No abstract

Disorder plays an important role in two dimensions, and is responsible for striking phenomena such as metal-insulator transition and the integral and fractional quantum Hall effects. In this Letter, we investigate the role of disorder in the context of the recently discovered topological insulator, which possesses a pair of helical edge states with opposing spins moving in opposite directions and exhibits the phenomenon of quantum spin Hall effect. We predict an unexpected and nontrivial quantum phase termed "topological Anderson insulator," which is obtained by introducing impurities in a two-dimensional metal; here disorder not only causes metal-insulator transition, as anticipated, but is fundamentally responsible for creating extended edge states. We determine the phase diagram of the topological Anderson insulator and outline its experimental consequences.

The hallmark of the spin-Hall insulator is the presence of gapless edge states of different spins moving in opposite directions. Through analytical solutions in a model calculation for a strip of finite width, we find that edge states on the two sides can couple together to produce a gap in the spectrum, destroying the quantum spin-Hall effect. The application of a magnetic field can however modify and even remove the gap by shifting the momenta of the edge states relative to each other.

Weyl semimetals provide the realization of Weyl fermions in solid-state physics. Among all the physical phenomena that are enabled by Weyl semimetals, the chiral anomaly is the most unusual one. Here, we report signatures of the chiral anomaly in the magneto-transport measurements on the first Weyl semimetal TaAs. We show negative magnetoresistance under parallel electric and magnetic fields, that is, unlike most metals whose resistivity increases under an external magnetic field, we observe that our high mobility TaAs samples become more conductive as a magnetic field is applied along the direction of the current for certain ranges of the field strength. We present systematically detailed data and careful analyses, which allow us to exclude other possible origins of the observed negative magnetoresistance. Our transport data, corroborated by photoemission measurements, first-principles calculations and theoretical analyses, collectively demonstrate signatures of the Weyl fermion chiral anomaly in the magneto-transport of TaAs.

Two-dimensional effective continuous models are derived for the surface states and thin films of the three-dimensional topological insulator (3DTI). Starting from an effective model for 3DTI based on the first principles calculation [Zhang et al, Nat. Phys. 5, 438 (2009)], we present solutions for both the surface states in a semi-infinite boundary condition and in thin film with finite thickness. The coupling between opposite topological surfaces and structure inversion asymmetry (SIA) give rise to gapped Dirac hyperbolas with Rashba-like splittings in energy spectrum. Besides, the SIA leads to asymmetric distributions of wavefunctions for the surface states along the film growth direction, making some branches in the energy spectra much harder than others to be probed by light. These features agree well with the recent angle-resolved photoemission spectra of Bi2Se3 films grown on SiC substrate [Zhang et al, arXiv: 0911.3706]. More importantly, using the parameters fitted by experimental data, the result indicates that the thin film Bi2Se3 lies in quantum spin Hall region based on the calculation of the Chern number and the Z2 invariant. In addition, strong SIA always intends to destroy the quantum spin Hall state.PACS numbers:

We study transport and optical properties of the surface states which lie in the bulk energy gap of a thin-film topological insulator. When the film thickness is comparable with the surface state decay length into the bulk, the tunneling between the top and bottom surfaces opens an energy gap and form two degenerate massive Dirac hyperbolas. Spin dependent physics emerges in the surface bands which are vastly different from the bulk behavior. These include the surface spin Hall effects, spin dependent orbital magnetic moment, and spin dependent optical transition selection rule which allows optical spin injection. We show a topological quantum phase transition where the Chern number of the surface bands changes when varying the thickness of the thin film.

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.PACS numbers: 73.25.+i, 03.65.Vf, Topological surface states, composed of an odd number of massless Dirac cones, are peculiar to threedimensional (3D) topological insulators [1][2][3]. Electrons in these states have a helical spin structure in momentum space, and acquire a π Berry's phase after completing a closed trajectory adiabatically around the Fermi surface. The π Berry phase could lead to the absence of backscattering[4], weak antilocalization [5], and the absence of Anderson localization [6,7]. In the quantum diffusion regime (mean free path ≪ system size ∼ phase coherent length), an electron maintains its phase coherence after being scattered by static centers for many times. As a result, the destructive interference due to the π Berry phase can give a quantum enhancement to the classical electronic conductivity, leading to weak antilocalization (WAL) [8,9]. Applying a magnetic field tends to break the destructive interference, giving rise to negative magnetoconductivity (MC), a key signature of WAL. WAL is expected in systems with symplectic symmetry. Much effort has been devoted to observing WAL in graphene [5,[10][11][12][13]. However, graphene has two valleys of gapless Dirac cones with opposite chiralities, and the intervalley scattering will inevitably suppress WAL [5,[10][11][12][13]. In contrast, the surface states of recently discovered topological insulators Bi 2 Te 3 and Bi 2 Se 3 have only one helical Dirac cone [14][15][16], and WAL is intrinsic to them. Many observations of WAL in Bi 2 Te 3 and Bi 2 Se 3 have been reported recently [17][18][19][20][21][22]. In particular, there is great interest in the effect of magnetic doping, which is considered to be an efficient way to open an energy gap in the Dirac cone by breaking time reversal symmetry (TRS) [23][24][25]. This gap is expected to give rise to many interesting phenomena, such as Majorana fermion [26], topological magnetoelectric effect [27] and quantized anomalous Hall effect [28]. These developments call for a thorough theoretical investigation on WAL in topological insulators, in particular, in the presence of magnetic doping.

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.