Inversion Symmetric Topological Insulators

We study translationally-invariant insulators with inversion symmetry that fall outside the established classification of topological insulators. These insulators are not required to have gapless boundary modes in the energy spectrum. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. Their entanglement entropy cannot be made to vanish adiabatically, and hence the insulators can be called topological. There is a direct connection between the inversion eigenvalues of the band structure and the mid-gap states in the entanglement spectrum. The classification of protected entanglement levels is given by an integer $n\in Z$, which is the difference between the negative inversion eigenvalues at inversion symmetric points in the Brillouin zone, taken in sets of two. When the Hamiltonian describes a Chern insulator or a non-trivial T-invariant topological insulator, the entanglement spectrum exhibits spectral flow. If the Chern number is zero for the former, or T is broken in the latter, the entanglement spectrum does \emph{not} have spectral flow, but, depending on the inversion eigenvalues, can still have protected midgap bands. Although spectral flow is broken, the mid-gap entanglement bands cannot be adiabatically removed, and the insulator is `topological.' In 1D, we establish a link between the product of the inversion eigenvalues of all occupied bands at all inversion momenta and charge polarization. In 2D, we prove a link between the product of the inversion eigenvalues and the parity of the Chern number. In 3D, we find a topological constraint on the product of the inversion eigenvalues indicating that some 3D materials are topological metals, and we show the link between the inversion eigenvalues and the 3D Quantum Hall Effect and the magnetoelectric polarization in the absence of T-symmetry.Comment: 42 pages, 13 figure

Nearsightedness of Electronic Matter in One Dimension

The concept of nearsightedeness of electronic matter (NEM) was introduced by W. Kohn in 1996 as the physical principal underlining Yang's electronic structure alghoritm of divide and conquer. It describes the fact that, for fixed chemical potential, local electronic properties at a point $r$, like the density $n(r)$, depend significantly on the external potential $v$ only at nearby points. Changes $\Delta v$ of that potential, {\it no matter how large}, beyond a distance $\textsf{R}$, have {\it limited} effects on local electronic properties, which tend to zero as function of $\textsf{R}$. This remains true even if the changes in the external potential completely surrounds the point $r$. NEM can be quantitatively characterized by the nearsightedness range, $\textsf{\textsf{R}}(r,\Delta n)$, defined as the smallest distance from $r$, beyond which {\it any} change of the external potential produces a density change, at $r$, smaller than a given $\Delta n$. The present paper gives a detailed analysis of NEM for periodic metals and insulators in 1D and includes sharp, explicit estimates of the nearsightedness range. Since NEM involves arbitrary changes of the external potential, strong, even qualitative changes can occur in the system, such as the discretization of energy bands or the complete filling of the insulating gap of an insulator with continuum spectrum. In spite of such drastic changes, we show that $\Delta v$ has only a limited effect on the density, which can be quantified in terms of simple parameters of the unperturbed system.Comment: 10 pages, 9 figure

Nearsightedness of Electronic Matter

In an earlier paper, W. Kohn had qualitatively introduced the concept of "nearsightedness" of electrons in many-atom systems. It can be viewed as underlying such important ideas as Pauling's "chemical bond," "transferability" and Yang's computational principle of "divide and conquer." It describes the fact that, for fixed chemical potential, local electronic properties, like the density $n(r)$, depend significantly on the effective external potential only at nearby points. Changes of that potential, {\it no matter how large}, beyond a distance $\textsf{R}$ have {\it limited} effects on local electronic properties, which rapidly tend to zero as function of $\textsf{R}$. In the present paper, the concept is first sharpened for representative models of uncharged fermions moving in external potentials, followed by a discussion of the effects of electron-electron interactions and of perturbing external charges.Comment: final for

Performance Evaluation of a Self-Organising Scheme for Multi-Radio Wireless Mesh Networks

Multi-Radio Wireless Mesh Networks (MR-WMN) can substantially increase the aggregate capacity of the Wireless Mesh Networks (WMN) if the channels are assigned to the nodes in an intelligent way so that the overall interference is limited. We propose a generic self-organisation algorithm that addresses the two key challenges of scalability and stability in a WMN. The basic approach is that of a distributed, light-weight, co-operative multiagent system that guarantees scalability. The usefulness of our algorithm is exhibited by the performance evaluation results that are presented for different MR-WMN node densities and typical topologies. In addition, our work complements the Task Group 802.11s Extended Service Set (ESS) Mesh networking project work that is in progress

Mott Transition of MnO under Pressure: Comparison of Correlated Band Theories

The electronic structure, magnetic moment, and volume collapse of MnO under pressure are obtained from four different correlated band theory methods; local density approximation + Hubbard U (LDA+U), pseudopotential self-interaction correction (pseudo-SIC), the hybrid functional (combined local exchange plus Hartree-Fock exchange), and the local spin density SIC (SIC-LSD) method. Each method treats correlation among the five Mn 3d orbitals (per spin), including their hybridization with three O $2p$ orbitals in the valence bands and their changes with pressure. The focus is on comparison of the methods for rocksalt MnO (neglecting the observed transition to the NiAs structure in the 90-100 GPa range). Each method predicts a first-order volume collapse, but with variation in the predicted volume and critical pressure. Accompanying the volume collapse is a moment collapse, which for all methods is from high-spin to low-spin (5/2 to 1/2), not to nonmagnetic as the simplest scenario would have. The specific manner in which the transition occurs varies considerably among the methods: pseudo-SIC and SIC-LSD give insulator-to-metal, while LDA+U gives insulator-to-insulator and the hybrid method gives an insulator-to-semimetal transition. Projected densities of states above and below the transition are presented for each of the methods and used to analyze the character of each transition. In some cases the rhombohedral symmetry of the antiferromagnetically ordered phase clearly influences the character of the transition.Comment: 14 pages, 9 figures. A 7 institute collaboration, Updated versio