Electromagnetic scattering by a time reversal symmetry broken topological insulator sphere

An exact solution of electromagnetic wave scattering by a time reversal symmetry broken topological insulator sphere is researched. According to the constitute relations of topological insulator, we modified magnetic vector potential and electric vector potential of standard Mie theory and derived scattered electromagnetic fields and scattered coefficients. Numerical results show that, when the time reversal symmetry is broken, the extinction efficiencies and the scattering efficiencies are influenced by topological magneto-electric polarizability.     

From magnetically doped topological insulator to the quantum anomalous Hall effect

Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landau levels so that neither external magnetic field nor high sample mobility is required for its study and application, Such a QHE free of Landau levels, can appear in topological insulators （TIs） with ferromagnetism as the quantized version of the anomalous Hall effect, i.e., quantum anomalous Hall （QAH） effect. Here we review our recent work on experimental realization of the QAH effect in magnetically doped TIs. With molecular beam epitaxy, we prepare thin films of Cr-doped （Bi,Sb）2Te3 TIs with well- controlled chemical potential and long-range ferromagnetic order that can survive the insulating phase. In such thin films, we eventually observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect provides a foundation for many other novel quantum phenomena predicted in TIs, and opens a route to practical applications of quantum Hall physics in low-power-consumption electronics.     

Crossover between weak antilocalization and weak localization in a magnetically doped topological insulator

We report transport studies on magnetically doped Bi(2)Se(3) topological insulator ultrathin films grown by molecular beam epitaxy. The magnetotransport behavior exhibits a systematic crossover between weak antilocalization and weak localization with the change of magnetic impurity concentration, temperature, and magnetic field. We show that the localization property is closely related to the magnetization of the sample, and the complex crossover is due to the transformation of Bi(2)Se(3) from a topological insulator to a topologically trivial dilute magnetic semiconductor driven by magnetic impurities. This work demonstrates an effective way to manipulate the quantum transport properties of the topological insulators by breaking time-reversal symmetry.     

Edge currents in superconductors with a broken time-reversal symmetry

We analyze edge currents and edge bands at the surface of a time-reversal symmetry breaking dx2-y2 + id(xy) superconductor. We show that the currents have large Friedel oscillations with two interfering frequencies: square root of 2kF from subgap states, and 2kF from the continuum. The results are based independently on a self-consistent slave-boson mean-field theory for the t-J model on a triangular lattice, and on a T-matrix scattering theory calculation. The shape of the edge-state band, as well as the particular frequency square root of 2kF of the Friedel oscillations, are attributes unique for the dx2-y2 + id(xy) case, and may be used as a fingerprint for its identification. Extensions to different time-reversal symmetry breaking superconductors can be achieved within the same approach.     

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.     

Ferromagnetic-insulators-modulated transport properties on the surface of a topological insulator

Transport properties on the surface of a topological insulator （TI） under the modulation of a two-dimensional （2D） ferromagnet/ferromagnet junction are investigated by the method of wave function matching. The single ferromagnetic barrier modulated transmission probability is expected to be a periodic function of the polarization angle and the planar rotation angle, that decreases with the strength of the magnetic proximity exchange increasing. However, the transmission probability for the double ferromagnetic insulators modulated n-n junction and n-p junction is not a periodic function of polarization angle nor planar rotation angle, owing to the combined effects of the double ferromagnetic insulators and the barrier potential. Since the energy gap between the conduction band and the valence band is narrowed and widened respectively in ranges of 0 ≤ 0 〈π/2 and r/2 〈 0 ≤ π, the transmission probability of the n-n junction first increases rapidly and then decreases slowly with the increase of the magnetic proximity exchange strength. While the transmission probability for the n-p junction demonstrates an opposite trend on the strength of the magnetic proximity exchange because the band gaps contrarily vary. The obtained results may lead to the possible realization of a magnetic/electric switch based on TIs and be useful in further understanding the surface states of TIs.     

Carrier mediated ferromagnetism on the surface of a topological insulator

We study the effect of magnetic doping at the surface of a three dimensional topological insulator (TI) on emergence of ferromagnetic ordering at the TI-surface assuming the exchange coupling between the Dirac fermions and the dilute magnetic ions. We show that this coupling results in an uniaxial magnetic anisotropy with out-of-plane magnetization direction. It is found that the system under consideration is unstable with respect to a spontaneous uniform magnetization along the easy axis, which is accompanied by opening a gap in a spectrum of the Dirac surface states. In the framework of a mean-field approach, we study the possibility of ferromagnetic order on the magnetically doped surface of TI at different temperatures and positions of the chemical potential.     

Fluctuations of expectation values in chaotic systems and broken time-reversal symmetry

Fluctuations of expectation values of observables are calculated in complex quantum systems, such as disordered metallic grains or quantum systems with classical chaotic motion. We derive an exact expression for these fluctuations valid for systems with and without time-reversal symmetry, as well as in the transition region between these two cases. We compare our results with those of a semiclassical theory and with simulations of random matrices.     

