View source for Physics:Persistent current

{{short description|Perpetual electric current, not requiring an external power source}}
In [[Physics:Physics|physics]], '''persistent current''' is a perpetual [[Physics:Electric current|electric current]] that does not require an external power source. Such a current is impossible in normal electrical devices, since all commonly-used conductors have a non-zero resistance, and this resistance would rapidly dissipate any such current as heat. However, in [[Physics:Superconductor|superconductor]]s and some [[Physics:Mesoscopic physics|mesoscopic devices]], persistent currents are possible and observed due to [[Physics:Quantum mechanics|quantum effects]]. In resistive materials, persistent currents can appear in microscopic samples due to size effects. 
Persistent currents are widely used in the form of [[Physics:Superconducting magnet|superconducting magnet]]s. 

== In magnetized objects ==

In electromagnetism, all magnetizations can be seen as microscopic persistent currents.
By definition a [[Physics:Magnetization|magnetization]] <math>\mathbf{M}</math> can be replaced by its corresponding microscopic form, which is an electric current density:
:<math> \mathbf{J} = \nabla\times\mathbf{M} </math>.
This current is a bound current, not having any charge accumulation associated with it since it is divergenceless.
What this means is that any permanently magnetized object, for example a piece of [[Physics:Lodestone|lodestone]], can be considered to have persistent electric currents running throughout it (the persistent currents are generally concentrated near the surface).

The converse is also true: any persistent electric current is divergence-free, and can therefore be represented instead by a magnetization.
Therefore, in the macroscopic [[Physics:Maxwell's equations|Maxwell's equations]], it is purely a choice of mathematical convenience, whether to represent persistent currents as magnetization or vice versa.
In the microscopic formulation of Maxwell's equations, however, <math>\mathbf{M}</math> does not appear and so any magnetizations must be instead represented by bound currents.

== In superconductors ==


In [[Physics:Superconductor|superconductor]]s, charge can flow without any resistance. It is possible to make pieces of superconductor with a large built-in persistent current, either by creating the superconducting state (cooling the material) while charge is flowing through it, or by changing the magnetic field around the superconductor after creating the superconducting state.<ref>{{Cite journal|journal = IEEE Trans. Appl. Supercond.|year = 2013|title = Induced Currents in Closed-Ended Type-II Superconducting Coils|first1 = F. |last1 = Yen|first2 = X. |last2 = Chen|first3 = R. B.|last3 = Wang|first4 = J. M.|last4 = Zhu|first5 = J.|last5 = Li|first6 = G. T.|last6 = Ma|volume = 23|issue = 6|pages = 8202005|doi = 10.1109/TASC.2013.2273534|bibcode = 2013ITAS...23...86Y|s2cid = 34374691}}</ref> This principle is used in superconducting electromagnets to generate sustained high magnetic fields that only require a small amount of power to maintain. The persistent current was first identified by [[Biography:Heike Kamerlingh Onnes|H. Kamerlingh Onnes]], and attempts to set a lower bound on their duration have reached values of over 100,000 years.<ref>[http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.10.93 File J, Mills, R ''Physical Review Letters'' 1963]</ref>

== In resistive conductors ==

[[Image:Persistent Current Ring.png|250px|thumb|right|Persistent current schematic. The green arrow indicates the direction of static applied magnetic field B which allows a net current I (blue arrow) to flow and create a magnetization M (black arrow) by breaking the [[Symmetry|symmetry]] between clockwise and counterclockwise currents. The yellow dot represents an electron traversing the disordered material of the ring (green stars) without [[Dissipation|dissipation]]. A typical ring current is 1 nanoampere for a ring diameter of 0.6 [[Micrometre|micrometer]] at a temperature below 0.5 [[Kelvin|kelvin]].<ref name=shanks/>]]

Surprisingly, it is also possible to have tiny persistent currents inside resistive metals that are placed in a magnetic field, even in metals that are nominally "non-magnetic".<ref>{{cite news|url=http://www.rdmag.com/News/2009/10/General-Sciences-Measuring-Elusive-Persistent-Current-That-Flows-Forever|title=Measuring elusive "persistent current" that flows forever|date=October 12, 2009|publisher=R&D Daily}}</ref>
The current is the result of a [[Physics:Quantum mechanical|quantum mechanical]] effect that influences how electrons travel through metals, and arises from the same kind of motion that allows the electrons inside an [[Physics:Atom|atom]] to orbit the [[Physics:Atomic nucleus|nucleus]] forever.

