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Topological Insulators
A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material. A topological insulator is an insulator for the same reason a "trivial" (ordinary) insulator is: there exists an energy gap between the valence and conduction bands of the material. But in a topological insulator, these bands are, in an informal sense, "twisted", relative to a trivial insulator. The topological insulator cannot be continuously transformed into a trivial one without untwisting the bands, which closes the band gap and creates a conducting state. Thus, due to the continuity of the underlying field, the border of a topological insulator with a trivial insulator (including vacuum, which is topologically trivial) is forced to support a conducting state. Since this results from a global property of the topological insulator's band structure, local (symmetry- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Insulator Informal Phase Diagram
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a ''topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connectedne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Table Of Topological Invariants
The periodic table of topological invariants is an application of topology to physics. It indicates the group of topological invariant for topological insulators and superconductors in each dimension and in each discrete symmetry class. Discrete symmetry classes There are ten discrete symmetry classes of topological insulators and superconductors, corresponding to the ten Altland–Zirnbauer classes of random matrices. They are defined by three symmetries of the Hamiltonian \hat = \sum_ H_ c_i^ c_j, (where c_i, and c_i^, are the annihilation and creation operators of mode i, in some arbitrary spatial basis) : time reversal symmetry, particle hole (or charge conjugation) symmetry, and chiral (or sublattice) symmetry. Chiral symmetry is a unitary operator S, that acts on c_i, as a unitary rotation (S c_i S^ = (U_S)_ c_j,) and satisfies S^2 = 1. A Hamiltonian H possesses chiral symmetry when S\hatS^=-\hat, for some choice of S (on the level of first-quantised Hamiltonians, this m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laurens W
Laurens may refer to: Places United States * Laurens County, Georgia * Laurens, Iowa, a city * Laurens (town), New York * Laurens (village), New York * Laurens, South Carolina, a city * Laurens County, South Carolina * Fort Laurens, an American Revolutionary War fort in what is now Ohio Elsewhere * Laurens, Hérault, commune in the Hérault département, southern France * Laurens Peninsula, Heard Island, Indian Ocean ** Cape Laurens, on the Laurens Peninsula Other uses * Laurens (given name) * Laurens (surname) * USS ''Laurens'' (APA-153), a World War II attack transport ship * Laurens Railroad (1854-1881), a railroad in South Carolina * Laurens Railway (1881-1894), successor of the Laurens Railroad * Laurens (horse) (born 2015), thoroughbred racehorse See also * Laurenz (name) * Lawrence (other) Lawrence may refer to: Education Colleges and universities * Lawrence Technological University, a university in Southfield, Michigan, United States * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cadmium Telluride
Cadmium telluride (CdTe) is a stable crystalline compound formed from cadmium and tellurium. It is mainly used as the semiconducting material in cadmium telluride photovoltaics and an infrared optical window. It is usually sandwiched with cadmium sulfide to form a p–n junction solar PV cell. Applications CdTe is used to make thin film solar cells, accounting for about 8% of all solar cells installed in 2011. They are among the lowest-cost types of solar cell, although a comparison of total installed cost depends on installation size and many other factors, and has changed rapidly from year to year. The CdTe solar cell market is dominated by First Solar. In 2011, around 2 GWp of CdTe solar cells were produced; For more details and discussion see cadmium telluride photovoltaics. CdTe can be alloyed with mercury to make a versatile infrared detector material ( HgCdTe). CdTe alloyed with a small amount of zinc makes an excellent solid-state X-ray and gamma ray detect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mercury Telluride
Mercury telluride (HgTe) is a binary chemical compound of mercury and tellurium. It is a semi-metal related to the II-VI group of semiconductor materials. Alternative names are mercuric telluride and mercury(II) telluride. HgTe occurs in nature as the mineral form coloradoite. Physical properties All properties are at standard temperature and pressure unless stated otherwise. The lattice parameter is about 0.646 nm in the cubic crystalline form. The bulk modulus is about 42.1 GPa. The thermal expansion coefficient is about 5.2×10−6/K. Static dielectric constant 20.8, dynamic dielectric constant 15.1. Thermal conductivity is low at 2.7 W·m2/(m·K). HgTe bonds are weak leading to low hardness values. Hardness 2.7×107 kg/m2. Doping N-type doping can be achieved with elements such as boron, aluminium, gallium, or indium. Iodine and iron will also dope n-type. HgTe is naturally p-type due to mercury vacancies. P-type doping is also achieved by introducing zinc, copper, si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tin Telluride
Tin telluride is a compound of tin and tellurium (SnTe); is a IV-VI narrow band gap semiconductor and has direct band gap of 0.18 eV. It is often alloyed with lead to make lead tin telluride, which is used as an infrared detector material. Tin telluride normally forms p-type semiconductor (Extrinsic semiconductor) due to tin vacancies and is a low temperature superconductor. SnTe exists in three crystal phases. At Low temperatures, where the concentration of hole carriers is less than 1.5x1020 cm−3 , Tin Telluride exists in rhombohedral phase also known as α-SnTe. At room temperature and atmospheric pressure, Tin Telluride exists in NaCl-like cubic crystal phase, known as β-SnTe. While at 18 kbar pressure, β-SnTe transforms to γ-SnTe, orthorhombic phase, space group Pnma. This phase change is characterized by 11 percent increase in density and 360 percent increase in resistance for γ-SnTe. Tin telluride is a thermoelectric material. Theoretical studies imply that the n- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lead Telluride
