Engineering Quantum Spin Hall Effect in Graphene Nanoribbons via Edge Functionalization

Kane and Mele predicted that in presence of spin-orbit interaction graphene realizes the quantum spin Hall state. However, exceptionally weak intrinsic spin-orbit splitting in graphene ($\approx 10^{-5}$ eV) inhibits experimental observation of this topological insulating phase. To circumvent this problem, we propose a novel approach towards controlling spin-orbit interactions in graphene by means of covalent functionalization of graphene edges with functional groups containing heavy elements. Proof-of-concept first-principles calculations show that very strong spin-orbit coupling can be induced in realistic models of narrow graphene nanoribbons with tellurium-terminated edges. We demonstrate that electronic bands with strong Rashba splitting as well as the quantum spin Hall state spanning broad energy ranges can be realized in such systems. Our work thus opens up new horizons towards engineering topological electronic phases in nanostructures based on graphene and other materials by means of locally introduced spin-orbit interactions.Comment: 5 pages, 3 figure

Existence of a multiplicative basis for a finitely spaced module over an aggregate

By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable representations admits a multiplicative basis. In Sections 4.10-4.12 of [P. Gabriel, A. V. Roiter, Representations of finite-dimensional algebras. Encyclopaedia of Math. Sci., vol. 73, Algebra 8, Springer-Verlag, 1992] an analogous hypothesis was formulated for finitely spaced modules over an aggregate. We prove this conjecture.Comment: 17 page

Structural insights into the membrane-extracted dimeric form of the ATPase TraB from the Escherichia coli pKM101 conjugation system

Background: Type IV secretion (T4S) systems are involved in secretion of virulence factors such as toxins or transforming molecules, or bacterial conjugation. T4S systems are composed of 12 proteins named VirB1-B11 and VirD4. Among them, three ATPases are involved in the assembly of the T4S system and/or provide energy for substrate transfer, VirB4, VirB11 and VirD4. The X-ray crystal structures of VirB11 and VirD4 have already been solved but VirB4 has proven to be reluctant to any structural investigation so far. Results: Here, we have used small-angle X-ray scattering to obtain the first structural models for the membrane-extracted, dimeric form of the TraB protein, the VirB4 homolog encoded by the E. coli pKM101 plasmid, and for the monomeric soluble form of the LvhB4 protein, the VirB4 homolog of the T4S system encoded by the Legionella pneumophila lvh operon. We have obtained the low resolution structures of the full-length TraB and of its N- and C-terminal halves. From these SAXS models, we derive the internal organisation of TraB. We also show that the two TraB N- and C-terminal domains are independently involved in the dimerisation of the full-length protein. Conclusions: These models provide the first structural insights into the architecture of VirB4 proteins. In particular, our results highlight the modular arrangement and functional relevance of the dimeric-membrane-bound form of TraB

Electronic properties of one-dimensional nanostructures of the Bi2_2Se3_3 topological insulator

We theoretically study the electronic structure and spin properties of one-dimensional nanostructures of the prototypical bulk topological insulator Bi$_2$Se$_3$. Realistic models of experimentally observed Bi$_2$Se$_3$ nanowires and nanoribbons are considered using the tight-binding method. At low energies, the band structures are composed of a series of evenly spaced degenerate sub-bands resulting from circumferential confinement of the topological surface states. The direct band gaps due to the non-trivial $\pi$ Berry phase show a clear dependence on the circumference. The spin-momentum locking of the topological surface states results in a pronounced 2$\pi$ spin rotation around the circumference with the degree of spin polarization dependent on the the momentum along the nanostructure. Overall, the band structures and spin textures are more complicated for nanoribbons, which expose two distinct facets. The effects of reduced dimensionality are rationalized with the help of a simple model that considers circumferential quantization of the topological surface states. Furthermore, the surface spin density induced by electric current along the nanostructure shows a pronounced oscillatory dependence on the charge-carrier energy, which can be exploited in spintronics applications.Comment: 10 pages, 9 figure

Criticality and the Onset of Ordering in the Standard Vicsek Model

Experimental observations of animal collective behavior have shown stunning evidence for the emergence of large-scale cooperative phenomena resembling phase transitions in physical systems. Indeed, quantitative studies have found scale-free correlations and critical behavior consistent with the occurrence of continuous, second-order phase transitions. The Standard Vicsek Model (SVM), a minimal model of self-propelled particles in which their tendency to align with each other competes with perturbations controlled by a noise term, appears to capture the essential ingredients of critical flocking phenomena. In this paper, we review recent finite-size scaling and dynamical studies of the SVM, which present a full characterization of the continuous phase transition through dynamical and critical exponents. We also present a complex network analysis of SVM flocks and discuss the onset of ordering in connection with XY-like spin models.Comment: 15 pages, 4 figures. To appear in Interface Focu

Complex Network Structure of Flocks in the Standard Vicsek Model

In flocking models, the collective motion of self-driven individuals leads to the formation of complex spatiotemporal patterns. The Standard Vicsek Model (SVM) considers individuals that tend to adopt the direction of movement of their neighbors under the influence of noise. By performing an extensive complex network characterization of the structure of SVM flocks, we show that flocks are highly clustered, assortative, and non-hierarchical networks with short-tailed degree distributions. Moreover, we also find that the SVM dynamics leads to the formation of complex structures with an effective dimension higher than that of the space where the actual displacements take place. Furthermore, we show that these structures are capable of sustaining mean-field-like orientationally ordered states when the displacements are suppressed, thus suggesting a linkage between the onset of order and the enhanced dimensionality of SVM flocks.Comment: 26 pages, 11 figures. To appear in J. Stat. Phy

Macroscopic Observables Detecting Genuine Multipartite Entanglement and Partial Inseparability in Many-Body Systems

We show a general approach for detecting genuine multipartite entanglement (GME) and partial inseparability in many-body-systems by means of macroscopic observables (such as the energy) only. We show that the obtained criteria, the "GME gap" and "the k-entanglement gap", detect large areas of genuine multipartite entanglement and partial entanglement in typical many body states, which are not detected by other criteria. As genuine multipartite entanglement is a necessary property for several quantum information theoretic applications such as e.g. secret sharing or certain kinds of quantum computation, our methods can be used to select or design appropriate condensed matter systems.Comment: 4 pages, 3 figures, published version, title extende