This type of persistent current is a [[Physics:Mesoscopic physics|mesoscopic]] low temperature effect: the magnitude of the current becomes appreciable when the size of the metallic system is reduced to the scale of the electron quantum phase [[Coherence length|coherence length]] and the thermal length. Persistent currents decrease with increasing temperature and will vanish exponentially above a temperature known as the Thouless temperature. This temperature scales as the inverse of the circuit diameter squared.<ref name="shanks" /> Consequently, it has been suggested that persistent currents could flow up to room temperature and above in nanometric metal structures such as metal (Au, Ag,...) [[Physics:Nanoparticle|nanoparticle]]s. This hypothesis has been offered for explaining the singular magnetic properties of nanoparticles made of gold and other metals.<ref>{{Cite journal|title = Magnetic Properties of Gold Nanoparticles: A Room-Temperature Quantum Effect|last = Gréget|first = Romain|date = 2012|journal = ChemPhysChem|volume = 13|issue = 13|pages = 3092–3097|doi = 10.1002/cphc.201200394|pmid = 22753262| s2cid=28725119 |url = https://univoak.eu/islandora/object/islandora%3A60483}}</ref> 
Unlike with superconductors, these persistent currents do not appear at zero magnetic field, as the current fluctuates symmetrically between positive and negative values; the magnetic field breaks that symmetry and allows a nonzero average current.
Although the persistent current in an individual ring is largely unpredictable due to uncontrolled factors like the disorder configuration, it has a slight bias so that an average persistent current appears even for an [[Physics:Statistical ensemble (mathematical physics)|ensemble]] of conductors with different disorder configurations.<ref name="akmo">{{cite book|last1=Akkermans |first1=Eric |last2=Montambaux |first2=Gilles|title=Mesoscopic Physics of Electrons and Photons|publisher=Cambridge University Press|year=2007|isbn=978-0-521-85512-9}}</ref>

This kind of persistent current was first predicted to be experimentally observable in micrometer-scale rings in 1983 by Markus Büttiker, Yoseph Imry, and [[Biography:Rolf Landauer|Rolf Landauer]].<ref>{{Cite journal
|journal = Phys. Lett. A
|year = 1983
|title = Josephson behavior in small normal one-dimensional rings 
|first1 = M.
|last1 = Büttiker
|first2 = Y.
|last2 = Imry
|first3 = R.
|last3 = Landauer
|volume = 96
|issue = 7
|pages = 365
|doi = 10.1016/0375-9601(83)90011-7 
|bibcode = 1983PhLA...96..365B |citeseerx = 10.1.1.205.7310
}}</ref> Because the effect requires the phase coherence of electrons around the entire ring, the current can not be observed when the ring is interrupted by an [[Engineering:Ammeter|ammeter]] and thus the current must by measured indirectly through its [[Physics:Magnetization|magnetization]].
In fact, all metals exhibit some magnetization in magnetic fields due a combination of [[Physics:De Haas–van Alphen effect|de Haas–van Alphen effect]], core [[Physics:Diamagnetism|diamagnetism]], Landau diamagnetism, Pauli paramagnetism, which all appear regardless of the shape of the metal.
The additional magnetization from persistent current becomes strong with a connected ring shape, and for example would disappear if the ring were cut.<ref name="akmo"/>

