Electronic band structureIn solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules.
Exchange interactionIn chemistry and physics, the exchange interaction or exchange splitting (with an exchange energy and exchange term) is a quantum mechanical effect that only occurs between identical particles. Despite sometimes being called an exchange force in an analogy to classical force, it is not a true force as it lacks a force carrier. The effect is due to the wave function of indistinguishable particles being subject to exchange symmetry, that is, either remaining unchanged (symmetric) or changing sign (antisymmetric) when two particles are exchanged.
Weak interactionIn nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, and gravitation. It is the mechanism of interaction between subatomic particles that is responsible for the radioactive decay of atoms: The weak interaction participates in nuclear fission and nuclear fusion.
Fundamental interactionIn physics, the fundamental interactions or fundamental forces are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: gravity electromagnetism weak interaction strong interaction The gravitational and electromagnetic interactions produce long-range forces whose effects can be seen directly in everyday life. The strong and weak interactions produce forces at minuscule, subatomic distances and govern nuclear interactions inside atoms.
Hubbard modelThe Hubbard model is an approximate model used to describe the transition between conducting and insulating systems. It is particularly useful in solid-state physics. The model is named for John Hubbard. The Hubbard model states that each electron experiences competing forces: one pushes it to tunnel to neighboring atoms, while the other pushes it away from its neighbors. Its Hamiltonian thus has two terms: a kinetic term allowing for tunneling ("hopping") of particles between lattice sites and a potential term reflecting on-site interaction.
C-symmetryIn physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-symmetry is an abbreviation of the phrase "charge conjugation symmetry", and is used in discussions of the symmetry of physical laws under charge-conjugation. Other important discrete symmetries are P-symmetry (parity) and T-symmetry (time reversal).
T-symmetryT-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal, Since the second law of thermodynamics states that entropy increases as time flows toward the future, in general, the macroscopic universe does not show symmetry under time reversal. In other words, time is said to be non-symmetric, or asymmetric, except for special equilibrium states when the second law of thermodynamics predicts the time symmetry to hold.
Dynamical mean-field theoryDynamical mean-field theory (DMFT) is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation of independent electrons, which is used in density functional theory and usual band structure calculations, breaks down. Dynamical mean-field theory, a non-perturbative treatment of local interactions between electrons, bridges the gap between the nearly free electron gas limit and the atomic limit of condensed-matter physics.
Strongly correlated materialStrongly correlated materials are a wide class of compounds that include insulators and electronic materials, and show unusual (often technologically useful) electronic and magnetic properties, such as metal-insulator transitions, heavy fermion behavior, half-metallicity, and spin-charge separation. The essential feature that defines these materials is that the behavior of their electrons or spinons cannot be described effectively in terms of non-interacting entities.
Symmetry (physics)In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries.
FerromagnetismFerromagnetism 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 familiar metals that are noticeably attracted to a magnet, 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.
BoronBoron is a chemical element with the symbol B and atomic number 5. In its crystalline form it is a brittle, dark, lustrous metalloid; in its amorphous form it is a brown powder. As the lightest element of the boron group it has three valence electrons for forming covalent bonds, resulting in many compounds such as boric acid, the mineral sodium borate, and the ultra-hard crystals of boron carbide and boron nitride. Boron is synthesized entirely by cosmic ray spallation and supernovae and not by stellar nucleosynthesis, so it is a low-abundance element in the Solar System and in the Earth's crust.
Condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. 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 superconducting phase exhibited by certain materials at extremely low cryogenic temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Bose–Einstein condensate found in ultracold atomic systems.
Chirality (physics)A chiral phenomenon is one that is not identical to its (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry. Helicity (particle physics) The helicity of a particle is positive (“right-handed”) if the direction of its spin is the same as the direction of its motion.
Magnetic domainA magnetic domain is a region within a magnetic material in which the magnetization is in a uniform direction. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction. When cooled below a temperature called the Curie temperature, the magnetization of a piece of ferromagnetic material spontaneously divides into many small regions called magnetic domains. The magnetization within each domain points in a uniform direction, but the magnetization of different domains may point in different directions.
Coupling constantIn physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared, , between the bodies; thus: in for Newtonian gravity and in for electrostatic.
AntiferromagnetismIn materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism. The phenomenon of antiferromagnetism was first introduced by Lev Landau in 1933.
Fermi's interactionIn particle physics, Fermi's interaction (also the Fermi theory of beta decay or the Fermi four-fermion interaction) is an explanation of the beta decay, proposed by Enrico Fermi in 1933. The theory posits four fermions directly interacting with one another (at one vertex of the associated Feynman diagram). This interaction explains beta decay of a neutron by direct coupling of a neutron with an electron, a neutrino (later determined to be an antineutrino) and a proton.
CaesiumCaesium (IUPAC spelling; cesium in American English) is a chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-golden alkali metal with a melting point of , which makes it one of only five elemental metals that are liquid at or near room temperature. Caesium has physical and chemical properties similar to those of rubidium and potassium. It is pyrophoric and reacts with water even at . It is the least electronegative element, with a value of 0.79 on the Pauling scale.
Yukawa interactionIn particle physics, Yukawa's interaction or Yukawa coupling, named after Hideki Yukawa, is an interaction between particles according to the Yukawa potential. Specifically, it is a scalar field (or pseudoscalar field) φ and a Dirac field ψ of the type The Yukawa interaction was developed to model the strong force between hadrons. A Yukawa interaction is thus used to describe the nuclear force between nucleons mediated by pions (which are pseudoscalar mesons).
