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Coulomb Gap
First introduced by M. Pollak, the Coulomb gap is a soft gap in the single-particle density of states (DOS) of a system of interacting localized electrons. Due to the long-range Coulomb interactions, the single-particle DOS vanishes at the chemical potential, at low enough temperatures, such that thermal excitations do not wash out the gap. Theory At zero temperature, a classical treatment of a system gives an upper bound for the DOS near the Fermi energy, first suggested by Efros and Shklovskii. The argument is as follows: Let us look at the ground state configuration of the system. Defining E_i as the energy of an electron at site i , due to the disorder and the Coulomb interaction with all other electrons (we define this both for occupied and unoccupied sites), it is easy to see that the energy needed to move an electron from an occupied site i to an unoccupied site j is given by the expression: :\Delta E=E_j-E_i-e^2/r_ . The subtraction of the last term accounts fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy Gap
In solid-state physics, an energy gap is an energy range in a solid where no electron states exist, i.e. an energy range where the density of states vanishes. Especially in condensed-matter physics, an energy gap is often known more abstractly as a spectral gap, a term which need not be specific to electrons or solids. Band gap If an energy gap exists in the band structure of a material, it is called band gap. The physical properties of semiconductors are to a large extent determined by their band gaps, but also for insulators and metals the band structure—and thus any possible band gaps—govern their electronic properties. Superconductors For superconductors the energy gap is a region of suppressed density of states around the Fermi energy, with the size of the energy gap much smaller than the energy scale of the band structure. The superconducting energy gap is a key aspect in the theoretical description of superconductivity and thus features prominently in BCS theory. Her ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Of States
In solid state physics and condensed matter physics, the density of states (DOS) of a system describes the number of modes per unit frequency range. The density of states is defined as D(E) = N(E)/V , where N(E)\delta E is the number of states in the system of volume V whose energies lie in the range from E to E+\delta E. It is mathematically represented as a distribution by a probability density function, and it is generally an average over the space and time domains of the various states occupied by the system. The density of states is directly related to the dispersion relations of the properties of the system. High DOS at a specific energy level means that many states are available for occupation. Generally, the density of states of matter is continuous. In isolated systems however, such as atoms or molecules in the gas phase, the density distribution is discrete, like a spectral density. Local variations, most often due to distortions of the original system, are often referr ... [...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] |
Alexei L
Alexey, Alexei, Alexie, Aleksei, or Aleksey (russian: Алексе́й ; bg, Алексей ) is a Russian language, Russian and Bulgarian language, Bulgarian male first name deriving from the Greek language, Greek ''Aléxios'' (), meaning "Defender", and thus of the same origin as the Latin Alexius. Alexey may also be Romanization of Russian, romanized as ''Aleksei'', ''Aleksey'', ''Alexej'', ''Aleksej'', etc. It has been commonly westernized as Alexis (given name), Alexis. Similar Ukraine, Ukrainian and Belarus, Belarusian names are romanized as Oleksii (Олексій) and Aliaksiej (Аляксей), respectively. The Russian Orthodox Church uses the Old Church Slavonic version, Alexiy (Алексiй, or Алексий in modern spelling), for its Saints and hierarchs (most notably, this is the form used for Patriarchs Partiarch Alexius I, Alexius I and Patriarch Alexius II, Alexius II). The common hypocoristic is Alyosha (other), Alyosha () or simply Lyosha () ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boris Shklovskii
Boris Ionovich Shklovskii (born 1944) is a theoretical physicist, at the William I Fine Theoretical Physics Institute, University of Minnesota, specializing in condensed matter. Shklovskii earned his A.B. degree in Physics, in 1966 and a Ph.D. in condensed matter theory, in 1968 from Leningrad University.UMN BIO physics Shklovskii Retrieved 28 April 2019. Shklovskii is known for the Efros–Shklovskii variable-range hopping conductivity, a model for the temperature dependence of the electrical conductivity in the variable-range hopping regime. He has also made important contributions to the theory of the |
Ground State
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator that acts non-trivially on a ground state and commutes with the Hamiltonian of the system. According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero. It is also possible for the highest excited state to have absolute zero temper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum ( spin) of a half-integer value, expressed in units of the reduced Planck constant, . Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable-range Hopping
Variable-range hopping is a model used to describe carrier transport in a disordered semiconductor or in amorphous solid by hopping in an extended temperature range. It has a characteristic temperature dependence of :\sigma= \sigma_0e^ where \sigma is the conductivity and \beta is a parameter dependent on the model under consideration. Mott variable-range hopping The Mott variable-range hopping describes low-temperature conduction in strongly disordered systems with localized charge-carrier states and has a characteristic temperature dependence of :\sigma= \sigma_0e^ for three-dimensional conductance (with \beta = 1/4), and is generalized to ''d''-dimensions :\sigma= \sigma_0e^. Hopping conduction at low temperatures is of great interest because of the savings the semiconductor industry could achieve if they were able to replace single-crystal devices with glass layers. Derivation The original Mott paper introduced a simplifying assumption that the hopping energy depends in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coulomb's Law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventionally called ''electrostatic force'' or Coulomb force. Although the law was known earlier, it was first published in 1785 by French physicist Charles-Augustin de Coulomb, hence the name. Coulomb's law was essential to the development of the theory of electromagnetism, maybe even its starting point, as it made it possible to discuss the quantity of electric charge in a meaningful way. The law states that the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. Coulomb studied the repulsive force between bodies having electrical charges of the same sign: Coulomb also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Band Structures
Electronic may refer to: *Electronics, the science of how to control electric energy in semiconductor * ''Electronics'' (magazine), a defunct American trade journal *Electronic storage, the storage of data using an electronic device *Electronic commerce or e-commerce, the trading in products or services using computer networks, such as the Internet *Electronic publishing or e-publishing, the digital publication of books and magazines using computer networks, such as the Internet *Electronic engineering, an electrical engineering discipline Entertainment *Electronic (band), an English alternative dance band ** ''Electronic'' (album), the self-titled debut album by British band Electronic *Electronic music, a music genre *Electronic musical instrument *Electronic game, a game that employs electronics See also *Electronica, an electronic music genre *Consumer electronics Consumer electronics or home electronics are electronic ( analog or digital) equipment intended for everyd ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions. This established the fields of statistical thermodynamics and statistical physics. The founding of the field of statistical mechanics is generally credited to three physicists: *Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates *James Clerk Maxwell, who developed models of probability distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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