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Crystal Momentum
In solid-state physics crystal momentum or quasimomentum is a momentum-like vector associated with electrons in a crystal lattice. It is defined by the associated wave vectors \mathbf of this lattice, according to :_ \equiv \hbar (where \hbar is the reduced Planck's constant). Frequently, crystal momentum is conserved like mechanical momentum, making it useful to physicists and materials scientists as an analytical tool. Lattice symmetry origins A common method of modeling crystal structure and behavior is to view electrons as quantum mechanical particles traveling through a fixed infinite periodic potential V(x) such that :V(+)=V(), where \mathbf is an arbitrary lattice vector. Such a model is sensible because crystal ions that form the lattice structure are typically on the order of tens of thousands of times more massive than electrons, making it safe to replace them with a fixed potential structure, and the macroscopic dimensions of a crystal are typically far greater t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasimomentum
In solid-state physics crystal momentum or quasimomentum is a momentum-like vector associated with electrons in a crystal lattice. It is defined by the associated wave vectors \mathbf of this lattice, according to :_ \equiv \hbar (where \hbar is the reduced Planck's constant). Frequently, crystal momentum is conserved like mechanical momentum, making it useful to physicists and materials scientists as an analytical tool. Lattice symmetry origins A common method of modeling crystal structure and behavior is to view electrons as quantum mechanical particles traveling through a fixed infinite periodic potential V(x) such that :V(+)=V(), where \mathbf is an arbitrary lattice vector. Such a model is sensible because crystal ions that form the lattice structure are typically on the order of tens of thousands of times more massive than electrons, making it safe to replace them with a fixed potential structure, and the macroscopic dimensions of a crystal are typically far greater than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modulo (jargon)
In mathematics, the term ''modulo'' ("with respect to a modulus of", the Latin ablative of '' modulus'' which itself means "a small measure") is often used to assert that two distinct mathematical objects can be regarded as equivalent—if their difference is accounted for by an additional factor. It was initially introduced into mathematics in the context of modular arithmetic by Carl Friedrich Gauss in 1801. Since then, the term has gained many meanings—some exact and some imprecise (such as equating "modulo" with "except for"). For the most part, the term often occurs in statements of the form: :''A'' is the same as ''B'' modulo ''C'' which means :''A'' and ''B'' are the same—except for differences accounted for or explained by ''C''. History ''Modulo'' is a mathematical jargon that was introduced into mathematics in the book ''Disquisitiones Arithmeticae'' by Carl Friedrich Gauss in 1801. Given the integers ''a'', ''b'' and ''n'', the expression "''a'' ≡ ''b'' (mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reviews Of Modern Physics
''Reviews of Modern Physics'' (abbreviated RMP) is a quarterly peer-reviewed scientific journal published by the American Physical Society. It was established in 1929 and the current editor-in-chief is Michael Thoennessen. The journal publishes review articles, usually by established researchers, on all aspects of physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ... and related fields. The reviews are usually accessible to non-specialists and serve as introductory material to graduate students, which survey recent work, discuss key problems to be solved and provide perspectives toward the end. References External links * Publications established in 1929 Physics review journals Quarterly journals English-language journals American Physical Society academic journ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle-resolved Photoemission Spectroscopy
Angle-resolved photoemission spectroscopy (ARPES) is an experimental technique used in condensed matter physics to probe the allowed energies and momenta of the electrons in a material, usually a crystalline solid. It is based on the photoelectric effect, in which an incoming photon of sufficient energy ejects an electron from the surface of a material. By directly measuring the kinetic energy and emission angle distributions of the emitted photoelectrons, the technique can map the electronic band structure and Fermi surfaces. ARPES is best suited for the study of one- or two-dimensional materials. It has been used by physicists to investigate high-temperature superconductors, graphene, Topological insulator, topological materials, quantum well states, and materials exhibiting charge density waves. ARPES systems consist of a monochromatic light source to deliver a narrow beam of photons, a sample holder connected to a manipulator used to position the sample of a material, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phonon
In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechanical Quantization (physics), quantization of the mode of vibration, modes of vibrations for elastic structures of interacting particles. Phonons can be thought of as quantized sound waves, similar to photons as quantized light waves. The study of phonons is an important part of condensed matter physics. They play a major role in many of the physical properties of condensed matter systems, such as thermal conductivity and electrical conductivity, as well as in models of neutron scattering and related effects. The concept of phonons was introduced in 1932 by Soviet Union, Soviet physicist Igor Tamm. The name ''phonon'' comes from the Ancient Greek language, Greek word (), which translates to ''so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystallographic Defect
