Electrical resistivity and conductivityElectrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m).
Percolation theoryIn statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles Network theory and Percolation (cognitive psychology).
PercolationIn physics, chemistry, and materials science, percolation () refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation.
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.
Percolation thresholdThe percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them.
SigmaSigma ('sɪgmə; uppercase Σ, lowercase σ, lowercase in word-final position ς; σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as an operator for summation. When used at the end of a letter-case word (one that does not use all caps), the final form (ς) is used. In Ὀδυσσεύς (Odysseus), for example, the two lowercase sigmas (σ) in the center of the name are distinct from the word-final sigma (ς) at the end.
Percolation critical exponentsIn the context of the physical and mathematical theory of percolation, a percolation transition is characterized by a set of universal critical exponents, which describe the fractal properties of the percolating medium at large scales and sufficiently close to the transition. The exponents are universal in the sense that they only depend on the type of percolation model and on the space dimension. They are expected to not depend on microscopic details such as the lattice structure, or whether site or bond percolation is considered.
Mott insulatorMott insulators are a class of materials that are expected to conduct electricity according to conventional band theories, but turn out to be insulators (particularly at low temperatures). These insulators fail to be correctly described by band theories of solids due to their strong electron–electron interactions, which are not considered in conventional band theory. A Mott transition is a transition from a metal to an insulator, driven by the strong interactions between electrons.
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.
SuperconductivitySuperconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered, even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero.
Overhead lineAn overhead line or overhead wire is an electrical cable that is used to transmit electrical energy to electric locomotives, trolleybuses or trams. The generic term used by the International Union of Railways for the technology is overhead line. It is known variously as overhead catenary, overhead contact line (OCL), overhead contact system (OCS), overhead equipment (OHE), overhead line equipment (OLE or OHLE), overhead lines (OHL), overhead wiring (OHW), traction wire, and trolley wire.
Electrical networkAn electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, current sources, resistances, inductances, capacitances). An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Thus all circuits are networks, but not all networks are circuits (although networks without a closed loop are often imprecisely referred to as "circuits").
Quantum tunnellingIn physics, quantum tunnelling, barrier penetration, or simply tunnelling is a quantum mechanical phenomenon in which an object such as an electron or atom passes through a potential energy barrier that, according to classical mechanics, the object does not have sufficient energy to enter or surmount. Tunneling is a consequence of the wave nature of matter, where the quantum wave function describes the state of a particle or other physical system, and wave equations such as the Schrödinger equation describe their behavior.
Electrical connectorComponents of an electrical circuit are electrically connected if an electric current can run between them through an electrical conductor. An electrical connector is an electromechanical device used to create an electrical connection between parts of an electrical circuit, or between different electrical circuits, thereby joining them into a larger circuit. Most electrical connectors have a gender - i.e. the male component, called a plug, connects to the female component, or socket.
Conductive polymerConductive polymers or, more precisely, intrinsically conducting polymers (ICPs) are organic polymers that conduct electricity. Such compounds may have metallic conductivity or can be semiconductors. The main advantage of conductive polymers is that they are easy to process, mainly by dispersion. Conductive polymers are generally not thermoplastics, i.e., they are not thermoformable. But, like insulating polymers, they are organic materials. They can offer high electrical conductivity but do not show similar mechanical properties to other commercially available polymers.
Coherent stateIn physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926, while searching for solutions of the Schrödinger equation that satisfy the correspondence principle.
SemiconductorA semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way. Its conducting properties may be altered in useful ways by introducing impurities ("doping") into the crystal structure. When two differently doped regions exist in the same crystal, a semiconductor junction is created.
Scanning tunneling microscopeA 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.
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.
ColloidA colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend the definition to include substances like aerosols and gels. The term colloidal suspension refers unambiguously to the overall mixture (although a narrower sense of the word suspension is distinguished from colloids by larger particle size).
