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Lindhard Theory
In condensed matter physics, Lindhard theoryN. W. Ashcroft and N. D. Mermin, ''Solid State Physics'' (Thomson Learning, Toronto, 1976) is a method of calculating the effects of electric field screening by electrons in a solid. It is based on quantum mechanics (first-order perturbation theory) and the random phase approximation. It is named after Danish physicist Jens Lindhard, who first developed the theory in 1954. Thomas–Fermi screening and the plasma oscillations can be derived as a special case of the more general Lindhard formula. In particular, Thomas–Fermi screening is the limit of the Lindhard formula when the wavevector (the reciprocal of the length-scale of interest) is much smaller than the Fermi wavevector, i.e. the long-distance limit. The Lorentz–Drude expression for the plasma oscillations are recovered in the dynamic case (long wavelengths, finite frequency). This article uses cgs-Gaussian units. Formula The Lindhard formula for the longitudinal dielec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Channelling (physics)
In condensed-matter physics, channelling (or channeling) is the process that constrains the path of a charged particle in a crystalline solid. Many physical phenomena can occur when a charged particle is incident upon a solid target, e.g., elastic scattering, inelastic energy-loss processes, secondary-electron emission, electromagnetic radiation, nuclear reactions, etc. All of these processes have cross sections which depend on the impact parameters involved in collisions with individual target atoms. When the target material is homogeneous and isotropic, the impact-parameter distribution is independent of the orientation of the momentum of the particle and interaction processes are also orientation-independent. When the target material is monocrystalline, the yields of physical processes are very strongly dependent on the orientation of the momentum of the particle relative to the crystalline axes or planes. Or in other words, the stopping power of the particle is much lower in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Electron Model
In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model. Given its simplicity, it is surprisingly successful in explaining many experimental phenomena, especially * the Wiedemann–Franz law which relates electrical conductivity and thermal conductivity; * the temperature dependence of the electron heat capacity; * the shape of the electronic density of states; * the range of binding energy values; * electrical conductivities; * the Seebeck coefficient of the thermoelectric effect; * thermal electron emission and field electron emission from bulk metals. The free electron model solved many of the inconsistencies related to the Drude model and gave insight into several other properties of metals. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pomeranchuk Instability
The Pomeranchuk instability is an instability in the shape of the Fermi surface of a material with interacting fermions, causing Landau’s Fermi liquid theory to break down. It occurs when a Landau parameter in Fermi liquid theory has a sufficiently negative value, causing deformations of the Fermi surface to be energetically favourable. It is named after the Soviet physicist Isaak Pomeranchuk. Introduction: Landau parameter for a Fermi liquid In a Fermi liquid, renormalized single electron propagators (ignoring spin) are G(K)=\frac\text where capital momentum letters denote four-vectors K=(k_0,\vec) and the Fermi surface has zero energy; poles of this function determine the quasiparticle energy-momentum dispersion relation. The four-point vertex function \Gamma_ describes the diagram with two incoming electrons of momentum K_1 and two outgoing electrons of momentum K_3 and and amputated external lines:\begin \Gamma_&=\int \\ &=(2\pi)^8 \delta(K_1-K_3)\delta(K_2-K_4) G(K_1) G(K_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kohn Anomaly
In the field of physics concerning Condensed matter physics, condensed matter, a Kohn anomaly (also called the Kohn effect) is an anomaly in the dispersion relation of a phonon branch in a metal. It is named for Walter Kohn. For a specific wavevector, the frequency (and thus the energy) of the associated phonon is considerably lowered, and there is a discontinuity in its derivative. They have been first proposed by Walter Kohn in 1959. In extreme cases (that can happen in low-dimensional materials), the energy of this phonon is zero, meaning that a static distortion of the lattice appears. This is one explanation for Spin density wave, charge density waves in solids. The wavevectors at which a Kohn anomaly is possible are the nesting vectors of the Fermi surface, that is vectors that connect a lot of points of the Fermi surface (for a one-dimensional chain of atoms this vector would be 2k_). The electron phonon interaction causes a rigid shift of the Fermi sphere and a failure of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Platinum
Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver". Platinum is a member of the platinum group of elements and group 10 of the periodic table of elements. It has six naturally occurring isotopes. It is one of the rarer elements in Earth's crust, with an average abundance of approximately 5 μg/kg. It occurs in some nickel and copper ores along with some native deposits, mostly in South Africa, which accounts for ~80% of the world production. Because of its scarcity in Earth's crust, only a few hundred tonnes are produced annually, and given its important uses, it is highly valuable and is a major precious metal commodity. Platinum is one of the least reactive metals. It has remarkable resistance to corrosion, even at high temperatures, and is therefore considered a noble metal. Consequent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-dimensional Electron Gas
