Wannier function, the Glossary

Table of Contents

1. 24 relations: Anomalous photovoltaic effect, Bloch's theorem, Bravais lattice, Brillouin zone, Crystal, Electron, Electronic band structure, Exponential function, Ferroelectricity, Geometric phase, Gregory Wannier, Hannay angle, Localized molecular orbitals, Magneto-optic effect, Orbital magnetization, Orthogonal functions, Orthonormal basis, Periodic boundary conditions, Polarization density, Reciprocal lattice, Separable partial differential equation, Solid-state physics, Spin Hall effect, Unit cell.

Anomalous photovoltaic effect

The anomalous photovoltaic effect (APE) is a type of a photovoltaic effect which occurs in certain semiconductors and insulators.

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Bloch's theorem

In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions. Wannier function and Bloch's theorem are condensed matter physics.

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Bravais lattice

In geometry and crystallography, a Bravais lattice, named after, is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by where the ni are any integers, and ai are primitive translation vectors, or primitive vectors, which lie in different directions (not necessarily mutually perpendicular) and span the lattice.

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Brillouin zone

In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space.

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Crystal

A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

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Electron

The electron (or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge.

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Electronic band structure

In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands).

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Exponential function

The exponential function is a mathematical function denoted by f(x).

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Ferroelectricity

Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field.

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Geometric phase

In classical and quantum mechanics, geometric phase is a phase difference acquired over the course of a cycle, when a system is subjected to cyclic adiabatic processes, which results from the geometrical properties of the parameter space of the Hamiltonian.

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Gregory Wannier

Gregory Hugh Wannier (1911–1983) was a Swiss physicist.

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Hannay angle

In classical mechanics, the Hannay angle is a mechanics analogue of the whirling geometric phase (or Berry phase).

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Localized molecular orbitals

Localized molecular orbitals are molecular orbitals which are concentrated in a limited spatial region of a molecule, such as a specific bond or lone pair on a specific atom.

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Magneto-optic effect

A magneto-optic effect is any one of a number of phenomena in which an electromagnetic wave propagates through a medium that has been altered by the presence of a quasistatic magnetic field.

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Orbital magnetization

In quantum mechanics, orbital magnetization, Morb, refers to the magnetization induced by orbital motion of charged particles, usually electrons in solids.

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Orthogonal functions

In mathematics, orthogonal functions belong to a function space that is a vector space equipped with a bilinear form.

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Orthonormal basis

In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.

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Periodic boundary conditions

Periodic boundary conditions (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a unit cell.

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Polarization density

In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the volumetric density of permanent or induced electric dipole moments in a dielectric material.

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Reciprocal lattice

In physics, the reciprocal lattice emerges from the Fourier transform of another lattice. Wannier function and reciprocal lattice are condensed matter physics.

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Separable partial differential equation

A separable partial differential equation can be broken into a set of equations of lower dimensionality (fewer independent variables) by a method of separation of variables.

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Solid-state physics

Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. Wannier function and solid-state physics are condensed matter physics.

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Spin Hall effect

The spin Hall effect (SHE) is a transport phenomenon predicted by Russian physicists Mikhail I. Dyakonov and Vladimir I. Perel in 1971. Wannier function and spin Hall effect are condensed matter physics.

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Unit cell

In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice.

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References

[1] https://en.wikipedia.org/wiki/Wannier_function

Also known as Wannier functions.