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Wannier Function
The Wannier functions are a complete set of orthogonal functions used in solid-state physics. They were introduced by Gregory Wannier in 1937. Wannier functions are the localized molecular orbitals of crystalline systems. The Wannier functions for different lattice sites in a crystal are orthogonal, allowing a convenient basis for the expansion of electron states in certain regimes. Wannier functions have found widespread use, for example, in the analysis of binding forces acting on electrons; the existence of exponentially localized Wannier functions in insulators was proved in 2006. Specifically, these functions are also used in the analysis of excitons and condensed Rydberg matter. Definition Although, like localized molecular orbitals, Wannier functions can be chosen in many different ways, the original, simplest, and most common definition in solid-state physics is as follows. Choose a single band in a perfect crystal, and denote its Bloch states by :\psi_(\mathbf) = e^u_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N2 Wannier
N, or n, is the fourteenth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''en'' (pronounced ), plural ''ens''. History One of the most common hieroglyphs, snake, was used in Egyptian writing to stand for a sound like the English , because the Egyptian word for "snake" was ''djet''. It is speculated by many that Semitic people working in Egypt adapted hieroglyphics to create the first alphabet, and that they used the same snake symbol to represent N, because their word for "snake" may have begun with that sound. However, the name for the letter in the Phoenician, Hebrew, Aramaic and Arabic alphabets is ''nun'', which means "fish" in some of these languages. The sound value of the letter was —as in Greek, Etruscan, Latin and modern languages. Use in writing systems represents a dental or alveolar nasal in virtually all languages that use the Latin alp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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''. PBCs are often used in computer simulations and mathematical models. The topology of two-dimensional PBC is equal to that of a ''world map'' of some video games; the geometry of the unit cell satisfies perfect two-dimensional tiling, and when an object passes through one side of the unit cell, it re-appears on the opposite side with the same velocity. In topological terms, the space made by two-dimensional PBCs can be thought of as being mapped onto a torus (compactification). The large systems approximated by PBCs consist of an infinite number of unit cells. In computer simulations, one of these is the original simulation box, and others are copies called ''images''. During the simulation, only the properties of the original simulation box need to be recorded and propagated. The ''minimum-image conventi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Magnetization
In quantum mechanics, orbital magnetization, Morb, refers to the magnetization induced by orbital motion of charged particles, usually electrons in solids. The term "orbital" distinguishes it from the contribution of spin degrees of freedom, Mspin, to the total magnetization. A nonzero orbital magnetization requires broken time-reversal symmetry, which can occur spontaneously in ferromagnetic and ferrimagnetic materials, or can be induced in a non-magnetic material by an applied magnetic field. Definitions The orbital magnetic moment of a finite system, such as a molecule, is given classically by : \mathbf_ = \frac\int d^3\mathbf \, \mathbf\times\mathbf(\mathbf) where J(r) is the current density at point r. (Here SI units are used; in Gaussian units, the prefactor would be 1/2''c'' instead, where ''c'' is the speed of light.) In a quantum-mechanical context, this can also be written as : \mathbf_ = \frac \langle\Psi \vert\mathbf \vert\Psi\rangle where −''e'' and ''me'' are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. It consists of the appearance of spin accumulation on the lateral surfaces of an electric current-carrying sample, the signs of the spin directions being opposite on the opposing boundaries. In a cylindrical wire, the current-induced surface spins will wind around the wire. When the current direction is reversed, the directions of spin orientation is also reversed. Definition The spin Hall effect is a transport phenomenon consisting of the appearance of spin accumulation on the lateral surfaces of a sample carrying electric current. The opposing surface boundaries will have spins of opposite sign. It is analogous to the classical Hall effect, where ''charges'' of opposite sign appear on the opposing lateral surfaces in an electric-current carrying sample in a magnetic field. In the case of the classical Hall effect the charge build up at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anomalous Photovoltaic Effect
The anomalous photovoltaic effect (APE), also called the bulk photovoltaic effect in certain cases, is a type of a photovoltaic effect which occurs in certain semiconductors and insulators. The "anomalous" refers to those cases where the photovoltage (i.e., the open-circuit voltage caused by the light) is larger than the band gap of the corresponding semiconductor. In some cases, the voltage may reach thousands of volts. Although the voltage is unusually high, the short-circuit current is unusually low. Overall, materials that exhibit the anomalous photovoltaic effect have very low power generation efficiencies, and are never used in practical power-generation systems. There are several situations in which APE can arise. First, in polycrystalline materials, each microscopic grain can act as a photovoltaic. Then the grains add in series, so that the overall open-circuit voltage across the sample is large, potentially much larger than the bandgap. Second, in a similar manner, certa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. In such a medium, which is also called gyrotropic or gyromagnetic, left- and right-rotating elliptical polarizations can propagate at different speeds, leading to a number of important phenomena. When light is transmitted through a layer of magneto-optic material, the result is called the Faraday effect: the plane of polarization can be rotated, forming a Faraday rotator. The results of reflection from a magneto-optic material are known as the magneto-optic Kerr effect (not to be confused with the nonlinear Kerr effect). In general, magneto-optic effects break time reversal symmetry locally (i.e. when only the propagation of light, and not the source of the magnetic field, is considered) as well as Lorentz reciprocity, which is a necessary condition to construct devices such as optical is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Magnetization
