The Anderson orthogonality theorem is a theorem in physics by the physicist P. W. Anderson.
It relates to the introduction of a magnetic impurity in a metal. When a magnetic impurity is introduced into a metal, the conduction electrons will tend to screen the potential that the impurity creates. The N-electron ground state for the system when , which corresponds to the absence of the impurity and , which corresponds to the introduction of the impurity are orthogonal in the thermodynamic limit .
BCS theory or Bardeen–Cooper–Schrieffer theory is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes superconductivity as a microscopic effect caused by a condensation of Cooper pairs. The theory is also used in nuclear physics to describe the pairing interaction between nucleons in an atomic nucleus.
The quantum Hall effect is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values
Spintronics, also known as spin electronics, is the study of the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-state devices. The field of spintronics concerns spin-charge coupling in metallic systems; the analogous effects in insulators fall into the field of multiferroics.
The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic potential, despite being confined to a region in which both the magnetic field B and electric field E are zero. The underlying mechanism is the coupling of the electromagnetic potential with the complex phase of a charged particle's wave function, and the Aharonov–Bohm effect is accordingly illustrated by interference experiments.
In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities, resulting in a characteristic change i.e. a minimum in electrical resistivity with temperature. The cause of the effect was first explained by Jun Kondo, who applied third-order perturbation theory to the problem to account for scattering of s-orbital conduction electrons off d-orbital electrons localized at impurities. Kondo's calculation predicted that the scattering rate and the resulting part of the resistivity should increase logarithmically as the temperature approaches 0 K. Experiments in the 1960s by Myriam Sarachik at Bell Laboratories provided the first data that confirmed the Kondo effect. Extended to a lattice of magnetic impurities, the Kondo effect likely explains the formation of heavy fermions and Kondo insulators in intermetallic compounds, especially those involving rare earth elements such as cerium, praseodymium, and ytterbium, and actinide elements such as uranium. The Kondo effect has also been observed in quantum dot systems.
A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. The polaron concept was proposed by Lev Landau in 1933 and Solomon Pekar in 1946 to describe an electron moving in a dielectric crystal where the atoms displace from their equilibrium positions to effectively screen the charge of an electron, known as a phonon cloud. For comparison of the models proposed in these papers see M. I. Dykman and E. I. Rashba, The roots of polaron theory, Physics Today 68, 10 (2015). This lowers the electron mobility and increases the electron's effective mass.
Jellium, also known as the uniform electron gas (UEG) or homogeneous electron gas (HEG), is a quantum mechanical model of interacting electrons in a solid where the positive charges are assumed to be uniformly distributed in space; the electron density is a uniform quantity as well in space. This model allows one to focus on the effects in solids that occur due to the quantum nature of electrons and their mutual repulsive interactions without explicit introduction of the atomic lattice and structure making up a real material. Jellium is often used in solid-state physics as a simple model of delocalized electrons in a metal, where it can qualitatively reproduce features of real metals such as screening, plasmons, Wigner crystallization and Friedel oscillations.
Koopmans' theorem states that in closed-shell Hartree–Fock theory (HF), the first ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital (HOMO). This theorem is named after Tjalling Koopmans, who published this result in 1934.
A two-dimensional electron gas (2DEG) is a scientific model in solid-state physics. It is an electron gas that is free to move in two dimensions, but tightly confined in the third. This tight confinement leads to quantized energy levels for motion in the third direction, which can then be ignored for most problems. Thus the electrons appear to be a 2D sheet embedded in a 3D world. The analogous construct of holes is called a two-dimensional hole gas (2DHG), and such systems have many useful and interesting properties.
A Josephson junction is a quantum mechanical device which is made of two superconducting electrodes separated by a barrier. A π Josephson junction is a Josephson junction in which the Josephson phase φ equals π in the ground state, i.e. when no external current or magnetic field is applied.
Spin-polarized scanning tunneling microscopy (SP-STM) is a type of scanning tunneling microscope (STM) that can provide detailed information of magnetic phenomena on the single-atom scale additional to the atomic topography gained with STM. SP-STM opened a novel approach to static and dynamic magnetic processes as precise investigations of domain walls in ferromagnetic and antiferromagnetic systems, as well as thermal and current-induced switching of nanomagnetic particles.
