Editing Superconductivity (section)

=== Zero electrical DC resistance ===
[[File:CERN-cables-p1030764.jpg|thumb|Electric cables for accelerators at [[CERN]]. Both the massive and slim cables are rated for 12,500 [[Amperes|A]]. ''Top:'' regular cables for [[Large Electron–Positron Collider|LEP]]; ''bottom:'' superconductor-based cables for the [[Large Hadron Collider|LHC]]]]
[[File:Cross_section_of_preform_superconductor_cable.jpg|thumb|Cross section of a preformed superconductor rod from the abandoned [[Superconducting Super Collider|Texas Superconducting Super Collider (SSC)]]]]
The simplest method to measure the [[electrical resistance]] of a sample of some material is to place it in an [[electrical circuit]] in series with a [[current source]] ''I'' and measure the resulting [[voltage]] ''V'' across the sample. The resistance of the sample is given by [[Ohm's law]] as ''R&nbsp;=&nbsp;V&nbsp;/&nbsp;I''. If the voltage is zero, this means that the resistance is zero.

Superconductors are also able to maintain a current with no applied voltage whatsoever, a property exploited in [[Superconducting magnet|superconducting electromagnets]] such as those found in [[Magnetic resonance imaging|MRI]] machines. Experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a lifetime of at least 100,000 years. Theoretical estimates for the lifetime of a persistent current can exceed the estimated lifetime of the universe, depending on the wire geometry and the temperature.<ref name="Gallop2" /> In practice, currents injected in superconducting coils persisted for 28 years, 7 months, 27 days in a superconducting gravimeter in Belgium, from August 4, 1995 until March 31, 2024.<ref>{{cite journal |last1=Van Camp |first1=Michel |last2=Francis |first2=Olivier |last3=Lecocq |first3=Thomas |year=2017 |title=Recording Belgium's Gravitational History |journal=Eos |language=en-US |volume=98 |doi=10.1029/2017eo089743 |doi-access=free}}</ref><ref>{{cite journal |last1=Van Camp |first1=Michel |last2=de Viron |first2=Olivier |last3=Watlet |first3=Arnaud |last4=Meurers |first4=Bruno |last5=Francis |first5=Olivier |last6=Caudron |first6=Corentin |year=2017 |title=Geophysics From Terrestrial Time-Variable Gravity Measurements |url=https://hal.archives-ouvertes.fr/hal-01631032/file/Reviews%20of%20Geophysics%20-%202017%20-%20Van%20Camp%20-%20Geophysics%20From%20Terrestrial%20Time%25u2010Variable%20Gravity%20Measurements.pdf |journal=[[Reviews of Geophysics]] |language=en |volume=55 |issue=4 |pages=2017RG000566 |bibcode=2017RvGeo..55..938V |doi=10.1002/2017rg000566 |issn=1944-9208 |s2cid=134876430}}</ref> In such instruments, the measurement is based on the monitoring of the levitation of a superconducting niobium sphere with a mass of four grams.

In a normal conductor, an electric current may be visualized as a fluid of [[Electron|electrons]] moving across a heavy ionic lattice. The electrons are constantly colliding with the ions in the lattice, and during each collision some of the energy carried by the current is absorbed by the lattice and converted into [[heat]], which is essentially the vibrational [[kinetic energy]] of the lattice ions. As a result, the energy carried by the current is constantly being dissipated. This is the phenomenon of electrical resistance and [[Joule heating]].

The situation is different in a superconductor. In a conventional superconductor, the electronic fluid cannot be resolved into individual electrons. Instead, it consists of bound ''pairs'' of electrons known as [[Cooper pair|Cooper pairs]]. This pairing is caused by an attractive force between electrons from the exchange of [[Phonon|phonons]]. This pairing is very weak, and small thermal vibrations can fracture the bond. Due to [[quantum mechanics]], the [[energy spectrum]] of this Cooper pair fluid possesses an ''[[energy gap]]'', meaning there is a minimum amount of energy Δ''E'' that must be supplied in order to excite the fluid. Therefore, if Δ''E'' is larger than the [[thermal energy]] of the lattice, given by ''kT'', where ''k'' is the [[Boltzmann constant]] and ''T'' is the [[temperature]], the fluid will not be scattered by the lattice.<ref>{{cite book |last1=Tinkham |first1=Michael |title=Introduction to Superconductivity |date=1996 |publisher=Dover Publications, Inc. |isbn=0486435032 |location=Mineola, New York |page=8}}</ref> The Cooper pair fluid is thus a [[superfluid]], meaning it can flow without energy dissipation.

In the class of superconductors known as [[Type II superconductor|type II superconductors]], including all known [[High-temperature superconductor|high-temperature superconductors]], an extremely low but non-zero resistivity appears at temperatures not too far below the nominal superconducting transition when an electric current is applied in conjunction with a strong magnetic field, which may be caused by the electric current. This is due to the motion of [[Abrikosov vortex|magnetic vortices]] in the electronic superfluid, which dissipates some of the energy carried by the current. If the current is sufficiently small, the vortices are stationary, and the resistivity vanishes. The resistance due to this effect is minuscule compared with that of non-superconducting materials, but must be taken into account in sensitive experiments. However, as the temperature decreases far enough below the nominal superconducting transition, these vortices can become frozen into a disordered but stationary phase known as a "vortex glass". Below this vortex glass transition temperature, the resistance of the material becomes truly zero.