Superconductivity 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. An electric current through a loop of superconducting wire can persist indefinitely with no power source.
The magnetic flux, represented by the symbol Φ, threading some contour or loop is defined as the magnetic field B multiplied by the loop area S, i.e. Φ = B ⋅ S. Both B and S can be arbitrary, meaning Φ can be as well. However, if one deals with the superconducting loop or a hole in a bulk superconductor, the magnetic flux threading such a hole/loop is quantized. The (superconducting) magnetic flux quantumΦ0 = h/(2e) ≈ 2.067833848...×10−15 Wb is a combination of fundamental physical constants: the Planck constant h and the electron charge e. Its value is, therefore, the same for any superconductor. The phenomenon of flux quantization was discovered experimentally by B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Näbauer, in 1961. The quantization of magnetic flux is closely related to the Little–Parks effect, but was predicted earlier by Fritz London in 1948 using a phenomenological model.
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mechanics are observable at ordinary, rather than atomic, scale. The Josephson effect has many practical applications because it exhibits a precise relationship between different physical measures, such as voltage and frequency, facilitating highly accurate measurements.
The Little–Parks effect was discovered in 1962 by William A. Little and Ronald D. Parks in experiments with empty and thin-walled superconducting cylinders subjected to a parallel magnetic field. It was one of the first experiments to indicate the importance of Cooper-pairing principle in BCS theory.
In physics and chemistry, the Nernst effect is a thermoelectric phenomenon observed when a sample allowing electrical conduction is subjected to a magnetic field and a temperature gradient normal (perpendicular) to each other. An electric field will be induced normal to both.
In physics, a fluxon is a quantum of electromagnetic flux. The term may have any of several related meanings.
In superconductivity, a semifluxon is a half integer vortex of supercurrent carrying the magnetic flux equal to the half of the magnetic flux quantum Φ0. Semifluxons exist in the 0-π long Josephson junctions at the boundary between 0 and π regions. This 0-π boundary creates a π discontinuity of the Josephson phase. The junction reacts to this discontinuity by creating a semifluxon. Vortex's supercurrent circulates around 0-π boundary. In addition to semifluxon, there exist also an antisemifluxon. It carries the flux −Φ0/2 and its supercurrent circulates in the opposite direction.
In superconductivity, fluxon is a vortex of supercurrent in a type-II superconductor, used by Alexei Abrikosov to explain magnetic behavior of type-II superconductors. Abrikosov vortices occur generically in the Ginzburg–Landau theory of superconductivity.
In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. It also features the formation of magnetic field vortices with an applied external magnetic field. This occurs above a certain critical field strength Hc1. The vortex density increases with increasing field strength. At a higher critical field Hc2, superconductivity is destroyed. Type-II superconductors do not exhibit a complete Meissner effect.
The Superconductor Insulator Transition is an example of a quantum phase transition, whereupon tuning some parameter in the Hamiltonian, a dramatic change in the behavior of the electrons occurs. The nature of how this transition occurs is disputed, and many studies seek to understand how the order parameter, , changes. Here is the amplitude of the order parameter, and is the phase. Most theories involve either the destruction of the amplitude of the order parameter - by a reduction in the density of states at the Fermi surface, or by destruction of the phase coherence; which results from the proliferation of vortices.
In quantum computing, more specifically in superconducting quantum computing, flux qubits are micrometer sized loops of superconducting metal that is interrupted by a number of Josephson junctions. These devices function as quantum bits. The flux qubit was first proposed by Terry P. Orlando et al. at MIT in 1999 and fabricated shortly thereafter. During fabrication, the Josephson junction parameters are engineered so that a persistent current will flow continuously when an external magnetic flux is applied. Only an integer number of flux quanta are allowed to penetrate the superconducting ring, resulting in clockwise or counter-clockwise mesoscopic supercurrents in the loop to compensate a non-integer external flux bias. When the applied flux through the loop area is close to a half integer number of flux quanta, the two lowest energy eigenstates of the loop will be a quantum superposition of the clockwise and counter-clockwise currents. The two lowest energy eigenstates differ only by the relative quantum phase between the composing current-direction states. Higher energy eigenstates correspond to much larger (macroscopic) persistent currents, that induce an additional flux quantum to the qubit loop, thus are well separated energetically from the lowest two eigenstates. This separation, known as the "qubit non linearity" criteria, allows operations with the two lowest eigenstates only, effectively creating a two level system. Usually, the two lowest eigenstates will serve as the computational basis for the logical qubit.
