Measurement of the topological surface state optical conductance in bulk-insulating Sn-doped Bi1.1_{1.1}Sb0.9_{0.9}Te2_2S single crystals

Topological surface states have been extensively observed via optics in thin films of topological insulators. However, in typical thick single crystals of these materials, bulk states are dominant and it is difficult for optics to verify the existence of topological surface states definitively. In this work, we studied the charge dynamics of the newly formulated bulk-insulating Sn-doped Bi$_{1.1}$Sb$_{0.9}$Te$_2$S crystal by using time-domain terahertz spectroscopy. This compound shows much better insulating behavior than any other bulk-insulating topological insulators reported previously. The transmission can be enhanced an amount which is 5$\%$ of the zero-field transmission by applying magnetic field to 7 T, an effect which we believe is due to the suppression of topological surface states. This suppression is essentially independent of the thicknesses of the samples, showing the two-dimensional nature of the transport. The suppression of surface states in field allows us to use the crystal slab itself as a reference sample to extract the surface conductance, mobility, charge density and scattering rate. Our measurements set the stage for the investigation of phenomena out of the semi-classical regime, such as the topological magneto-electric effect.Comment: 5 pages, 3 figures, submitted in Augus

Anomalous conductivity tensor in the Dirac semimetal Na_3Bi

Na3Bi is a Dirac semimetal with protected nodes that may be sensitive to the breaking of time-reversal invariance in a magnetic field B. We report experiments which reveal that both the conductivity and resistivity tensors exhibit robust anomalies in B. The resistivity $\rho_{xx}$ is B-linear up to 35 T, while the Hall angle exhibits an unusual profile approaching a step-function. The conductivities $\sigma_{xx}$ and $\sigma_{xy}$ share identical power-law dependences at large B. We propose that these significant deviations from conventional transport result from an unusual sensitivity of the transport lifetime to B. Comparison with Cd3As2 is made.Comment: 8 pages, 5 figure

Experimental tests of the chiral anomaly magnetoresistance in the Dirac-Weyl semimetals Na3_3Bi and GdPtBi

In the Dirac/Weyl semimetal, the chiral anomaly appears as an "axial" current arising from charge-pumping between the lowest (chiral) Landau levels of the Weyl nodes, when an electric field is applied parallel to a magnetic field $\bf B$. Evidence for the chiral anomaly was obtained from the longitudinal magnetoresistance (LMR) in Na$_3$Bi and GdPtBi. However, current jetting effects (focussing of the current density $\bf J$) have raised general concerns about LMR experiments. Here we implement a litmus test that allows the intrinsic LMR in Na$_3$Bi and GdPtBi to be sharply distinguished from pure current jetting effects (in pure Bi). Current jetting enhances $J$ along the mid-ridge (spine) of the sample while decreasing it at the edge. We measure the distortion by comparing the local voltage drop at the spine (expressed as the resistance $R_{spine}$) with that at the edge ($R_{edge}$). In Bi, $R_{spine}$ sharply increases with $B$ but $R_{edge}$ decreases (jetting effects are dominant). However, in Na$_3$Bi and GdPtBi, both $R_{spine}$ and $R_{edge}$ decrease (jetting effects are subdominant). A numerical simulation allows the jetting distortions to be removed entirely. We find that the intrinsic longitudinal resistivity $\rho_{xx}(B)$ in Na$_3$Bi decreases by a factor of 10.9 between $B$ = 0 and 10 T. A second litmus test is obtained from the parametric plot of the planar angular magnetoresistance. These results strenghthen considerably the evidence for the intrinsic nature of the chiral-anomaly induced LMR. We briefly discuss how the squeeze test may be extended to test ZrTe$_5$.Comment: 17 pages, 8 figures, new co-authors added, new Fig. 6a added. In press, PR

Scattering of elastic waves by periodic arrays of spherical bodies

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lam\'e coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.Comment: 19 pages, 5 figures, Phys. Rev. B (in press

Simple Procedures for Left and Right Keys of semi-standard Young tableaux

We give simple procedures to obtain the left and right keys of a semi-standard Young tableau.Comment: 17 page

Au9+ swift heavy ion irradiation of Zn[CS(NH2)2]3SO4 crystal: Crystalline perfection and optical properties

The single crystal of tris(thiourea)zinc sulphate (Zn[CS(NH2)2]3SO4) was irradiated by 150 MeV Au9+ swift heavy ions and analyzed in comparison with pure crystal for crystalline perfection and optical properties. The Fourier transform infrared and x-ray powder diffraction inferred that swift ions lead the disordering and breaking of molecular bonds in lattice without formation of new structural phases. High resolution X-ray diffraction (HRXRD) revealed the abundance of point defects, and formation of mosaics and low angle grain boundaries in the irradiated region of crystal. The swift ion irradiation found to affect the lattice vibrational modes and functional groups significantly. The defects induced by heavy ions act as the color centers and resulted in enhance of photoluminescence emission intensity. The optical transparency and band gap found to be decreased.Comment: 7 page

Unique Measure for Geometrical Shape Object Detection-based on Area Matching

Object classifier often operates by making decisions based on the values of several shape properties measured from an image of the object. The paper introduces a unique definition of measure for 2-D geometrical object shape detection. Using this definition different object shapes can be identified on the basis of their degree of fitness parameter. Basically, we have fitted a 2-D polygon/curve on the object as a best fitted polygon/curve and computed the parameter degree of fitness which is the ratio of the matching area and non-matching area due to the fitted polygon/curve and the object both. The results show the effectiveness of the proposed measure.Defence Science Journal, 2012, 62(1), pp.58-66, DOI:http://dx.doi.org/10.14429/dsj.62.94