Bulk-boundary correspondence in three dimensional topological insulators

We discuss the relation between bulk topological invariants and the spectrum of surface states in three dimensional non-interacting topological insulators. By studying particular models, and considering general boundary conditions for the electron wavefunction on the crystal surface, we demonstrate that using experimental techniques that probe surface states, only strong topological and trivial insulating phases can be distinguished; the latter state being equivalent to a weak topological insulator. In a strong topological insulator, only the {\it parity} of the number of surface states, but not the number itself, is robust against time-reversal invariant boundary perturbations. Our results suggest a \z definition of the bulk-boundary correspondence, compatible with the \z classification of topological insulators.Comment: TeXLive (Unix), revtex4-1, 7 pages, 3 figure

First-principles envelope-function theory for lattice-matched semiconductor heterostructures

In this paper a multi-band envelope-function Hamiltonian for lattice-matched semiconductor heterostructures is derived from first-principles norm-conserving pseudopotentials. The theory is applicable to isovalent or heterovalent heterostructures with macroscopically neutral interfaces and no spontaneous bulk polarization. The key assumption -- proved in earlier numerical studies -- is that the heterostructure can be treated as a weak perturbation with respect to some periodic reference crystal, with the nonlinear response small in comparison to the linear response. Quadratic response theory is then used in conjunction with k.p perturbation theory to develop a multi-band effective-mass Hamiltonian (for slowly varying envelope functions) in which all interface band-mixing effects are determined by the linear response. To within terms of the same order as the position dependence of the effective mass, the quadratic response contributes only a bulk band offset term and an interface dipole term, both of which are diagonal in the effective-mass Hamiltonian. Long-range multipole Coulomb fields arise in quantum wires or dots, but have no qualitative effect in two-dimensional systems beyond a dipole contribution to the band offsets.Comment: 25 pages, no figures, RevTeX4; v3: final published versio

Reflection of light and heavy holes from a linear potential barrier

In this paper we study reflection of holes in direct-band semiconductors from the linear potential barrier. It is shown that light-heavy hole transformation matrix is universal. It depends only on a dimensionless product of the light hole longitudinal momentum and the characteristic length determined by the slope of the potential and doesn't depend on the ratio of light and heavy hole masses, provided this ratio is small. It is shown that the transformation coefficient goes to zero both in the limit of small and large longitudinal momenta, however the phase of a reflected hole is different in these limits. An approximate analytical expression for the light-heavy hole transformation coefficient is found.Comment: 6 pages, 2 figure

Tunable unconventional Kondo effect on topological insulator surfaces

We study Kondo physics of a spin-12 impurity in electronic matter with strong spin-orbit interaction, which can be realized by depositing magnetic adatoms on the surface of a three-dimensional topological insulator. We show that magnetic properties of topological surface states and the very existence of Kondo screening strongly depend on details of the bulk material, and specifics of surface preparation encoded in time-reversal preserving boundary conditions for electronic wavefunctions. When this tunable Kondo effect occurs, the impurity spin is screened by purely orbital motion of surface electrons. This mechanism gives rise to a transverse magnetic response of the surface metal, and to spin textures that can be used to experimentally probe signatures of a Kondo resonance. Our predictions are particularly relevant for STM measurements in PbTe-class crystalline topological insulators, but we also discuss implications for other classes of topological materials

Tunnelling Studies of Two-Dimensional States in Semiconductors with Inverted Band Structure: Spin-orbit Splitting, Resonant Broadening

The results of tunnelling studies of the energy spectrum of two-dimensional (2D) states in a surface quantum well in a semiconductor with inverted band structure are presented. The energy dependence of quasimomentum of the 2D states over a wide energy range is obtained from the analysis of tunnelling conductivity oscillations in a quantizing magnetic field. The spin-orbit splitting of the energy spectrum of 2D states, due to inversion asymmetry of the surface quantum well, and the broadening of 2D states at the energies, when they are in resonance with the heavy hole valence band, are investigated in structures with different strength of the surface quantum well. A quantitative analysis is carried out within the framework of the Kane model of the energy spectrum. The theoretical results are in good agreement with the tunnelling spectroscopy data.Comment: 29 pages, RevTeX, submitted in Phys.Rev.B. Figures available on request from [email protected]

Interface electronic states and boundary conditions for envelope functions

The envelope-function method with generalized boundary conditions is applied to the description of localized and resonant interface states. A complete set of phenomenological conditions which restrict the form of connection rules for envelope functions is derived using the Hermiticity and symmetry requirements. Empirical coefficients in the connection rules play role of material parameters which characterize an internal structure of every particular heterointerface. As an illustration we present the derivation of the most general connection rules for the one-band effective mass and 4-band Kane models. The conditions for the existence of Tamm-like localized interface states are established. It is shown that a nontrivial form of the connection rules can also result in the formation of resonant states. The most transparent manifestation of such states is the resonant tunneling through a single-barrier heterostructure.Comment: RevTeX4, 11 pages, 5 eps figures, submitted to Phys.Rev.

Topics on modular Galois representations modulo prime powers

This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes algorithms and a database of modular forms orbits and higher congruences

Phosphatidylserine Targets Single-Walled Carbon Nanotubes to Professional Phagocytes In Vitro and In Vivo

Broad applications of single-walled carbon nanotubes (SWCNT) dictate the necessity to better understand their health effects. Poor recognition of non-functionalized SWCNT by phagocytes is prohibitive towards controlling their biological action. We report that SWCNT coating with a phospholipid “eat-me” signal, phosphatidylserine (PS), makes them recognizable in vitro by different phagocytic cells - murine RAW264.7 macrophages, primary monocyte-derived human macrophages, dendritic cells, and rat brain microglia. Macrophage uptake of PS-coated nanotubes was suppressed by the PS-binding protein, Annexin V, and endocytosis inhibitors, and changed the pattern of pro- and anti-inflammatory cytokine secretion. Loading of PS-coated SWCNT with pro-apoptotic cargo (cytochrome c) allowed for the targeted killing of RAW264.7 macrophages. In vivo aspiration of PS-coated SWCNT stimulated their uptake by lung alveolar macrophages in mice. Thus, PS-coating can be utilized for targeted delivery of SWCNT with specified cargoes into professional phagocytes, hence for therapeutic regulation of specific populations of immune-competent cells

Prospects for Creation of Cardioprotective and Antiarrhythmic Drugs Based on Opioid Receptor Agonists

It has now been demonstrated that the μ, δ(1), δ(2), and κ(1) opioid receptor (OR) agonists represent the most promising group of opioids for the creation of drugs enhancing cardiac tolerance to the detrimental effects of ischemia/reperfusion (I/R). Opioids are able to prevent necrosis and apoptosis of cardiomyocytes during I/R and improve cardiac contractility in the reperfusion period. The OR agonists exert an infarct‐reducing effect with prophylactic administration and prevent reperfusion‐induced cardiomyocyte death when ischemic injury of heart has already occurred; that is, opioids can mimic preconditioning and postconditioning phenomena. Furthermore, opioids are also effective in preventing ischemia‐induced arrhythmias