Half moons are pinch points with dispersion

"Pinch points," singular features observed in (quasi-)elastic neutron scattering, are a widely discussed hallmark of spin liquids with an emergent gauge symmetry. Much less attention has been paid to "half moons," distinctive crescent patterns at finite energy, which have been observed in experiments on a number of pyrochlore magnets, and in a wide range of model calculations. Here we unify these two phenomena within a single framework, paying particular attention to the case of ordered, or field-saturated states, where pinch points and half moons can be found in bands of excitations above a gap. We find that half moons are nothing other than pinch points inscribed on a dispersing band. Molecular dynamics simulations of the kagome lattice antiferromagnet are used to explore how these bands evolve into the ground state and excitations of a classical spin liquid. We explicitly demonstrate that this theory can reproduce the pinch points and half moons observed in Nd$_2$Zr$_2$O$_7$.Comment: 6 pages, 4 figures. Supplementary material: 10 pages, 3 figure

Symmetry and optical selection rules in graphene quantum dots

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}{($10 \lesssim L \lesssim 50\ \text{nm}$)} 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

Aktuelle Trends: Fremdenfeindlichkeit als Standortnachteil im Osten? Besonders viele rechtsextremistisch motivierte Gewalttaten in den Neuen Ländern

Ostdeutschland steht mit anderen Regionen im Wettbewerb um gut qualifizierte Arbeitskräfte. Insbesondere wissensintensive Bereiche (z. B. Universitäten, Forschungseinrichtungen und technologieorientierte Unternehmen) profitieren stark von qualifizierten Fachkräften aus der ganzen Welt

Direct investment as seen by German Industry

The pros and cons of direct investment are attracting more and more attention in public discussion. In the following article, Dr Pohle, who was not only a highly successful businessman but also an influential and much respected Member of Federal Parliament, examined the possible positive and negative repercussions of direct investment from the point of view of German industry