Lead telluride is a compound of lead and tellurium (PbTe). It crystallizes in the NaCl crystal structure with Pb atoms occupying the cation and Te forming the anionic lattice. It is a narrow gap semiconductor with a band gap of 0.32 eV. It occurs naturally as the mineral altaite. Properties * Dielectric constant ~1000. * Electron Effective mass ~ 0.01 ''m''e * Hole mobility, μp = 600 cm2 V−1 s−1 (0 K); 4000 cm2 V−1 s−1 (300 K) Applications PbTe has proven to be a very important intermediate thermoelectric material. The performance of thermoelectric materials can be evaluated by the figure of merit, ZT=S^2\sigma T/\kappa, in which S is the Seebeck coefficient, \sigma is the electrical conductivity and \kappa is the thermal conductivity. In order to improve the thermoelectric performance of materials, the power factor (S^2\sigma) needs to be maximized and the thermal conductivity needs to be minimized. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acoustics
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries. Hearing is one of the most crucial means of survival in the animal world and speech is one of the most distinctive characteristics of human development and culture. Accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound and hearing as a key element of mating rituals or for marking territories. Art, craft, science and technology have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Topological Insulators
Magnetic topological insulators are three dimensional magnetic materials with a non-trivial topological index protected by a symmetry other than time-reversal. In contrast with a non-magnetic topological insulator, a magnetic topological insulator can have naturally gapped surface states as long as the quantizing symmetry is broken at the surface. These gapped surfaces exhibit a topologically protected half-quantized surface anomalous Hall conductivity (e^2/2h) perpendicular to the surface. The sign of the half-quantized surface anomalous Hall conductivity depends on the specific surface termination. Theory Axion coupling The \mathbb_2 classification of a 3D crystalline topological insulator can be understood in terms of the axion coupling \theta. A scalar quantity that is determined from the ground state wavefunction :\theta = -\frac\int_ d^3k \, \epsilon^ \text \Big \mathcal_\alpha \partial_\beta \mathcal_\gamma -i\frac \mathcal_\alpha \mathcal_\beta \mathcal_\gamma \Big ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photonic Topological Insulator
Photonic topological insulators are artificial electromagnetic materials that support topologically non-trivial, unidirectional states of light. Photonic topological phases are classical electromagnetic wave analogues of electronic topological phases studied in condensed matter physics. Similar to their electronic counterparts, they, can provide robust unidirectional channels for light propagation. The field that studies these phases of light is referred to as topological photonics, even though the working frequency of these ''electromagnetic'' topological insulators may fall in other parts of the electromagnetic spectrum such as the microwave range. History Topological order in solid state systems has been studied in condensed matter physics since the discovery of integer quantum Hall effect. But topological matter attracted considerable interest from the physics community after the proposals for possible observation of symmetry-protected topological phases (or the so-called ''t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Umklapp Scattering
In crystalline materials, Umklapp scattering (also U-process or Umklapp process) is a scattering process that results in a wave vector (usually written ''k'') which falls outside the first Brillouin zone. If a material is periodic, it has a Brillouin zone, and any point outside the first Brillouin zone can also be expressed as a point inside the zone. So, the wave vector is then mathematically transformed to a point inside the first Brillouin zone. This transformation allows for scattering processes which would otherwise violate the conservation of momentum: two wave vectors pointing to the right can combine to create a wave vector that points to the left. This non-conservation is why crystal momentum is not a true momentum. Examples include electron-lattice potential scattering or an anharmonic phonon-phonon (or electron-phonon) scattering process, reflecting an electronic state or creating a phonon with a momentum ''k''-vector outside the first Brillouin zone. Umklapp scatt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Quantum Number
In atomic physics, the spin quantum number is a quantum number (designated ) which describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. The phrase was originally used to describe the fourth of a set of quantum numbers (the principal quantum number , the azimuthal quantum number , the magnetic quantum number , and the spin quantum number ), which completely describe the quantum state of an electron in an atom. The name comes from a physical spinning of the electron about an axis, as proposed by Uhlenbeck and Goudsmit. The value of is the component of spin angular momentum parallel to a given direction (the –axis), which can be either +1/2 or –1/2 (in units of the reduced Planck constant). However this simplistic picture was quickly realized to be physically impossible because it would require the electrons to rotate faster than the speed of light. It was therefore replaced by a more abstract quantum-mechan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