A charge density wave (CDW) is an ordered quantum fluid of electrons in a linear chain compound or layered crystal. The electrons within a CDW form a standing wave pattern and sometimes collectively carry an electric current. The electrons in such a CDW, like those in a superconductor, can flow through a linear chain compound en masse, in a highly correlated fashion. Unlike a superconductor, however, the electric CDW current often flows in a jerky fashion, much like water dripping from a faucet due to its electrostatic properties. In a CDW, the combined effects of pinning and electrostatic interactions likely play critical roles in the CDW current's jerky behavior, as discussed in sections 4 & 5 below.
In solid-state physics, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons in unfilled electron bands. Electrons are one type of fermion, and when they are found in such materials, they are sometimes referred to as heavy electrons. Heavy fermion materials have a low-temperature specific heat whose linear term is up to 1000 times larger than the value expected from the free electron model. The properties of the heavy fermion compounds often derive from the partly filled f-orbitals of rare-earth or actinide ions, which behave like localized magnetic moments. The name "heavy fermion" comes from the fact that the fermion behaves as if it has an effective mass greater than its rest mass. In the case of electrons, below a characteristic temperature (typically 10 K), the conduction electrons in these metallic compounds behave as if they had an effective mass up to 1000 times the free particle mass. This large effective mass is also reflected in a large contribution to the resistivity from electron-electron scattering via the Kadowaki–Woods ratio. Heavy fermion behavior has been found in a broad variety of states including metallic, superconducting, insulating and magnetic states. Characteristic examples are CeCu6, CeAl3, CeCu2Si2, YbAl3, UBe13 and UPt3.
The Anderson impurity model, named after Philip Warren Anderson, is a Hamiltonian that is used to describe magnetic impurities embedded in metals. It is often applied to the description of Kondo effect-type problems, such as heavy fermion systems and Kondo insulators. In its simplest form, the model contains a term describing the kinetic energy of the conduction electrons, a two-level term with an on-site Coulomb repulsion that models the impurity energy levels, and a hybridization term that couples conduction and impurity orbitals. For a single impurity, the Hamiltonian takes the form
A magnetic impurity is an impurity in a host metal that has a magnetic moment. The magnetic impurity can then interact with the conduction electrons of the metal, leading to interesting physics such as the Kondo effect, and heavy fermion behaviour. Some examples of magnetic impurities that metals can be doped with are iron and nickel. Such an impurity will contribute a Curie-Weiss term to the magnetic susceptibility,
The slave boson method is a technique for dealing with models of strongly correlated systems, providing a method to second-quantize valence fluctuations within a restrictive manifold of states. In the 1960s the physicist John Hubbard introduced an operator, now named the "Hubbard operator" to describe the creation of an electron within a restrictive manifold of valence configurations. Consider for example, a rare earth or actinide ion in which strong Coulomb interactions restrict the charge fluctuations to two valence states, such as the Ce4+(4f0) and Ce3+ (4f1) configurations of a mixed-valence cerium compound. The corresponding quantum states of these two states are the singlet state and the magnetic state, where is the spin. The fermionic Hubbard operators that link these states are then
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.
A composite fermion is the topological bound state of an electron and an even number of quantized vortices, sometimes visually pictured as the bound state of an electron and, attached, an even number of magnetic flux quanta. Composite fermions were originally envisioned in the context of the fractional quantum Hall effect, but subsequently took on a life of their own, exhibiting many other consequences and phenomena.
The Kondo model is a model for a single localized quantum impurity coupled to a large reservoir of delocalized and noninteracting electrons. The quantum impurity is represented by a spin-1/2 particle, and is coupled to a continuous band of noninteracting electrons by an antiferromagnetic exchange coupling . The Kondo model is used as a model for metals containing magnetic impurities, as well as quantum dot systems.
In quantum mechanics, the Byers-Yang theorem states that all physical properties of a doubly connected system enclosing a magnetic flux through the opening are periodic in the flux with period . The theorem was first stated and proven by Nina Byers and Chen-Ning Yang (1961), and further developed by Felix Bloch (1970).
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