by a periodic electric field is considered for the electrons in a mesoscopic quantum dot formed at the edge of the two-dimensional HgTe/CdTe topological insulator with Dirac–Weyl massless energy spectra, where the motion of carriers is less sensitive to disorder and impurity potentials. It is observed that the interplay of strongly coupled spin and charge degrees of freedom creates the regimes of irregular dynamics in both coordinate and spin channels. The border between the regular and irregular regimes determined by the strength and frequency of the driving field is found analytically within the quasiclassical approach by means of the Ince–Strutt diagram for the Mathieu equation, and is supported by full quantum-mechanical simulations of the driven dynamics. The investigation of quasienergy spectrum by Floquet approach reveals the presence of non-Poissonian level statistics, which indicates the possibility of chaotic quantum dynamics and corresponds to the areas of parameters for irregular regimes within the quasiclassical approach. We find that the influence of weak disorder leads to partial suppression of the dynamical chaos. Our findings are of interest both for progress in the fundamental field of quantum chaotic dynamics and for further experimental and technological applications of spindependent phenomena in nanostructures based on topological insulators.     

Double topological edge states investigation in sonic metamaterials

We investigate the topologically protected sound propagation in sonic metamaterials, analogous to quantum spin hall effect (QSHE). The sonic metamaterials consist of circular rods and meta-molecules arranged in air with a honeycomb-lattice. The on-demand inversion in topological phase can be achieved by two ways of scatterer controls at locally resonant frequency and Bragg frequency. The Helmholtz resonators in the structure are contributed to the formation of subwavelength double Dirac cones which are more likely to appear due to local resonance enhancement with more number of resonators. By combining two sonic metamaterials with different topological invariants, we demonstrate the robust sound propagation and pseudospin-dependent one-way acoustic propagation at the interface. Experimental measurement of the topologically protected acoustic wave transmission matches well with the simulation result.     

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.     

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.     

A new topological insulator built from quasi one‐dimensional atomic ribbons

A novel topological insulator with orthorhombic crystal structure is demonstrated. It is characterized by quasi one‐dimensional, conducting atomic chains instead of the layered, two‐dimensional sheets known from the established Bi₂(Se,Te)₃ system. The Sb‐doped Bi₂Se₃ nanowires are grown in a TiO₂‐catalyzed process by chemical vapor deposition. The binary Bi₂Se₃ is transformed from rhombohedral to orthorhombic by substituting Sb on ～38% of the Bi sites. Pure Sb₂Se₃ is a topologically trivial band insulator with an orthorhombic crystal structure at ambient conditions, and it is known to transform into a topological insulator at high pressure. Angle‐resolved photoemission spectroscopy shows a topological surface state, while Sb doping also tunes the Fermi level to reside in the bandgap. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

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.     

Appearance and disappearance of edge states in topological insulators

We investigate the relationship between spin Chern numbers and edge state properties in general situations, where the time-reversal symmetry may be broken. As an example, we consider a thin film of three-dimensional topological insulators sandwiched between two ferromagnetic insulators with an antiparallel magnetization configuration. A topological quantum spin Hall phase with quantized spin Chern numbers C _± =  ±1, and a trivial insulator with C _± = 0 are found in different parameter regions. With tuning parameters, the quantum phase transition between the two phases can occur through closing of the spin spectrum gap rather than energy gap. It is further shown that for a junction between samples with different parameters, appearance of edge states at the interface is always related to the mismatch of spin Chern numbers, independent of symmetries.     

