751 research outputs found

    Symmetry and optical selection rules in graphene quantum dots

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    Graphene quantum dots (GQD's) have optical properties which are very different from those of an extended graphene sheet. In this Article we explore how the size, shape and edge--structure of a GQD affect its optical conductivity. Using representation theory, we derive optical selection rules for regular-shaped dots, starting from the symmetry properties of the current operator. We find that, where the x- and y-components of the current operator transform with the same irreducible representation (irrep) of the point group - for example in triangular or hexagonal GQD's - the optical conductivity is independent of the polarisation of the light. On the other hand, where these components transform with different irreps - for example in rectangular GQD's - the optical conductivity depends on the polarisation of light. We find that GQD's with non-commuting point-group operations - for example dots of rectangular shape - can be distinguished from GQD's with commuting point-group operations - for example dots of triangular or hexagonal shape - by using polarized light. We carry out explicit calculations of the optical conductivity of GQD's described by a simple tight--binding model and, for dots of intermediate size, \textcolor{blue}{(10L50 nm10 \lesssim L \lesssim 50\ \text{nm})} find an absorption peak in the low--frequency range of the spectrum which allows us to distinguish between dots with zigzag and armchair edges. We also clarify the one-dimensional nature of states at the van Hove singularity in graphene, providing a possible explanation for very high exciton-binding energies. Finally we discuss the role of atomic vacancies and shape asymmetry.Comment: 24 pages, 15 figure

    Toward the Gravity Dual of Heterotic Small Instantons

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    The question of what happens when the heterotic SO(32) instanton becomes small was answered sometime back by Witten. The heterotic theory develops an enhanced Sp(2k) gauge symmetry for k small instantons, besides the allowed SO(32) gauge symmetry. An interesting question now is to ask what happens when we take the large k limit. In this paper we argue that in some special cases, where Gauss' law allows the large k limit, the dynamics of the large k small instantons can be captured by a dual gravitational description. For the cases that we elaborate in this paper, the gravity duals are non-Kahler manifolds although in general they could be non-geometric. These small instantons are heterotic five-branes and the duality allows us to study the strongly coupled field theories on these five-branes. We review and elaborate on some of the recent observations pointing towards this duality, and argue that in certain cases the gauge/gravity duality may be understood as small instanton transitions under which the instantons smoothen out and consequently lose the Sp(2k) gauge symmetry. This may explain how branes disappear on the dual side and are replaced by fluxes. We analyse the torsion classes before and after the transitions, and discuss briefly how the ADHM sigma model and related vector bundles could be studied for these scenarios.Comment: 47 pages, 3 eps figures, LaTex, JHEP3 file; v2: Another consistency check added, typos corrected and a reference added; v3: Text expanded a bit, minor typos corrected and a few references updated. Final version to appear in Phys. Rev.

    Ultrafast Control of the Dimensionality of Exciton-Exciton Annihilation in Atomically Thin Black Phosphorus

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    Using microtransient absorption spectroscopy, we show that the dynamical form of exciton-exciton annihilation in atomically thin black phosphorous can be made to switch between time varying 1D scattering and time-independent 2D scattering. At low carrier densities, anisotropy drives the 1D behavior, but as the photoexcitation density approaches the exciton saturation limit, the 2D nature of exciton-exciton scattering takes over. Furthermore, lowering the temperature provides a handle on the ultrafast timescale at which the 1D to 2D transition occurs. We understand our results quantitatively using a diffusion based model of exciton-exciton scattering
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