A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell parameters in crystals, exhibit a periodic crystal structure, but this is usually imperfect.Ehrhart, P. (1991Properties and interactions of atomic defects in metals and alloys, volume 25 of Landolt-Börnstein, New Series III, chapter 2, p. 88, Springer, Berlin Several types of defects are often characterized: point defects, line defects, planar defects, bulk defects. Topological homotopy establishes a mathematical method of characterization. Point defects Point defects are defects that occur only at or around a single lattice point. They are not extended in space in any dimension. Strict limits for how small a point defect is are generally not defined explicitly. However, these defects typically involve at most a few extra or missing atoms. La ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Scattering
Electron scattering occurs when electrons are deviated from their original trajectory. This is due to the electrostatic forces within matter interaction or, if an external magnetic field is present, the electron may be deflected by the Lorentz force. This scattering typically happens with solids such as metals, semiconductors and insulators; and is a limiting factor in integrated circuits and transistors. The application of electron scattering is such that it can be used as a high resolution microscope for hadronic systems, that allows the measurement of the distribution of charges for nucleons and nuclear structure. The scattering of electrons has allowed us to understand that protons and neutrons are made up of the smaller elementary subatomic particles called quarks. Electrons may be scattered through a solid in several ways: *Not at all: no electron scattering occurs at all and the beam passes straight through. *Single scattering: when an electron is scattered just once. *Plu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Packet
In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere. Each component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant (no dispersion, see figure) or it may change (dispersion) while propagating. Quantum mechanics ascribes a special significance to the wave packet; it is interpreted as a probability amplitude, its norm squared describing the probability density that a particle or particles in a particular state will be measured to have a given position or momentum. The wave equation is in this case the Schrödinger equation, and through its ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heisenberg Uncertainty Principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, ''x'', and momentum, ''p'', can be predicted from initial conditions. Such variable pairs are known as complementary variables or canonically conjugate variables; and, depending on interpretation, the uncertainty principle limits to what extent such conjugate properties maintain their approximate meaning, as the mathematical framework of quantum physics does not support the notion of simultaneously well-defined conjugate properties expressed by a single value. The uncertainty principle implies that it is in general not possible to predict the value of a quantity with arbitrary certainty, even if all initial conditions are specified. Introduced first in 1927 by the German physicist Werner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Velocity
The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the ''modulation'' or ''envelope'' of the wave—propagates through space. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as a capillary wave. The expanding ring of waves is the wave group, within which one can discern individual waves that travel faster than the group as a whole. The amplitudes of the individual waves grow as they emerge from the trailing edge of the group and diminish as they approach the leading edge of the group. Definition and interpretation Definition The group velocity is defined by the equation: :v_ \ \equiv\ \frac\, where is the wave's angular frequency (usually expressed in radians per second), and is the angular wavenumber (usually expressed in radians per meter). The phase velocity is: . The function , which gi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Packet (dispersion)
In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere. Each component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant (no dispersion, see figure) or it may change (dispersion) while propagating. Quantum mechanics ascribes a special significance to the wave packet; it is interpreted as a probability amplitude, its norm squared describing the probability density that a particle or particles in a particular state will be measured to have a given position or momentum. The wave equation is in this case the Schrödinger equation, and through its ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Mass (solid-state Physics)
In solid state physics, a particle's effective mass (often denoted m^*) is the mass that it ''seems'' to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles in a periodic potential, over long distances larger than the lattice spacing, can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass. For some purposes and some materials, the effective mass can be considered to be a simple constant of a material. In general, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated as a factor multiplying the rest mass of an electron, ''m'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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