Competition between weak localization and antilocalization in topological surface states

A magnetoconductivity formula is presented for the surface states of a magnetically doped topological insulator. It reveals a competing effect of weak localization and weak antilocalization in quantum transport when an energy gap is opened at the Dirac point by magnetic doping. It is found that, while random magnetic scattering always drives the system from the symplectic to the unitary class, the gap could induce a crossover from weak antilocalization to weak localization, tunable by the Fermi energy or the gap. This crossover presents a unique feature characterizing the surface states of a topological insulator with the gap opened at the Dirac point in the quantum diffusion regime.     

Impurity effect on weak antilocalization in the topological insulator Bi2Te3

We study the weak antilocalization (WAL) effect in topological insulator Bi(2)Te(3) thin films at low temperatures. The two-dimensional WAL effect associated with surface carriers is revealed in the tilted magnetic field dependence of magnetoconductance. Our data demonstrate that the observed WAL is robust against deposition of nonmagnetic Au impurities on the surface of the thin films, but it is quenched by the deposition of magnetic Fe impurities which destroy the π Berry phase of the topological surface states. The magnetoconductance data of a 5 nm Bi(2)Te(3) film suggests that a crossover from symplectic to unitary classes is observed with the deposition of Fe impurities.     

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.     

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.     

Direct observation of broken time-reversal symmetry on the surface of a magnetically doped topological insulator

We study interference patterns of a magnetically doped topological insulator Bi(2-x)Fe(x)Te(3+d) by using Fourier transform scanning tunneling spectroscopy and observe several new scattering channels. A comparison with angle-resolved photoemission spectroscopy allows us to unambiguously ascertain the momentum-space origin of distinct dispersing channels along high-symmetry directions and identify those originating from time-reversal symmetry breaking. Our analysis also reveals that the surface state survives far above the energy where angle-resolved photoemission spectroscopy finds the onset of continuum bulk bands.     

Quantum anomalous Hall effect in magnetically modulated topological insulator/normal insulator heterostructures

We theoretically study how magnetic modulation can be used to manipulate the transport properties of heterostructures formed by a thin film of a three-dimensional topological insulator sandwiched between slabs of a normal insulator. Employing the k ? p scheme, in the framework of a continual approach, we argue that electron states of the system are spin-polarized when ultrathin magnetic insertions are incorporated into the film. We demonstrate that (i) the spin-polarization magnitude depends strongly on the magnetic insertion position in the film and (ii) there is the optimal insertion position to realize quantum anomalous Hall effect, which is a function of the material parameters, the film thickness and the topological insulator/normal insulator interface potential. For the heterostructure with a pair of symmetrically placed magnetic insertions, we calculate a phase diagram that shows a series of transitions between distinct quantum regimes of transverse conductivity. We provide consistent interpretation of recent experimental findings in the context of our results.     

Al0.22Ga0.78N/GaN二维电子气中的弱局域和反弱局域效应

通过磁输运测量研究了Al_0.22Ga_0.78N/GaN二维电子气的电子相干散射中的弱局域和反弱局域化现象.在外加弱磁场的情况下，该系统表现出正-负磁阻的变化，说明在Al_0.22Ga_0.78N/GaN异质结中存在晶体场引起的电子自旋-轨道散射.同时讨论了二维电子气中不同的散射时间对温度的依赖关系，实验得到的非弹性散射时间与温度成反比，表明非弹性散射机理主要来源于小能量转移的电子-电子散射. 关键词： 二维电子气 弱局域 磁阻     

Weak antilocalization and interaction-induced localization of Dirac and Weyl Fermions in topological insulators and semimetals

Weak localization and antilocalization are quantum transport phenomena that arise from the quantum interference in disordered metals.At low temperatures,they can give distinct temperature and magnetic field dependences in conductivity,allowing the symmetry of the system to be explored.In the past few years,they have also been observed in newly emergent topological materials,including topological insulators and topological semimetals.In contrast from the conventional electrons,in these new materials the quasiparticles are described as Dirac or Weyl fermions.In this article,we review our recent efforts on the theories of weak antilocalization and interaction-induced localization for Dirac and Weyl fermions in topological insulators and topological semimetals.     

Quantum transport and two-parameter scaling at the surface of a weak topological insulator

Weak topological insulators have an even number of Dirac cones in their surface spectrum and are thought to be unstable to disorder, which leads to an insulating surface. Here we argue that the presence of disorder alone will not localize the surface states; rather, the presence of a time-reversal symmetric mass term is required for localization. Through numerical simulations, we show that in the absence of the mass term the surface always flow to a stable metallic phase and the conductivity obeys a one-parameter scaling relation, just as in the case of a strong topological insulator surface. With the inclusion of the mass, the transport properties of the surface of a weak topological insulator follow a two-parameter scaling form.     

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.     

Weak antilocalization in HgTe quantum wells near a topological transition

The anomalous alternating magnetoresistivity in HgTe quantum wells with thicknesses of 5.8 and 8.3 nm, i.e., near the transition from the direct band spectrum to an inverted spectrum, has been revealed and analyzed. It has been shown that the revealed anomalous alternating magnetoresistivity in wells with an inverted spectrum is well described by the theory developed by S.V. Iordanskii et al. [JETP Lett. 60, 206 (1994)] and W. Knap et al. [Phys. Rev. B 53, 3912 (1996)]. A detailed comparison of the experimental data with the theory indicates the presence of only the cubic term in the spin splitting of the electronic spectrum. The applicability conditions of the mentioned theory are not satisfied in a well with a direct gap and, for this reason, such a certain conclusion is impossible. The results indicate the existence of a strong spin-orbit interaction in symmetric HgTe quantum wells near the topological transition.     

