|
Local Density Of States
In condensed matter physics, the density of states (DOS) of a system describes the number of allowed modes or states per unit energy range. The density of states is defined as 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 referred to as local densities o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconductivity, superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of Spin (physics), spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theoretical physics, physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutron Matter
Degenerate matter occurs when the Pauli exclusion principle significantly alters a state of matter at low temperature. The term is used in astrophysics to refer to dense stellar objects such as white dwarfs and neutron stars, where thermal pressure alone is not enough to prevent gravitational collapse. The term also applies to metals in the Fermi gas approximation. Degenerate matter is usually modelled as an ideal Fermi gas, an ensemble of non-interacting fermions. In a quantum mechanical description, particles limited to a finite volume may take only a discrete set of energies, called quantum states. The Pauli exclusion principle prevents identical fermions from occupying the same quantum state. At lowest total energy (when the thermal energy of the particles is negligible), all the lowest energy quantum states are filled. This state is referred to as full degeneracy. This degeneracy pressure remains non-zero even at absolute zero temperature.see http://apod.nasa.gov/apod/ap10022 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nanotechnology
Nanotechnology is the manipulation of matter with at least one dimension sized from 1 to 100 nanometers (nm). At this scale, commonly known as the nanoscale, surface area and quantum mechanical effects become important in describing properties of matter. This definition of nanotechnology includes all types of research and technologies that deal with these special properties. It is common to see the plural form "nanotechnologies" as well as "nanoscale technologies" to refer to research and applications whose common trait is scale. An earlier understanding of nanotechnology referred to the particular technological goal of precisely manipulating atoms and molecules for fabricating macroscale products, now referred to as molecular nanotechnology. Nanotechnology defined by scale includes fields of science such as surface science, organic chemistry, molecular biology, semiconductor physics, energy storage, engineering, microfabrication, and molecular engineering. The associated rese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luttinger Liquid
A Luttinger liquid, or Tomonaga–Luttinger liquid, is a theoretical model describing interacting electrons (or other fermions) in a one-dimensional conductor (e.g. quantum wires such as carbon nanotubes). Such a model is necessary as the commonly used Fermi liquid model breaks down for one dimension. The Tomonaga–Luttinger's liquid was first proposed by Sin-Itiro Tomonaga in 1950. The model showed that under certain constraints, second-order interactions between electrons could be modelled as bosonic interactions. In 1963, J.M. Luttinger reformulated the theory in terms of Bloch sound waves and showed that the constraints proposed by Tomonaga were unnecessary in order to treat the second-order perturbations as bosons. But his solution of the model was incorrect; the correct solution was given by and Elliot H. Lieb 1965. Theory Luttinger liquid theory describes low energy excitations in a 1D electron gas as bosons. Starting with the free electron Hamiltonian: H = \sum_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Wire
In mesoscopic physics, a quantum wire is an electrically conducting wire in which quantum effects influence the transport properties. Usually such effects appear in the dimension of nanometers, so they are also referred to as nanowires. Quantum effects If the diameter of a wire is sufficiently small, electrons will experience quantum confinement in the transverse direction. As a result, their transverse energy will be limited to a series of discrete values. One consequence of this quantization is that the classical formula for calculating the electrical resistance of a wire, : R = \rho \frac, is not valid for quantum wires (where \rho is the material's resistivity, l is the length, and A is the cross-sectional area of the wire). Instead, an exact calculation of the transverse energies of the confined electrons has to be performed to calculate a wire's resistance. Following from the quantization of electron energy, the electrical conductance (the inverse of the resistance) is fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carbon Nanotubes
A carbon nanotube (CNT) is a tube made of carbon with a diameter in the nanometre range (nanoscale). They are one of the allotropes of carbon. Two broad classes of carbon nanotubes are recognized: * ''Single-walled carbon nanotubes'' (''SWCNTs'') have diameters around 0.5–2.0 nanometer, nanometres, about 100,000 times smaller than the width of a human hair. They can be idealised as cutouts from a two-dimensional graphene sheet rolled up to form a hollow cylinder. * ''Multi-walled carbon nanotubes'' (''MWCNTs'') consist of nested single-wall carbon nanotubes in a nested, tube-in-tube structure. Double- and triple-walled carbon nanotubes are special cases of MWCNT. Carbon nanotubes can exhibit remarkable properties, such as exceptional tensile strength and thermal conductivity because of their nanostructure and bond strength, strength of the bonds between carbon atoms. Some SWCNT structures exhibit high electrical conductivity while others are semiconductors. In addition, ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MOSFET
upright=1.3, Two power MOSFETs in amperes">A in the ''on'' state, dissipating up to about 100 watt">W and controlling a load of over 2000 W. A matchstick is pictured for scale. In electronics, the metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, MOS FET, or MOS transistor) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which determines the conductivity of the device. This ability to change conductivity with the amount of applied voltage can be used for amplifying or switching electronic signals. The term ''metal–insulator–semiconductor field-effect transistor'' (''MISFET'') is almost synonymous with ''MOSFET''. Another near-synonym is ''insulated-gate field-effect transistor'' (''IGFET''). The main advantage of a MOSFET is that it requires almost no input current to control the load current under steady-state or low-frequency conditions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Hall Effect
The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exhibits steps that take on the quantized values : R_ = \frac = \frac , where is the Hall voltage, is the channel current, is the elementary charge and is the Planck constant. The divisor can take on either integer () or fractional () values. Here, is roughly but not exactly equal to the filling factor of Landau levels. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether is an integer or fraction, respectively. The striking feature of the integer quantum Hall effect is the persistence of the quantization (i.e. the Hall plateau) as the electron density is varied. Since the electron density remains constant when the Fermi level is in a clean spectral gap, this situation corre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphite
Graphite () is a Crystallinity, crystalline allotrope (form) of the element carbon. It consists of many stacked Layered materials, layers of graphene, typically in excess of hundreds of layers. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on a large scale (1.3million metric tons per year in 2022) for uses in many critical industries including refractories (50%), lithium-ion batteries (18%), foundries (10%), and lubricants (5%), among others (17%). Graphite converts to diamond under extremely high pressure and temperature. Graphite's low cost, thermal and chemical inertness and characteristic conductivity of heat and electricity finds numerous applications in high energy and high temperature processes. Types and varieties Graphite can occur naturally or be produced synthetically. Natural graphite is obtained from naturally occurring geologic deposits and synthetic graphite is produced t ... [...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 Fermi gas, 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 electron hole, 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 layer (semiconductors), inversion mode, the electrons underneath the gate oxide are confined to the semiconductor-oxide interface, and thus occupy well defined energy levels. For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Topology
In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on n-dimensional Euclidean space \R^n by the Euclidean metric. Definition The Euclidean norm on \R^n is the non-negative function \, \cdot\, : \R^n \to \R defined by \left\, \left(p_1, \ldots, p_n\right)\right\, ~:=~ \sqrt. Like all norms, it induces a canonical metric defined by d(p, q) = \, p - q\, . The metric d : \R^n \times \R^n \to \R induced by the Euclidean norm is called the Euclidean metric or the Euclidean distance and the distance between points p = \left(p_1, \ldots, p_n\right) and q = \left(q_1, \ldots, q_n\right) is d(p, q) ~=~ \, p - q\, ~=~ \sqrt. In any metric space In mathematics, a metric space is a Set (mathematics), set together with a notion of ''distance'' between its Element (mathematics), elements, usually called point (geometry), points. The distance is measured by a function (mathematics), functi ..., the open balls form a base fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi Gas
A Fermi gas is an idealized model, 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 is useful for certain 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–Dirac statistics. The e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
