Koszul differential graded algebras and BGG correspondence

The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When the Koszul DG algebra $A$ is AS-regular, the Ext-algebra $E$ of $A$ is Frobenius. In this case, similar to the classical BGG correspondence, there is an equivalence between the stable category of finitely generated left $E$-modules, and the quotient triangulated category of the full triangulated subcategory of the derived category of right DG $A$-modules consisting of all compact DG modules modulo the full triangulated subcategory consisting of all the right DG modules with finite dimensional cohomology. The classical BGG correspondence can derived from the DG version.Comment: 29 page

Surface-directed spinodal decomposition in the pseudobinary alloy (HfO_2)_x(SiO_2)_{1-x}

Hf silicate films (HfO_2)_{0.25}(SiO_2)_{0.75} with thicknesses in the range 4-20 nm were grown on silicon substrate by atomic layer deposition at 350 deg.C.The Hf distributions in as-grown and 800 deg.C annealed films were investigated by high resolution transmission electron microscopy (HRTEM), angle-resolved x-ray photoelectron spectroscopy (ARXPS) and medium energy ion scattering (MEIS). HRTEM images show a layered structure in films thinner than 8 nm. The ARXPS data also reveal a non-uniform distribution of Hf throughout the film depth. Diffusion of SiO_2 to the film surface after a longer time anneal was observed by MEIS. All these observations provide evidence for surface-directed spinodal decomposition in the pseudobinary (HfO_2)_x(SiO_2)_{1-x} alloy system.Comment: 1o figures, one tabl

Intense terahertz laser fields on a two-dimensional electron gas with Rashba spin-orbit coupling

The spin-dependent density of states and the density of spin polarization of an InAs-based two-dimensional electron gas with the Rashba spin-orbit coupling under an intense terahertz laser field are investigated by utilizing the Floquet states to solve the time-dependent Schr\"odinger equation. It is found that both densities are strongly affected by the terahertz laser field. Especially a terahertz magnetic moment perpendicular to the external terahertz laser field in the electron gas is induced. This effect can be used to convert terahertz electric signals into terahertz magnetic ones efficiently.Comment: 3 pages, 3 figures, a typo in Fig. 3(b) is correcte