Observation of broken time-reversal symmetry with Andreev bound state tunneling spectroscopy

Quasiparticle (QP) planar tunneling spectroscopy is used to investigate the density of states (DoS) of YBa₂Cu₃O₇ (YBCO). Temperature, crystallographic orientation, doping, damage and magnetic field dependencies confirm that the observed zero-bias conductance peak (ZBCP) is an Andreev bound state (ABS), an intrinsic property of a d-wave superconducting order parameter (OP) at an interface. In zero applied field, the splitting of the ZBCP below 8 K confirms a near-surface phase transition into a superconducting state with spontaneously broken time-reversal symmetry (BTRS). Tunneling into the ABS provides a phase-sensitive spectroscopy that can be used to measure a variety of DoS properties in an unconventional superconductor.     

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).     

Magneto transport on the surface of a topological insulator spin valve

The effects of the magnetization on the transport properties of a ferromagnet/barrier/ferromagnet spin valve fabricated with a topological insulator are studied. We consider two types of junctions, (i) an F₁/normal barrier (NB)/F₂ junction and (ii) an F₁/magnetic barrier (FB)/F₂ junction. The junctions in both cases lie in the xy-plane with the magnetizations in both ferromagnetic regions, F₁ and F₂ aligned in the z-direction. The charge carriers in the topological insulator have a Dirac like energy spectrum of a massive relativistic particle with the magnetization M playing the role of the mass. The gap opening is a special magneto feature of topological insulators. In an anti parallel alignment of the two magnetizations, the mass of the carriers is negative in the region where M is in the negative direction. The negative mass leads the behaviors of the magneto transport properties and the tunneling magneto resistance of these junctions to be quite different from those of graphene-based spin values.     

Ferromagnetic barrier-induced negative differential conductance on the surface of a topological insulator

The effect of the negative differential conductance of a ferromagnetic barrier on the surface of a topological insulat（ is theoretically investigated. Due to the changes of the shape and position of the Fermi surfaces in the ferromagnetic barrie the transport processes can be divided into three kinds： the total, partial, and blockade transmission mechanisms. The bias voltage can give rise to the transition of the transport processes from partial to blockade transmission mechanisms, which results in a considerable effect of negative differential conductance. With appropriate structural parameters, the currenl voltage characteristics show that the minimum value of the current can reach to zero in a wide range of the bias voltag and then a large peak-to-valley current ratio can be obtained.     

Nonlinear optical probe of tunable surface electrons on a topological insulator

We use ultrafast laser pulses to experimentally demonstrate that the second-order optical response of bulk single crystals of the topological insulator Bi(2)Se(3) is sensitive to its surface electrons. By performing surface doping dependence measurements as a function of photon polarization and sample orientation we show that second harmonic generation can simultaneously probe both the surface crystalline structure and the surface charge of Bi(2)Se(3). Furthermore, we find that second harmonic generation using circularly polarized photons reveals the time-reversal symmetry properties of the system and is surprisingly robust against surface charging, which makes it a promising tool for spectroscopic studies of topological surfaces and buried interfaces.     

Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry

We show how, in principle, to construct analogs of quantum Hall edge states in "photonic crystals" made with nonreciprocal (Faraday-effect) media. These form "one-way waveguides" that allow electromagnetic energy to flow in one direction only.     

Momentum and spin filtering of electrons on the surface of a topological insulator

We study theoretically electron tunneling through planar magnetic barrier arrays on the surface of a three-dimensional topological insulator. Interestingly, the transmission displays a collimation behavior at some specific incident angles. This feature provides us a new way to construct a momentum and spin filter in topological insulators.     

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.     

Giant mesoscopic spin Hall effect on the surface of topological insulator

We study mesoscopic spin Hall effect on the surface of a topological insulator with a step-function potential by using the McMillan method commonly used in the study of superconductor junctions. In the ballistic transport regime, we predict a giant spin polarization induced by a transverse electric current with parameter suitable to the topological insulator thin film Bi(2)Se(3). The spin polarization oscillates across the potential boundary with no confinement due to the Klein paradox, and should be observable in a spin resolved scanning tunneling microscope.     

Spatial distribution of spin polarization in a channel on the surface of a topological insulator

We study the spatial distribution of electron spin polarization for a gate-controlled T-shaped channel on the surface of a three-dimensional topological insulator (3D TI). We demonstrate that an energy gap depending on channel geometry parameters is definitely opened due to the spatial confinement. Spin surface locking in momentum space for a uniform wide channel with Hamiltonian linearity in the wavevector is still kept, but it is broken with Hamiltonian nonlinearity in the wavevector, like that for two-dimensional surface states widely studied in the literature. However, the spin surface locking for a T-shaped channel is broken even with Hamiltonian linearity in the wavevector. Interestingly, the magnitude and direction of the in-plane spin polarization are spatially dependent in all regions due to the breaking of translational symmetry of the T-shaped channel system. These interesting findings for an electrically controlled nanostructure based on the 3D TI surface may be testable with the present experimental technique, and may provide further understanding the nature of 3D TI surface states.