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

Multiferroic BiFeO3-BiMnO3 Nanocheckerboard From First Principles

We present a first principles study of an unusual heterostructure, an atomic-scale checkerboard of BiFeO3-BiMnO3, and compare its properties to the two bulk constituent materials, BiFeO3 and BiMnO3. The "nanocheckerboard" is found to have a multiferroic ground state with the desired properties of each constituent: polar and ferrimagnetic due to BiFeO3 and BiMnO3, respectively. The effect of B-site cation ordering on magnetic ordering in the BiFeO3-BiMnO3 system is studied. The checkerboard geometry is seen to give rise to a a novel magnetostructural effect that is neither present in the bulk constituent materials, nor in the layered BiFeO3-BiMnO3 superlattice.Comment: 15 pages, 14 figure

Topological quantum phase transition in the BEC-BCS crossover phenomena

A crossover between the Bose Einstein condensation (BEC) and BCS superconducting state is described topologically in the chiral symmetric fermion system with attractive interaction. Using a local Z_2 Berry phase, we found a quantum phase transition between the BEC and BCS phases without accompanying the bulk gap closing.Comment: 4 pages, 5 figure

Strong-correlation effects in Born effective charges

Large values of Born effective charges are generally considered as reliable indicators of the genuine tendency of an insulator towards ferroelectric instability. However, these quantities can be very much influenced by strong electron correlation and metallic behavior, which are not exclusive properties of ferroelectric materials. In this paper we compare the Born effective charges of some prototypical ferroelectrics with those of magnetic, non-ferroelectric compounds using a novel, self-interaction free methodology that improves on the local-density approximation description of the electronic properties. We show that the inclusion of strong-correlation effects systermatically reduces the size of the Born effective charges and the electron localization lengths. Furthermore we give an interpretation of the Born effective charges in terms of band energy structure and orbital occupations which can be used as a guideline to rationalize their values in the general case.Comment: 10 pages, 4 postscript figure

Non-Abelian Braiding of Lattice Bosons

We report on a numerical experiment in which we use time-dependent potentials to braid non-abelian quasiparticles. We consider lattice bosons in a uniform magnetic field within the fractional quantum Hall regime, where $\nu$, the ratio of particles to flux quanta, is near 1/2, 1 or 3/2. We introduce time-dependent potentials which move quasiparticle excitations around one another, explicitly simulating a braiding operation which could implement part of a gate in a quantum computation. We find that different braids do not commute for $\nu$ near $1$ and $3/2$, with Berry matrices respectively consistent with Ising and Fibonacci anyons. Near $\nu=1/2$, the braids commute.Comment: 5 pages, 1 figur

Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension

In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twisting operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values $z_L$ measure the overlap between the unique ground state and an excited state. Insulators are characterized by $z_{\infty}\neq 0$. We identify $z_L$ with ground-state expectation values of vertex operators in the sine-Gordon model. This allows an accurate detection of quantum phase transitions in the universality classes of the Gaussian model. We apply this theory to the half-filled extended Hubbard model and obtain agreement with the level-crossing approach.Comment: 4 pages, 3 figure

The effects of interface morphology on Schottky barrier heights: a case study on Al/GaAs(001)

The problem of Fermi-level pinning at semiconductor-metal contacts is readdressed starting from first-principles calculations for Al/GaAs. We give quantitative evidence that the Schottky barrier height is very little affected by any structural distortions on the metal side---including elongations of the metal-semiconductor bond (i.e. interface strain)---whereas it strongly depends on the interface structure on the semiconductor side. A rationale for these findings is given in terms of the interface dipole generated by the ionic effective charges.Comment: 5 pages, latex file, 2 postscript figures automatically include

Quantum-Mechanical Position Operator and Localization in Extended Systems

We introduce a fundamental complex quantity, $z_{L}$, which allows us to discriminate between a conducting and non-conducting thermodynamic phase in extended quantum systems. Its phase can be related to the expectation value of the position operator, while its modulus provides an appropriate definition of a localization length. The expressions are valid for {\it any} fractional particle filling. As an illustration we use $z_{L}$ to characterize insulator to ``superconducting'' and Mott transitions in one-dimensional lattice models with infinite on-site Coulomb repulsion at quarter filling.Comment: 4 pages, REVTEX, 1 ps figure