In quantum mechanics, orbital magnetization, Morb, refers to the magnetization induced by orbital motion of charged particles, usually electrons in solids. The term "orbital" distinguishes it from the contribution of spin degrees of freedom, Mspin, to the total magnetization. A nonzero orbital magnetization requires broken time-reversal symmetry, which can occur spontaneously in ferromagnetic and ferrimagnetic materials, or can be induced in a non-magnetic material by an applied magnetic field. Definitions The orbital magnetic moment of a finite system, such as a molecule, is given classically by : \mathbf_ = \frac\int d^3\mathbf \, \mathbf\times\mathbf(\mathbf) where J(r) is the current density at point r. (Here SI units are used; in Gaussian units, the prefactor would be 1/2''c'' instead, where ''c'' is the speed of light.) In a quantum-mechanical context, this can also be written as : \mathbf_ = \frac \langle\Psi \vert\mathbf \vert\Psi\rangle where −''e'' and ''me'' are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hall Effect
The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor that is transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current. It was discovered by Edwin Hall in 1879. A Hall effect can also occur across a void or hole in a semiconductor or metal plate, when current is injected via contacts that lie on the boundary or edge of the void or hole, and the charge flows outside the void or hole, in the metal or semiconductor. This Hall effect becomes observable in a perpendicular applied magnetic field across voltage contacts that lie on the boundary of the void on either side of a line connecting the current contacts. It exhibits apparent sign reversal in comparison to the standard "ordinary Hall effect" in the simply connected specimen, and depends only on the current injected from within the void. Superposition may also be realized in the Hall effect: first imagine the standard ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tight Binding
In solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site. The method is closely related to the LCAO method (linear combination of atomic orbitals method) used in chemistry. Tight-binding models are applied to a wide variety of solids. The model gives good qualitative results in many cases and can be combined with other models that give better results where the tight-binding model fails. Though the tight-binding model is a one-electron model, the model also provides a basis for more advanced calculations like the calculation of surface states and application to various kinds of many-body problem and quasiparticle calculations. Introduction The name "tight binding" of this electronic band structure model suggests that this quantum mechanical model describes the properties of tightly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berry 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. The phenomenon was independently discovered by S. Pancharatnam (1956), in classical optics and by H. C. Longuet-Higgins (1958)See page 12 in molecular physics; it was generalized by Sir Michael Berry in (1984). It is also known as the Pancharatnam–Berry phase, Pancharatnam phase, or Berry phase. It can be seen in the conical intersection of potential energy surfaces and in the Aharonov–Bohm effect. Geometric phase around the conical intersection involving the ground electronic state of the C6H3F3+ molecular ion is discussed on pages 385–386 of the textbook by Bunker and Jensen. In the case of the Aharonov–Bohm effect, the adiabatic parameter is the magnetic field enclosed by two interference paths, and it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. All ferroelectrics are also piezoelectric and pyroelectric, with the additional property that their natural electrical polarization is reversible. The term is used in analogy to ferromagnetism, in which a material exhibits a permanent magnetic moment. Ferromagnetism was already known when ferroelectricity was discovered in 1920 in Rochelle salt by Joseph Valasek.See and Thus, the prefix ''ferro'', meaning iron, was used to describe the property despite the fact that most ferroelectric materials do not contain iron. Materials that are both ferroelectric ''and'' ferromagnetic are known as multiferroics. Polarization When most materials are electrically polarized, the polarization induced, ''P'', is almost exactly proportional to the applied external electric field ''E''; so the polarization is a linear fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polarization Density
In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is said to be polarized. The electric dipole moment induced per unit volume of the dielectric material is called the electric polarization of the dielectric.''Introduction to Electrodynamics'' (3rd Edition), D.J. Griffiths, Pearson Education, Dorling Kindersley, 2007, ''McGraw Hill Encyclopaedia of Physics'' (2nd Edition), C.B. Parker, 1994, Polarization density also describes how a material responds to an applied electric field as well as the way the material changes the electric field, and can be used to calculate the forces that result from those interactions. It can be compared to magnetization, which is the measure of the corresponding ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
