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Peierls Transition
A Peierls transition or Peierls distortion is a distortion of the periodic lattice of a one-dimensional crystal. Atomic positions oscillate, so that the perfect order of the 1-D crystal is broken. Peierls’ theorem Peierls' theorem states that ''a one-dimensional equally spaced chain with one electron per ion is unstable''. This theorem was first espoused in the 1930s by Rudolf Peierls. It can be proven using a simple model of the potential for an electron in a 1-D crystal with lattice spacing a. The periodicity of the crystal creates energy band gaps in the \epsilon-k diagram at the edge of the Brillouin zone ka=\pm\pi (similar to the result of the Kronig–Penney model, which helps to explain the origin of band gaps in semiconductors). If the ions each contribute one electron, then the band will be half-filled, up to values of ka=\pm \pi/2 in the ground state. Imagine a lattice distortion where every other ion moves closer to one neighbor and further away from the other, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peierls Instability Before
Sir Rudolf Ernst Peierls, (; ; 5 June 1907 – 19 September 1995) was a German-born British physicist who played a major role in Tube Alloys, Britain's nuclear weapon programme, as well as the subsequent Manhattan Project, the combined Allied nuclear bomb programme. His obituary in ''Physics Today'' described him as "a major player in the drama of the eruption of nuclear physics into world affairs". Peierls studied physics at the University of Berlin, at the University of Munich under Arnold Sommerfeld, the University of Leipzig under Werner Heisenberg, and ETH Zurich under Wolfgang Pauli. After receiving his DPhil from Leipzig in 1929, he became an assistant to Pauli in Zurich. In 1932, he was awarded a Rockefeller Fellowship, which he used to study in Rome under Enrico Fermi, and then at the Cavendish Laboratory at the University of Cambridge under Ralph H. Fowler. Because of his Jewish background, he elected to not return home after Adolf Hitler's rise to power in 1933, but ... [...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 liquid was first proposed by 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_ \epsilon_k c_ ... [...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] |
Renormalization Exponent
Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian. For example, an electron theory may begin by postulating an electron with an initial mass and charge. In quantum field theory a cloud of virtual particles, such as photons, positrons, and others surrounds and interacts with the initial electron. Accounting for the interactions of the surrounding particles (e.g. collisions at different energies) shows that the electron-system behaves as if it had a different mass and charge than initially postulated. Renormalization, in thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lithium Molybdenum Purple Bronze
Lithium molybdenum purple bronze is a chemical compound with formula , that is, a mixed oxide of molybdenum and lithium. It can be obtained as flat crystals with a purple-red color and metallic sheen (hence the "purple bronze" name). This compound is one of several molybdenum bronzes with general formula where A is an alkali metal or thallium Tl. It stands out among them (and also among the sub-class of "purple" molybdenum bronzes) for its peculiar electrical properties, including a marked isotropic, anisotropy that makes it a "quasi-1D" conductor, and a metal-to-insulator transition as it is cooled below 30 kelvin, K. Preparation The compound was first obtained by Martha Greenblatt and others by a temperature gradient flux technique. In a typical preparation, a stoichometric melt of , and is maintained in a temperature gradient from 490 to 640 °C oven 15 cm in vacuum over several days. Excess reagents are dissolved with a hot potassium carbonate solution releasing met ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review Letters
''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. As also confirmed by various measurement standards, which include the ''Journal Citation Reports'' impact factor and the journal ''h''-index proposed by Google Scholar, many physicists and other scientists consider ''Physical Review Letters'' to be one of the most prestigious journals in the field of physics. ''According to Google Scholar, PRL is the journal with the 9th journal h-index among all scientific journals'' ''PRL'' is published as a print journal, and is in electronic format, online and CD-ROM. Its focus is rapid dissemination of significant, or notable, results of fundamental research on all topics related to all fields of physics. This is accomplished by rapid publication of short reports, called "Letters". Papers are published and available electronically one article at a time. When published in s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ARPES
Angle-resolved photoemission spectroscopy (ARPES) is an experimental technique used in condensed matter physics to probe the allowed energies and momenta of the electrons in a material, usually a crystalline solid. It is based on the photoelectric effect, in which an incoming photon of sufficient energy ejects an electron from the surface of a material. By directly measuring the kinetic energy and emission angle distributions of the emitted photoelectrons, the technique can map the electronic band structure and Fermi surfaces. ARPES is best suited for the study of one- or two-dimensional materials. It has been used by physicists to investigate high-temperature superconductors, graphene, Topological insulator, topological materials, quantum well states, and materials exhibiting charge density waves. ARPES systems consist of a monochromatic light source to deliver a narrow beam of photons, a sample holder connected to a manipulator used to position the sample of a material, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scanning Tunneling Microscope
A scanning tunneling microscope (STM) is a type of microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986. STM senses the surface by using an extremely sharp conducting tip that can distinguish features smaller than 0.1 nm with a 0.01 nm (10 pm) depth resolution. This means that individual atoms can routinely be imaged and manipulated. Most microscopes are built for use in ultra-high vacuum at temperatures approaching zero kelvin, but variants exist for studies in air, water and other environments, and for temperatures over 1000 °C. STM is based on the concept of quantum tunneling. When the tip is brought very near to the surface to be examined, a bias voltage applied between the two allows electrons to tunnel through the vacuum separating them. The resulting ''tunneling current'' is a function of the tip position, applied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Low-energy Electron Diffraction
Low-energy electron diffraction (LEED) is a technique for the determination of the surface structure of single-crystalline materials by bombardment with a collimated beam of low-energy electrons (30–200 eV) and observation of diffracted electrons as spots on a fluorescent screen. LEED may be used in one of two ways: # Qualitatively, where the diffraction pattern is recorded and analysis of the spot positions gives information on the symmetry of the surface structure. In the presence of an adsorbate the qualitative analysis may reveal information about the size and rotational alignment of the adsorbate unit cell with respect to the substrate unit cell. # Quantitatively, where the intensities of diffracted beams are recorded as a function of incident electron beam energy to generate the so-called I–V curves. By comparison with theoretical curves, these may provide accurate information on atomic positions on the surface at hand. Historical perspective An electron-diffractio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Physical Chemistry A
''The Journal of Physical Chemistry A'' is a scientific journal which reports research on the chemistry of molecules - including their dynamics, spectroscopy, kinetics, structure, bonding, and quantum chemistry. It is published weekly by the American Chemical Society. Before 1997 the title was simply ''Journal of Physical Chemistry''. Owing to the ever-growing amount of research in the area, in 1997 the journal was split into ''Journal of Physical Chemistry A'' (molecular theoretical and experimental physical chemistry) and '' The Journal of Physical Chemistry B'' (solid state, soft matter, liquids, etc.). Beginning in 2007, the latter underwent a further split, with ''The Journal of Physical Chemistry C'' now being dedicated to nanotechnology, molecular electronics, and related subjects. Editors-in-chief *1896–1932 Wilder Dwight Bancroft, Joseph E. Trevor *1933–1951 S. C. Lind *1952–1964 William A. Noyes *1965–1969 F. T. Wall *1970–1980 Bryce Crawford *1980†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Functional Theory
Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry. DFT has been very popular for calculations in solid-state physics since the 1970s. However, DFT was not considered accurate enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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