We study complex Dirac structures, that is, structures in the complexified generalized tangent bundle. These include presymplectic foliations, transverse holomorphic CR-related geometries and structures. introduce two invariants, order (normalized) type. show that, together with real index, they allow us to obtain a pointwise classification of For constant order, we prove existence an underlyin...

The Dirac structure of confinement is shown to be of timelike-vector nature in the heavy quark limit of QCD. This stands in contradiction with the phenomenological success of the Dirac scalar confining potential. A resolution is achieved through the demonstration that an effective scalar interaction is dynamically generated by nonperturbative mixing between ordinary and hybrid QQ̄ states. The re...

Dirac materials have attracted great interest for both fundamental research and electronic devices due to their unique band structures, but the usual near zero bandgap of graphene results in a poor on-off ratio in the corresponding transistors. Here, we report on tinene, monolayer gray tin, as a new two-dimensional material with both Dirac characteristics and a remarkable 72 meV bandgap based o...

We use first-principles electronic structure calculations to predict a new class of two-dimensional (2D) topological insulators (TIs) in binary compositions of group III elements (B, Al, Ga, In, and Tl) and bismuth (Bi) in a buckled honeycomb structure. We identify band inversions in pristine GaBi, InBi, and TlBi bilayers, with gaps as large as 560 meV, making these materials suitable for room-...

We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational eld with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new eld equation generalizing the notion of Killing spinors. The solutions of this spinor eld equation are called weak Killing spinors (WK-spinors). They are special solutions of the Einstein-Di...

We give a local normal form for Dirac structures. As a consequence, we show that the dimensions of the pre-symplectic leaves of a Dirac manifold have the same parity. We also show that, given a point m of a Dirac manifold M , there is a well-defined transverse Poisson structure to the pre-symplectic leaf P through m. Finally, we describe the neighborhood of a pre-symplectic leaf in terms of geo...