Zero-energy states bound to a magnetic π-flux vortex in a two-dimensional topological insulator

We show that the existence of a pair of zero-energy modes bound to a vortex carrying a π-flux is a generic feature of the topologically non-trivial phase of the M–B model, which was introduced to describe the topological band insulator in HgTe quantum wells. We explicitly find the form of the zero-energy states of the corresponding Dirac equation, which contains a novel momentum-dependent mass term and describes a generic topological transition in a band insulator. The obtained modes are exponentially localized in the vortex-core, with the dependence of characteristic length on the parameters of the model matching the dependence extracted from a lattice version of the model. We consider in full generality the short-distance regularization of the vector potential of the vortex, and show that a particular choice yields the modes localized and simultaneously regular at the origin. Finally, we also discuss a realization of two-dimensional spin-charge separation through the vortex zero-modes.     

Strong homology of inverse systems. III

In previous parts I and II of this paper [4] strong homology groups of inverse systems were introduced and studied. In this part III of the paper we define strong homology groups of inverse systems of pairs and show that they have suitable exactness and excision properties. As a consequence of these results the Steenrod-Sitnikov homology [1] for pairs (X,A), where X is a paracompact space and A is a closed subset of X, is exact and satisfies the excision axiom.     

An analysis of the binary and ternary fission of uranium induced by 12.2 GeV protons

In this work the binary and ternary fission of uranium induced by 12.2 GeV protons has been investigated with a polycarbonate detector registering the tracks of particles with mass numbersA>16. The basic characteristics of binary and ternary fission are discussed and the corresponding cross-sections are given. The values of the cross-sections for binary and ternary fission are calculated to be σ _b =(915 ± 120) mb and σ _t -(12.8 ± 2.5) mb, respectively.     

Thirring sine-Gordon relationship by canonical methods

Using the canonical method developed for anomalous theories, we present the independent rederivation of the quantum relationship between the massive Thirring and the sine-Gordon models. The same method offers the possibility to obtain the Mandelstam soliton operators as a solution of the Poisson brackets equation for the fermionic fields. We checked the anticommutation and basic Poisson brackets relations for these composite operators. The transition from the Hamiltonian to the corresponding Lagrangian variables produces the known Mandelstams result.Received: 7 July 2003, Published online: 26 November 2003     

Total reflection X-ray fluorescence analysis of fly ash from Bulgarian coal-fired power plants

The contents of Cl, Ca, K, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, As, Se, Rb, Sr, Ba and Pb in raw coal fly ash from five Bulgarian power plants were determined by total reflection X-ray fluorescence (TXRF), using gallium as the internal standard. The samples were analysed as in slurry form in Triton? X-114. The experimental parameters, such as grain size, concentrations of fly ash slurry and excitation time were optimised. For validation of the method, the certified reference material BCR-176R fly ash was used. The precision of the results obtained is characterised by a relative standard deviation of approximately 10%. The resulting data confirm the suitability of TXRF for the simultaneous determination of major, minor and trace elements in coal fly ash samples. Further advantages provided by TXRF are easy sample preparation (no sample dissolution) and the small sample amount required for analysis.     

Femtosecond single-mode diode-pumped Cr:LiSAF laser mode-locked with single-walled carbon nanotubes

A low threshold Cr:LiSAF laser pumped with an inexpensive single-mode laser diode emitting 120 mW was passively mode-locked with a novel ultrafast saturable absorber mirror based on single-walled carbon nanotubes (SWCNT-SAM). Pulses as short as 122 fs were achieved, tunable across 14 nm. A second pump diode coupled in polarization allowed to shorten the pulse duration to 106 fs, with up to 24-mW output power.     

Universal probes of two-dimensional topological insulators: dislocation and π flux

We show that the π flux and the dislocation represent topological observables that probe two-dimensional topological order through binding of the zero-energy modes. We analytically demonstrate that π flux hosts a Kramers pair of zero modes in the topological Γ (Berry phase Skyrmion at the zero momentum) and M (Berry phase Skyrmion at a finite momentum) phases of the M-B model introduced for the HgTe quantum spin Hall insulator. Furthermore, we analytically show that the dislocation acts as a π flux, but only so in the M phase. Our numerical analysis confirms this through a Kramers pair of zero modes bound to a dislocation appearing in the M phase only, and further demonstrates the robustness of the modes to disorder and the Rashba coupling. Finally, we conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.