Surface states of charge carriers in epitaxial films of the topological insulator Bi2Te3

The galvanomagnetic properties of p-type bismuth telluride heteroepitaxial films grown by the hot wall epitaxy method on oriented muscovite mica substrates have been investigated. Quantum oscillations of the magnetoresistance associated with surface electronic states in three-dimensional topological insulators have been studied in strong magnetic fields ranging from 6 to 14 T at low temperatures. The cyclotron effective mass, charge carrier mobility, and parameters of the Fermi surface have been determined based on the results of analyzing the magnetoresistance oscillations. The dependences of the cross-sectional area of the Fermi surface S(k _F), the wave vector k _F, and the surface concentration of charge carriers n _s on the frequency of magnetoresistance oscillations in p-type Bi₂Te₃ heteroepitaxial films have been obtained. The experimentally observed shift of the Landau level index is consistent with the value of the Berry phase, which is characteristic of topological surface states of Dirac fermions in the films. The properties of topological surface states of charge carriers in p-type Bi₂Te₃ films obtained by analyzing the magnetoresistance oscillations significantly expand fields of practical application and stimulate the investigation of transport properties of chalcogenide films.     

Thin-film magnetization dynamics on the surface of a topological insulator

We theoretically study the magnetization dynamics of a thin ferromagnetic film exchange coupled with a surface of a strong three-dimensional topological insulator. We focus on the role of electronic zero modes imprinted by domain walls (DWs) or other topological textures in the magnetic film. Thermodynamically reciprocal hydrodynamic equations of motion are derived for the DW responding to electronic spin torques, on the one hand, and fictitious electromotive forces in the electronic chiral mode fomented by the DW, on the other. An experimental realization illustrating this physics is proposed based on a ferromagnetic strip, which cuts the topological insulator surface into two gapless regions. In the presence of a ferromagnetic DW, a chiral mode transverse to the magnetic strip acts as a dissipative interconnect, which is itself a dynamic object that controls (and, inversely, responds to) the magnetization dynamics.     

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.     

Spin-plasmons in topological insulator

Collective plasmon excitations in a helical electron liquid on the surface of strong three-dimensional topological insulator are considered. The properties and internal structure of these excitations are studied. Due to spin-momentum locking in helical liquid on a surface of topological insulator, the collective excitations should manifest themselves as coupled charge- and spin-density waves.     

Surface scattering via bulk continuum states in the 3D topological insulator Bi2Se3

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.     

Structure, stability, edge states, and aromaticity of graphene ribbons

We determine the stability, the geometry, the electronic, and magnetic structure of hydrogen-terminated graphene-nanoribbon edges as a function of the hydrogen content of the environment by means of density functional theory. Antiferromagnetic zigzag ribbons are stable only at extremely low ultravacuum pressures. Under more standard conditions, the most stable structures are the mono- and dihydrogenated armchair edges and a zigzag edge reconstruction with one di- and two monohydrogenated sites. At high hydrogen concentration "bulk" graphene is not stable and spontaneously breaks to form ribbons, in analogy to the spontaneous breaking of graphene into small-width nanoribbons observed experimentally in solution. The stability and the existence of exotic edge electronic states and/or magnetism is rationalized in terms of simple concepts from organic chemistry (Clar's rule).     

Electron states scattering off line edges on the surface of topological insulator

We study the local density of states （LDOS） for electrons scattering off the line edge of an atomic step defect on the surface of a three-dimensional （3D） topological insulator （TI） and the line edge of a finite 3D TI, where the front surface and side surface meet with different Fermi velocities, respectively. By using a S-function potential to model the edges, we find that the bound states existed along the step line edge significantly contribute to the LDOS near the edge, but do not modify the exponential behavior away from it. In addition, the power-law decaying behavior for LDOS oscillation away from the step is understood from the spin rotation for surface states scattering off the step defect with magnitude depending on the strength of the potential. Furthermore, the electron refraction and total reflection analogous to optics occurred at the line edge where two surfaces meet with different Fermi velocities, which leads to the LDOS decaying behavior in the greater Fermi velocity side similar to that for a step line edge. However, in the smaller velocity side the LDOS shows a different decaying behavior as x-1/2, and the wavevector of LDOS oscillation is no longer equal to the diameter of the constant energy contour of surface band, but is sensitively dependent on the ratio of the two Fermi velocities. These effects may be verified by STM measurement with high precision.