While evidence of a topologically nontrivial surface state has been identified in surface-sensitive measurements of Bi 2 Se 3 , a significant experimental concern is that no signatures have been observed in bulk transport. In a search for such states, nominally undoped single crystals of Bi 2 Se 3 with carrier densities approaching 10 16 cm −3 and very high mobilities exceeding 2 m 2 V −1 s −1 have been studied. A comprehensive analysis of Shubnikov-de Haas oscillations, Hall effect, and optical reflectivity indicates that the measured electrical transport can be attributed solely to bulk states, even at 50 mK at low Landau-level filling factor, and in the quantum limit. The absence of a significant surface contribution to bulk conduction demonstrates that even in very clean samples, the surface mobility is lower than that of the bulk, despite its topological protection.

Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant topological insulator in three dimensions exhibits a topological magnetoelectric effect quantized in units of the fine structure constant α = e 2 / c. In this Letter, we propose an optical experiment to directly measure this topological quantization phenomenon, independent of material details. Our proposal also provides a way to measure the half-quantized Hall conductances on the two surfaces of the topological insulator independently of each other.PACS numbers: 78.20.Ls, 78.68.+m Topological phenomena in condensed matter physics are typically characterized by the exact quantization of the electromagnetic response in units of fundamental constants. In a superconductor (SC), the magnetic flux is quantized in units of the flux quantum φ 0 ≡ h 2e ; in the quantum Hall effect (QHE), the Hall conductance is quantized in units of the conductance quantum G 0 ≡ e 2 h . Not only are these fundamental physical phenomena, they also provide the most precise metrological definition of basic physical constants. For instance, the Josephson effect in SC allows the most precise measurement of the flux quantum which, combined with the measurement of the quantized Hall conductance, provides the most accurate determination of Planck's constant h to date [1]. The remarkable observation of such precise quantization phenomena in these imprecise, macroscopic condensed matter systems can be understood from the fact that they are described in the low-energy limit by topological field theories (TFT) with quantized coefficients. For instance, the QHE is described by the topological Chern-Simons theory [2] in 2 + 1 dimensions, with coefficient given by the quantized Hall conductance. SC can be described by the topological BF theory [3] with coefficient corresponding to the flux quantum.More recently, a new topological state in condensed matter physics, the time-reversal (T ) invariant topological insulator (TI), has been investigated extensively [4][5][6]. The concept of TI can be defined most generally in terms of the TFT [7] with effective Lagrangianwhere E and B are the electromagnetic fields, ε and µ are the dielectric constant and magnetic permeability, respectively, and θ is an angular variable known in particle physics as the axion angle [8]. Under periodic boundary conditions, the partition function and all physical quantities are invariant under shifts of θ by any multiple of 2π. Since E · B is odd under T , the only values of θ allowed by T are 0 or π (modulo 2π). The second term of Eq. (1) thus defines a TFT with coefficient quantized in units of the fine structure constant α ≡ e 2 c . The TFT is generally valid for interacting systems, and describes a quantized magnetoelectric response denoted topological magnetoelectric effect (TME) [7]. The quantization of the axion angle θ depends only on the ...

The spin-lattice coupling plays an important role in strongly frustrated magnets. In ZnCr2O4, an excellent realization of the Heisenberg antiferromagnet on the pyrochlore network, a lattice distortion relieves the geometrical frustration through a spin-Peierls-like phase transition at T(c)=12.5 K. Conversely, spin correlations strongly influence the elastic properties of a frustrated magnet. By using infrared spectroscopy and published data on magnetic specific heat, we demonstrate that the frequency of an optical phonon triplet in ZnCr2O4 tracks the nearest-neighbor spin correlations above T(c). The splitting of the phonon triplet below T(c) provides a way to measure the spin-Peierls order parameter.

A Weyl semimetallic state with pairs of nondegenerate Dirac cones in three dimensions was recently predicted to occur in the antiferromagnetic state of the pyrochlore iridates. Here, we show that the THz optical conductivity and temperature dependence of the free carrier response in pyrochlore Eu2Ir2O7 match the predictions for a Weyl semimetal and suggest novel Dirac liquid behavior. The interband optical conductivity vanishes continuously at low frequencies signifying a semimetal. The metal-semimetal transition at TN = 110 K is manifested in the Drude spectral weight, which is independent of temperature in the metallic phase, and which decreases smoothly in the ordered phase. The temperature dependence of the free carrier weight below TN is in good agreement with theoretical predictions for a Dirac material. The data yield a Fermi velocity vF ≈ 4 • 10 7 cm/s, a logarithmic renormalization scale ΛL ≈ 600 K, and require a Fermi temperature of TF ≈ 100 K associated with residual unintentional doping to account for the low temperature optical response and dc resistivity.

Pulsed laser deposited films of Co doped anatase TiO 2 are examined for Co substitutionality, ferromagnetism, transport, magnetotransport and optical properties. Our