Theory of polarization of crystalline solids
TL;DR: It is shown that physically $\ensuremath{\Delta}P can be interpreted as a displacement of the center of charge of the Wannier functions.
Abstract: We consider the change in polarization \ensuremath{\Delta}P which occurs upon making an adiabatic change in the Kohn-Sham Hamiltonian of the solid. A simple expression for \ensuremath{\Delta}P is derived in terms of the valence-band wave functions of the initial and final Hamiltonians. We show that physically \ensuremath{\Delta}P can be interpreted as a displacement of the center of charge of the Wannier functions. The formulation is successfully applied to compute the piezoelectric tensor of GaAs in a first-principles pseudopotential calculation.
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TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.
11,092 citations
TL;DR: In this paper, a selfconsistent density functional method using standard norm-conserving pseudopotentials and a flexible, numerical linear combination of atomic orbitals basis set, which includes multiple-zeta and polarization orbitals, was developed and implemented.
Abstract: We have developed and implemented a selfconsistent density functional method using standard norm-conserving pseudopotentials and a flexible, numerical linear combination of atomic orbitals basis set, which includes multiple-zeta and polarization orbitals. Exchange and correlation are treated with the local spin density or generalized gradient approximations. The basis functions and the electron density are projected on a real-space grid, in order to calculate the Hartree and exchange-correlation potentials and matrix elements, with a number of operations that scales linearly with the size of the system. We use a modified energy functional, whose minimization produces orthogonal wavefunctions and the same energy and density as the Kohn-Sham energy functional, without the need for an explicit orthogonalization. Additionally, using localized Wannier-like electron wavefunctions allows the computation time and memory required to minimize the energy to also scale linearly with the size of the system. Forces and stresses are also calculated efficiently and accurately, thus allowing structural relaxation and molecular dynamics simulations.
8,723 citations
TL;DR: In this paper, the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method, is reviewed.
Abstract: This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.
6,917 citations
Cites methods from "Theory of polarization of crystalli..."
...It is worth mentioning that effective charges can be calculated using an approach to the electrostatics of quantum dielectrics based on topological concepts, the Berry’s phase approach to macroscopic polarization (King-Smith and Vanderbilt, 1993; Resta, 1994)....
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TL;DR: A ferroelectric crystal exhibits a stable and switchable electrical polarization that is manifested in the form of cooperative atomic displacements that arises through the quantum mechanical phenomenon of exchange.
Abstract: A ferroelectric crystal exhibits a stable and switchable electrical polarization that is manifested in the form of cooperative atomic displacements. A ferromagnetic crystal exhibits a stable and switchable magnetization that arises through the quantum mechanical phenomenon of exchange. There are very few 'multiferroic' materials that exhibit both of these properties, but the 'magnetoelectric' coupling of magnetic and electrical properties is a more general and widespread phenomenon. Although work in this area can be traced back to pioneering research in the 1950s and 1960s, there has been a recent resurgence of interest driven by long-term technological aspirations.
6,813 citations
TL;DR: Enhanced polarization and related properties in heteroepitaxially constrained thin films of the ferroelectromagnet, BiFeO3, and combined functional responses in thin film form present an opportunity to create and implement thin film devices that actively couple the magnetic and ferroelectric order parameters.
Abstract: Enhancement of polarization and related properties in heteroepitaxially constrained thin films of the ferroelectromagnet, BiFeO3, is reported. Structure analysis indicates that the crystal structure of film is monoclinic in contrast to bulk, which is rhombohedral. The films display a room-temperature spontaneous polarization (50 to 60 microcoulombs per square centimeter) almost an order of magnitude higher than that of the bulk (6.1 microcoulombs per square centimeter). The observed enhancement is corroborated by first-principles calculations and found to originate from a high sensitivity of the polarization to small changes in lattice parameters. The films also exhibit enhanced thickness-dependent magnetism compared with the bulk. These enhanced and combined functional responses in thin film form present an opportunity to create and implement thin film devices that actively couple the magnetic and ferroelectric order parameters.
5,387 citations