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Fermi Surface
In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied electron states from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic band structure, electronic energy bands. The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle, which allows a maximum of one electron per quantum state. The study of the Fermi surfaces of materials is called fermiology. Theory Consider a Spin (physics), spin-less ideal Fermi gas of N particles. According to Fermi–Dirac statistics, the mean occupation number of a state with energy \epsilon_i is given by : \langle n_i\rangle =\frac, where * \left\langle n_i\right\rangle is the mean occupation number of the ith state * \epsilon_i is the kinetic energy of the ith state * \mu is the chemical potential (at zero temperature, this is th ... [...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] |
Electrical Insulation
Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwell's equations. Common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others. The presence of either a positive or negative electric charge produces an electric field. The motion of electric charges is an electric current and produces a magnetic field. In most applications, Coulomb's law determines the force acting on an electric charge. Electric potential is the work done to move an electric charge from one point to another within an electric field, typically measured in volts. Electricity plays a central role in many modern technologies, serving in electric power where electric current is used to energise equipment, and in electronics dealing wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermion
In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and all composite particles made of an even and odd, odd number of these, such as all baryons and many atoms and atomic nucleus, nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics. Some fermions are elementary particles (such as electrons), and some are composite particles (such as protons). For example, according to the spin-statistics theorem in Theory of relativity, relativistic quantum field theory, particles with integer Spin (physics), spin are bosons. In contrast, particles with half-integer spin are fermions. In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is usually referr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Density Wave
Spin-density wave (SDW) and charge-density wave (CDW) are names for two similar low-energy ordered states of solids. Both these states occur at low temperature in anisotropic, low-dimensional materials or in metals that have high densities of states at the Fermi level N(E_F). Other low-temperature ground states that occur in such materials are superconductivity, ferromagnetism and antiferromagnetism. The transition to the ordered states is driven by the condensation energy which is approximately N(E_F) \Delta^2 where \Delta is the magnitude of the energy gap opened by the transition. Fundamentally SDWs and CDWs involve the development of a superstructure in the form of a periodic modulation in the density of the electronic spins and charges with a characteristic spatial frequency q that does not transform according to the symmetry group that describes the ionic positions. The new periodicity associated with CDWs can easily be observed using scanning tunneling microscopy or elect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jahn–Teller Effect
The Jahn–Teller effect (JT effect or JTE) is an important mechanism of spontaneous symmetry breaking in molecular and solid-state systems which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science. The effect is named for Hermann Arthur Jahn and Edward Teller, who first reported studies about it in 1937. Simplified overview The Jahn–Teller effect, sometimes also referred to as Jahn–Teller distortion, describes the geometrical distortion of molecules and ions that results from certain electron configurations. The Jahn–Teller theorem essentially states that any non-linear molecule with a spatially degenerate energy level, degenerate electronic ground state will undergo a geometrical distortion that removes that degeneracy, because the distortion lowers the overall energy of the species. For a description of another type of geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ferromagnet
Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagnetic materials are noticeably attracted to a magnet, which is a consequence of their substantial magnetic permeability. Magnetic permeability describes the induced magnetization of a material due to the presence of an external magnetic field. For example, this temporary magnetization inside a steel plate accounts for the plate's attraction to a magnet. Whether or not that steel plate then acquires permanent magnetization depends on both the strength of the applied field and on the coercivity of that particular piece of steel (which varies with the steel's chemical composition and any heat treatment it may have undergone). In physics, multiple types of material magnetism have been distinguished. Ferromagnetism (along with the similar eff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. 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 temperature for sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Constant
A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal. A simple cubic crystal has only one lattice constant, the distance between atoms, but, in general, lattices in three dimensions have six lattice constants: the lengths ''a'', ''b'', and ''c'' of the three cell edges meeting at a vertex, and the angles ''α'', ''β'', and ''γ'' between those edges. The crystal lattice parameters ''a'', ''b'', and ''c'' have the dimension of length. The three numbers represent the size of the unit cell, that is, the distance from a given atom to an identical atom in the same position and orientation in a neighboring cell (except for very simple crystal structures, this will not necessarily be distance to the nearest neighbor). Their SI unit is the meter, and they are traditionally specified in angstroms (Å); an angstrom being 0.1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Arithmetic
In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book '' Disquisitiones Arithmeticae'', published in 1801. A familiar example of modular arithmetic is the hour hand on a 12-hour clock. If the hour hand points to 7 now, then 8 hours later it will point to 3. Ordinary addition would result in , but 15 reads as 3 on the clock face. This is because the hour hand makes one rotation every 12 hours and the hour number starts over when the hour hand passes 12. We say that 15 is ''congruent'' to 3 modulo 12, written 15 ≡ 3 (mod 12), so that 7 + 8 ≡ 3 (mod 12). Similarly, if one starts at 12 and waits 8 hours, the hour hand will be at 8. If one instead waited twice as long, 16 hours, the hour hand would be on 4. This ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brillouin Zone
In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space Reciprocal lattice is a concept associated with solids with translational symmetry which plays a major role in many areas such as X-ray diffraction, X-ray and Electron diffraction, electron diffraction as well as the Electronic band structure, e .... In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones. The boundaries of this cell are given by planes related to points on the reciprocal lattice. The importance of the Brillouin zone stems from the description of waves in a periodic medium given by Bloch's theorem, in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone. The first Brillouin zone is the locus of points in reciprocal space that are closer to the or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