Surface waves at the interface between a dielectric and a topological insulator

Surface waves that propagate along the interface between an isotropic linear or nonlinear (of the Kerr type) dielectric and a topological insulator have been studied theoretically. A dispersion relation for surface waves, which are represented by superpositions of TE and TM waves, has been obtained. This hybridization occurs because, upon passage through the interface, the polarization of a surface wave changes, which is caused by an induced surface current (which is transverse to the electric field vector of the wave). The surface current of this kind is characteristic of topological insulators. Expressions for the energy flux transferred by a surface wave have been given.     

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.     

Magnetic ordering in Ho‐doped Bi2Te3 topological insulator

We investigate the magnetic properties of Ho‐doped Bi₂Te₃ thin films grown by molecular beam epitaxy. Analysis of the polarized X‐ray absorption spectra at the Ho M₅ absorption edge gives an effective 4f magnetic moment which is ～45% of the Hund's rule ground state value. X‐ray magnetic circular dichroism (XMCD) shows no significant anisotropy, which suggests that the reduced spin moment is not due to the crystal field effects, but rather the presence of non‐magnetic or antiferromagnetic Ho sites. Extrapolating the temperature dependence of the XMCD measured in total electron yield and fluorescence yield mode in a field of 7 T gives a Curie–Weiss temperature of ?_CW ≈ –30 K, which suggests antiferromagnetic ordering, in contrast to the paramagnetic behavior observed with SQUID magnetometry. From the anomaly of the XMCD signal at low temperatures, a Néel temperature T_N between 10 K and 25 K is estimated. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Weyl semimetal in a topological insulator multilayer

We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically doped 3D topological insulator, separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite chirality, separated in momentum space, in its band structure. This Weyl semimetal has a finite anomalous Hall conductivity and chiral edge states and occurs as an intermediate phase between an ordinary insulator and a 3D quantum anomalous Hall insulator. We find that the Weyl semimetal has a nonzero dc conductivity at zero temperature, but Drude weight vanishing as T(2), and is thus an unusual metallic phase, characterized by a finite anomalous Hall conductivity and topologically protected edge states.     

Superconductivity in a doped mott insulator

Starting from the d-wave resonating-valence-bond mean-field theory of Kotliar and Liu, we present a new, long-wavelength/low-energy exact, treatment of gauge fluctuations. The result is a theory of gapless fermion quasiparticles coupled to superconducting phase fluctuations. We will discuss the physical implications, and the similarity and differences to a theory of superconductors with phase fluctuations.     

Guided electromagnetic waves at the interface between a dielectric and a topological insulator

Surface electromagnetic waves that propagate within the interface between a conventional dielectric or a metamaterial and a topological insulator with an undamped surface electric current are considered. Dispersion relations are given for guided waves that are surface waves polarized differently on either side of the media interface and create a coupling state due to the magnetoelectric effect.     

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.     

Crossover from weak localization to Shubnikov-de Haas oscillations in a high-mobility 2D electron gas

We study the magnetoresistance deltarho(xx)(B)/rho(0) of a high-mobility 2D electron gas in the domain of magnetic fields B, intermediate between the weak localization and the Shubnikov-de Haas oscillations, where deltarho(xx)(B)/rho(0) is governed by the interaction effects. Assuming short-range impurity scattering, we demonstrate that in the second order in the interaction parameter lambda a linear B dependence, deltarho(xx)(B)/rho(0) approximately lambda(2)omega(c)/E(F) with a temperature-independent slope, emerges in this domain of B (here omega(c) and E(F) are the cyclotron frequency and the Fermi energy, respectively). Unlike previous mechanisms, the linear magnetoresistance is unrelated to the electron executing the full Larmour circle, but rather originates from the impurity scattering via the B dependence of the phase of the impurity-induced Friedel oscillations.     

Similarities between normal- and super-currents in topological insulator magnetic tunnel junctions

This work compares the normal-current in a NM/Fi/NM junction with the super-current in a SC/Fi/SC junction, where both are topological insulator systems. NM and Fi are normal region and ferromagnetic region of thickness d with exchange energy m playing a role of the mass of the Dirac electrons and with the gate voltage V_G, respectively. SC is superconducting region induced by a s-wave superconductor. We show that, interestingly, the critical super-current passing through a SC/Fi/SC junction behaves quite similar to the normal-current passing through a NM/Fi/NM junction. The normal-current and super-current exhibit N-peak oscillation, found when currents are plotted as a function of the magnetic barrier strength χ ∼ md  /?$?$v_F. With the barrier strength Z ∼ V_Gd  /?$?$v_F, the number of peaks N is determined through the relation Z ∼ Nπ + σπ (with 0 < σ?1$\sigma ?1$ for χ < Z). The normal- and the super-currents also exhibit oscillating with the same height for all of peaks, corresponding to the Dirac fermion tunneling behavior. These anomalous oscillating currents due to the interplay between gate voltage and magnetic field in the barrier were not found in graphene-based NM/Fi/NM and SC/Fi/SC junctions. This is due to the different magnetic effect between the Dirac fermions in topological insulator and graphene.