Experimental evidence of the observation of persistent currents were first reported in 1990 by a research group at Bell Laboratories using a superconducting resonator to study an array of [[Chemistry:Copper|copper]] rings.<ref>{{Cite journal|journal = Phys. Rev. Lett.|year = 1990|title = Magnetization of mesoscopic copper rings: Evidence for persistent currents|first1 = L. P.|last1 = Lévy|first2 = G.|last2 = Dolan|first3 = J.|pmid = 10041570|last3 = Dunsmuir|first4 = H.|last4 = Bouchiat|author4-link= Hélène Bouchiat |volume = 64|issue = 17|pages = 2074–2077|doi = 10.1103/PhysRevLett.64.2074|bibcode=1990PhRvL..64.2074L}}</ref> Subsequent measurements using [[Physics:Superconducting|superconducting]] resonators and extremely sensitive magnetometers known as [[Physics:SQUID|superconducting quantum interference devices]] (SQUIDs) produced inconsistent results.<ref>{{cite news|url=https://www.sciencedaily.com/releases/2009/10/091011071349.htm|title=Physicists Measure Elusive 'Persistent Current' That Flows Forever|date=October 12, 2009|publisher=ScienceDaily}}</ref>
In 2009, physicists at [[Organization:Stanford University|Stanford University]] using a scanning SQUID<ref>{{Cite journal|journal = Phys. Rev. Lett.|year = 2009|title = Persistent Currents in Normal Metal Rings|first1 = H. |last1 = Bluhm|first2 = N. |last2 = Koshnick|first3 = J.|last3 = Bert|pmid = 19392385|first4 = M.|last4 = Huber|first5 = K.|last5 = Moler|volume = 102|issue = 13|pages = 136802|doi = 10.1103/PhysRevLett.102.136802|bibcode=2009PhRvL.102m6802B|arxiv = 0810.4384 |s2cid = 16760003}}</ref> and at [[Organization:Yale University|Yale University]] using [[Engineering:Microelectromechanical systems|microelectromechanical]] cantilevers<ref name=shanks>{{Cite journal|journal = Science|year = 2009|title = Persistent Currents in Normal Metal Rings|first1 = A. C. |last1 = Bleszynski-Jayich|first2 = W. E. |last2 = Shanks
|first3 = B.|last3 = Peaudecerf|first4 = E.|last4 = Ginossar|pmid = 19815772|first5 = F.|last5 = von Oppen|first6 = L.|last6 = Glazman|first7 = J. G. E.|last7 = Harris|volume = 326|issue = 5950|pages = 272–5|doi = 10.1126/science.1178139|arxiv = 0906.4780v1|bibcode = 2009Sci...326..272B |s2cid = 37548342|url = http://epubs.surrey.ac.uk/808207/1/0906.4780v1.pdf}}</ref> reported measurements of persistent currents in nanoscale [[Chemistry:Gold|gold]] and [[Chemistry:Aluminum|aluminum]] rings respectively that both showed a strong agreement with the simple theory for non-interacting electrons.

{{quote|"These are ordinary, non-superconducting metal rings, which we typically think of as resistors, yet these currents will flow forever, even in the absence of an applied voltage."|Jack Harris, Associate Professor of Physics and Applied Physics at Yale.}}

The 2009 measurements both reported greater sensitivity to persistent currents than previous measurements and made several other improvements to persistent current detection. The scanning SQUID's ability to change the position of the SQUID detector relative to the ring sample allowed for a number of rings to be measured on one sample chip and better extraction of the current signal from [[Physics:Background noise|background noise]]. The cantilever detector's mechanical detection technique made it possible to measure the rings in a clean [[Physics:Electromagnetism|electromagnetic]] environment over a large range of [[Physics:Magnetic field|magnetic field]] and also to measure a number of rings on one sample chip.<ref>{{Cite journal|journal = Science|year = 2009|title = Sensing a Small But Persistent Current|first1 = Norman O. |last1 = Birge|pmid = 19815766|volume = 326|issue = 5950|pages = 244–5|doi = 10.1126/science.1180577|bibcode = 2009Sci...326..244B |s2cid = 9674177|url = https://zenodo.org/record/894880}}</ref>

==See also==
{{div col}}
*{{annotated link|Physics:Aharonov–Bohm effect}}
*{{annotated link|Physics:Byers-Yang theorem}}
*{{annotated link|Physics:Mesoscopic physics}}
*{{annotated link|Unsolved:Perpetual motion}}
{{div col end}}

==References==
{{reflist|2}}
[[Category:Mesoscopic physics]]
[[Category:Electrical engineering]]
[[Category:Electric current]]

{{Sourceattribution|Persistent current}}