Group theory of Wannier functions providing the basis for a deeper understanding of magnetism and superconductivity

The paper presents the group theory of best localized and symmetry-adapted Wannier functions in a crystal of any given space group G or magnetic group M. Provided that the calculated band structure of the considered material is given and that the symmetry of the Bloch functions at all the points of symmetry in the Brillouin zone is known, the paper details whether or not the Bloch functions of particular energy bands can be unitarily transformed into best localized Wannier functions symmetry-adapted to the space group G, to the magnetic group M, or to a subgroup of G or M. In this context, the paper considers usual as well as spin-dependent Wannier functions, the latter representing the most general definition of Wannier functions. The presented group theory is a review of the theory published by one of the authors in several former papers and is independent of any physical model of magnetism or superconductivity. However, it is suggested to interpret the special symmetry of the best localized Wannier functions in the framework of a nonadiabatic extension of the Heisenberg model, the nonadiabatic Heisenberg model. On the basis of the symmetry of the Wannier functions, this model of strongly correlated localized electrons makes clear predictions whether or not the system can possess superconducting or magnetic eigenstates

Negotiating the Great Recession: How Teacher Collective Bargaining Outcomes Change in Times of Financial Duress

This article examines how teacher collective bargaining agreements (CBAs), teacher salaries, and class sizes changed during the Great Recession. Using a district-level data set of California teacher CBAs that includes measures of subarea contract strength and salaries from 2005–2006 and 2011–2012 tied to district-level longitudinal data, we estimate difference-in-difference models to examine bargaining outcomes for districts that should have been more or less fiscally constrained. We find that unions and administrators change critical elements of CBAs and district policy during times of fiscal duress. This includes increasing class sizes, reducing instructional time, and lowering base salaries to relieve financial pressures and negotiating increased protections for teachers in areas with less direct financial implications, including grievance procedures and nonteaching duties

Defect structure of web silicon ribbon

The results of a preliminary study of two dendritic web samples are presented. The structure and electrical activity of the defects in the silicon webs were studied. Optical microscopy of chemically etched specimens was used to determine dislocation densities. Samples were mechanically polished, then Secco etched for approximately 5 minutes. High voltage transmission electron microscopy was used to characterize the crystallographic nature of the defects