A two-dimensional electron gas (2DEG) is a scientific model in solid-state physics. It is an electron gas that is free to move in two dimensions, but tightly confined in the third. This tight confinement leads to quantized energy levels for motion in the third direction, which can then be ignored for most problems. Thus the electrons appear to be a 2D sheet embedded in a 3D world. The analogous construct of holes is called a two-dimensional hole gas (2DHG), and such systems have many useful and interesting properties. Realizations Most 2DEGs are found in transistor-like structures made from semiconductors. The most commonly encountered 2DEG is the layer of electrons found in MOSFETs (metal-oxide-semiconductor field-effect transistors). When the transistor is in inversion mode, the electrons underneath the gate oxide are confined to the semiconductor-oxide interface, and thus occupy well defined energy levels. For thin-enough potential wells and temperatures not too high, only ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Debye Length
In plasmas and electrolytes, the Debye length \lambda_ (also called Debye radius), is a measure of a charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists. With each Debye length the charges are increasingly electrically screened and the electric potential decreases in magnitude by 1/ e. A Debye sphere is a volume whose radius is the Debye length. Debye length is an important parameter in plasma physics, electrolytes, and colloids (DLVO theory). The corresponding Debye screening wave vector k_=1/\lambda_ for particles of density n, charge q at a temperature T is given by k_^2=4\pi n q^2/(k_T) in Gaussian units. Expressions in MKS units will be given below. The analogous quantities at very low temperatures (T \to 0) are known as the Thomas–Fermi length and the Thomas–Fermi wave vector. They are of interest in describing the behaviour of electrons in metals at room temperature. The Debye length is named after the Dutch-America ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi Energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band. The term "Fermi energy" is often used to refer to a different yet closely related concept, the Fermi ''level'' (also called electrochemical potential).The use of the term "Fermi energy" as synonymous with Fermi level (a.k.a. electrochemical potential) is widespread in semiconductor physics. For example:''Electronics (fundamentals And Applications)''by D. Chattopadhyay''Semiconductor Physics and Applications''by Balkanski and Wallis. There are a few key differences between the Fermi level and Fermi energy, at least as they are used in this article: * The Fermi energy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi Gas
An ideal Fermi gas is a state of matter which is an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer spin. These statistics determine the energy distribution of fermions in a Fermi gas in thermal equilibrium, and is characterized by their number density, temperature, and the set of available energy states. The model is named after the Italian physicist Enrico Fermi. This physical model can be accurately applied to many systems with many fermions. Some key examples are the behaviour of charge carriers in a metal, nucleons in an atomic nucleus, neutrons in a neutron star, and electrons in a white dwarf. Description An ideal Fermi gas or free Fermi gas is a physical model assuming a collection of non-interacting fermions in a constant potential well. Fermions are elementary or composite particles with half-integer spin, thus follow Fermi-Dira ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Screening
Screening may refer to: * Screening cultures, a type a medical test that is done to find an infection * Screening (economics), a strategy of combating adverse selection (includes sorting resumes to select employees) * Screening (environmental), a set of analytical techniques used to monitor levels of potentially hazardous organic compounds in the environment * Screening (medicine), a strategy used in a population to identify an unrecognised disease in individuals without signs or symptoms * Screening (printing), a process that represents lighter shades as tiny dots, rather than solid areas, of ink by passing ink through * Screening (process stage), process stage when cleaning paper pulp * Screening (tactical), one military unit providing cover for another in terms of both physical presence and firepower * Baggage screening, a security measure * Call screening, the process of evaluating the characteristics of a telephone call before deciding how or whether to answer it * Electric- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yukawa Potential
In particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential named after the Japanese physicist Hideki Yukawa. The potential is of the form: :V_\text(r)= -g^2\frac, where is a magnitude scaling constant, i.e. is the amplitude of potential, is the mass of the particle, is the radial distance to the particle, and is another scaling constant, so that r \approx \tfrac is the approximate range. The potential is monotonically increasing in and it is negative, implying the force is attractive. In the SI system, the unit of the Yukawa potential is (1/meters). The Coulomb potential of electromagnetism is an example of a Yukawa potential with the e^ factor equal to 1, everywhere. This can be interpreted as saying that the photon mass is equal to 0. The photon is the force-carrier between interacting, charged particles. In interactions between a meson field and a fermion field, the constant is equal to the gauge c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Drude Model
The Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials (especially metals). Basically, Ohm's law was well established and stated that the current ''J'' and voltage ''V'' driving the current are related to the resistance ''R'' of the material. The inverse of the resistance is known as the conductance. When we consider a metal of unit length and unit cross sectional area, the conductance is known as the conductivity, which is the inverse of resistivity. The Drude model attempts to explain the resistivity of a conductor in terms of the scattering of electrons (the carriers of electricity) by the relatively immobile ions in the metal that act like obstructions to the flow of electrons. The model, which is an application of kinetic theory, assumes that the microscopic behaviour of electrons in a solid may be treated classically and behaves much like a pinball machine, with a sea of constantly jittering e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