In physics, a quantum vortex represents a quantized flux circulation of some physical quantity. In most cases, quantum vortices are a type of topological defect exhibited in superfluids and superconductors. The existence of quantum vortices was first predicted by Lars Onsager in 1949 in connection with superfluid helium. Onsager reasoned that quantisation of vorticity is a direct consequence of the existence of a superfluid order parameter as a spatially continuous wavefunction. Onsager also pointed out that quantum vortices describe the circulation of superfluid and conjectured that their excitations are responsible for superfluid phase transitions. These ideas of Onsager were further developed by Richard Feynman in 1955 and in 1957 were applied to describe the magnetic phase diagram of type-II superconductors by Alexei Alexeyevich Abrikosov. In 1935 Fritz London published a very closely related work on magnetic flux quantization in superconductors. London's fluxoid can also be viewed as a quantum vortex.
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.
Proximity effect or Holm–Meissner effect is a term used in the field of superconductivity to describe phenomena that occur when a superconductor (S) is placed in contact with a "normal" (N) non-superconductor. Typically the critical temperature of the superconductor is suppressed and signs of weak superconductivity are observed in the normal material over mesoscopic distances. The proximity effect is known since the pioneering work by R. Holm and W. Meissner. They have observed zero resistance in SNS pressed contacts, in which two superconducting metals are separated by a thin film of a non-superconducting metal. The discovery of the supercurrent in SNS contacts is sometimes mistakenly attributed to Brian Josephson's 1962 work, yet the effect was known long before his publication and was understood as the proximity effect.
In a standard superconductor, described by a complex field fermionic condensate wave function, vortices carry quantized magnetic fields because the condensate wave function is invariant to increments of the phase by . There a winding of the phase by creates a vortex which carries one flux quantum. See quantum vortex.
Type-1.5 superconductors are multicomponent superconductors characterized by two or more coherence lengths, at least one of which is shorter than the magnetic field penetration length , and at least one of which is longer. This is in contrast to single-component superconductors, where there is only one coherence length and the superconductor is necessarily either type 1 or type 2. When placed in magnetic field, type-1.5 superconductors should form quantum vortices: magnetic-flux-carrying excitations. They allow magnetic field to pass through superconductors due to a vortex-like circulation of superconducting particles. In type-1.5 superconductors these vortices have long-range attractive, short-range repulsive interaction. As a consequence a type-1.5 superconductor in a magnetic field can form a phase separation into domains with expelled magnetic field and clusters of quantum vortices which are bound together by attractive intervortex forces. The domains of the Meissner state retain the two-component superconductivity, while in the vortex clusters one of the superconducting components is suppressed. Thus such materials should allow coexistence of various properties of type-I and type-II superconductors.
The Aharonov–Casher effect is a quantum mechanical phenomenon predicted in 1984 by Yakir Aharonov and Aharon Casher, in which a traveling magnetic dipole is affected by an electric field. It is dual to the Aharonov–Bohm effect, in which the quantum phase of a charged particle depends upon which side of a magnetic flux tube it comes through. In the Aharonov–Casher effect, the particle has a magnetic moment and the tubes are charged instead. It was observed in a gravitational neutron interferometer in 1989 and later by fluxon interference of magnetic vortices in Josephson junctions. It has also been seen with electrons and atoms.
In superconductivity, a Pearl vortex is a vortex of supercurrent in a thin film of type-II superconductor, first described in 1964 by Judea Pearl. A Pearl vortex is similar to Abrikosov vortex except for its magnetic field profile which, due to the dominant air-metal interface, diverges sharply as 1/ at short distances from the center, and decays slowly, like 1/ at long distances. Abrikosov's vortices, in comparison, have very short range interaction and diverge as near the center.
Macroscopic quantum phenomena are processes showing quantum behavior at the macroscopic scale, rather than at the atomic scale where quantum effects are prevalent. The best-known examples of macroscopic quantum phenomena are superfluidity and superconductivity; other examples include the quantum Hall effect and topological order. Since 2000 there has been extensive experimental work on quantum gases, particularly Bose–Einstein condensates.
A φ Josephson junction is a particular type of the Josephson junction, which has a non-zero Josephson phase φ across it in the ground state. A π Josephson junction, which has the minimum energy corresponding to the phase of π, is a specific example of it.
