Electron Localization in the Insulating State

The insulating state of matter is characterized by the excitation spectrum, but also by qualitative features of the electronic ground state. The insulating ground wavefunction in fact: (i) sustains macroscopic polarization, and (ii) is localized. We give a sharp definition of the latter concept, and we show how the two basic features stem from essentially the same formalism. Our approach to localization is exemplified by means of a two--band Hubbard model in one dimension. In the noninteracting limit the wavefunction localization is measured by the spread of the Wannier orbitals.Comment: 5 pages including 3 figures, submitted to PR

The Quantum-Mechanical Position Operator in Extended Systems

The position operator (defined within the Schroedinger representation in the standard way) becomes meaningless when periodic boundary conditions are adopted for the wavefunction, as usual in condensed matter physics. We show how to define the position expectation value by means of a simple many-body operator acting on the wavefunction of the extended system. The relationships of the present findings to the Berry-phase theory of polarization are discussed.Comment: Four pages in RevTe

Nested Kirkpatrick–Baez (Montel) optics for hard X-rays

A comprehensive description and ray-tracing simulations are presented for symmetric nested Kirkpatrick-Baez (KB) mirrors, commonly used at synchrotrons and in commercial X-ray sources. This paper introduces an analytical procedure for determining the proper orientation between the two surfaces composing the nested KB optics. This procedure has been used to design and simulate collimating optics for a hard-X-ray inverse Compton scattering source. The resulting optical device is composed of two 12 cm-long parabolic surfaces coated with a laterally graded multilayer and is capable of collimating a 12 keV beam with a divergence of 5 mrad (FWHM) by a factor of ~250. A description of the ray-tracing software that was developed to simulate the graded multilayer mirrors is included