Physics:Quantum Superconductivity: Difference between revisions
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{{Short description|Quantum Collection topic on Quantum Superconductivity}} | {{Short description|Quantum Collection topic on Quantum Superconductivity}} | ||
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'''Quantum superconductivity''' is the study of [[superconductivity]] as a macroscopic [[quantum mechanics|quantum]] phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the | '''Quantum superconductivity''' is the study of [[superconductivity]] as a macroscopic [[quantum mechanics|quantum]] phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the Meissner effect. These effects arise because electrons form a coherent quantum state, often described as a charged quantum fluid. | ||
Superconductivity is one of the best-known examples of a '''macroscopic quantum phenomenon''', together with [[superfluidity]], the | Superconductivity is one of the best-known examples of a '''macroscopic quantum phenomenon''', together with [[superfluidity]], the Josephson effect, the [[quantum Hall effect]], and Bose–Einstein condensatess. Such systems show quantum behaviour not merely at the atomic scale but across macroscopic distances.<ref>D.R. Tilley and J. Tilley, ''Superfluidity and Superconductivity'', Adam Hilger, Bristol and New York, 1990</ref><ref>{{cite journal|last1=Jaeger|first1=Gregg|title=What in the (quantum) world is macroscopic?|journal=American Journal of Physics|date=September 2014|volume=82|issue=9|pages=896–905|doi=10.1119/1.4878358|bibcode=2014AmJPh..82..896J}}</ref> | ||
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== Cooper pairs == | == Cooper pairs == | ||
In conventional superconductors, the particles forming the macroscopic quantum state are | In conventional superconductors, the particles forming the macroscopic quantum state are Cooper pairss. A Cooper pair consists of two electrons bound together by an effective attraction mediated by lattice vibrations, or [[phonon]]s. | ||
Although electrons are [[fermion]]s, a Cooper pair behaves as a composite [[boson]]. The paired electrons can therefore occupy a collective quantum state. This coherent state is responsible for zero electrical resistance and the Meissner effect. | Although electrons are [[fermion]]s, a Cooper pair behaves as a composite [[boson]]. The paired electrons can therefore occupy a collective quantum state. This coherent state is responsible for zero electrical resistance and the Meissner effect. | ||
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'''Type-II superconductors''' have two critical fields. Between the lower critical field <math>H_{c1}</math> and the upper critical field <math>H_{c2}</math>, magnetic flux penetrates the superconductor in quantized vortex tubes. The material remains superconducting around these vortices. | '''Type-II superconductors''' have two critical fields. Between the lower critical field <math>H_{c1}</math> and the upper critical field <math>H_{c2}</math>, magnetic flux penetrates the superconductor in quantized vortex tubes. The material remains superconducting around these vortices. | ||
This mixed state was explained by | This mixed state was explained by Alexei Abrikosov using Ginzburg–Landau theory. In a type-II superconductor, the vortices can form an ordered triangular lattice, now called the Abrikosov vortex lattice.<ref>{{Cite journal|last1=Landau|first1=Lev Davidovich|last2=Ginzburg|first2=Vitaly L|date=1950|title=On the theory of superconductivity|url=https://cds.cern.ch/record/486430|journal=Zh. Eksp. Teor. Fiz.|volume=20}}</ref><ref>{{Cite journal |last=Abrikosov |first=Alexei A. |date=2004-07-19 |title=Type H Superconductors and the Vortex Lattice |journal=ChemPhysChem |volume=5 |issue=7 |pages=924–929 |doi=10.1002/cphc.200400138 |pmid=15298378 |doi-access=free}}</ref> | ||
== Josephson effect == | == Josephson effect == | ||
The | The Josephson effect occurs when two superconductors are separated by a thin insulating barrier or weak link. Even without a voltage, a supercurrent can tunnel through the barrier. | ||
The DC Josephson relation is | The DC Josephson relation is | ||
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:<math>\nu = \frac{2eV}{h} = \frac{V}{\Phi_0}.</math> | :<math>\nu = \frac{2eV}{h} = \frac{V}{\Phi_0}.</math> | ||
Josephson junctions are essential in superconducting electronics, | Josephson junctions are essential in superconducting electronics, SQUIDss, voltage standards, and superconducting quantum circuits. | ||
== SQUIDs == | == SQUIDs == | ||
A | A SQUIDs is a superconducting quantum interference device. It usually consists of a superconducting loop interrupted by one or more Josephson junctions. Because the total flux through the loop is quantized, the current through the SQUID depends sensitively on the applied magnetic field. | ||
This makes SQUIDs among the most sensitive magnetometers known. They are used in physics, materials science, geophysics, and biomedical measurements. | This makes SQUIDs among the most sensitive magnetometers known. They are used in physics, materials science, geophysics, and biomedical measurements. | ||
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== Superconductivity and phonons == | == Superconductivity and phonons == | ||
In conventional superconductors, phonons provide the attractive interaction that binds electrons into Cooper pairs. This electron–phonon mechanism is central to | In conventional superconductors, phonons provide the attractive interaction that binds electrons into Cooper pairs. This electron–phonon mechanism is central to BCS theory. The isotope effect, in which the superconducting critical temperature depends on ionic mass, provides evidence for the role of lattice vibrations in conventional superconductivity. | ||
Not all superconductors are fully explained by simple electron–phonon coupling. High-temperature superconductors, heavy-fermion superconductors, and unconventional superconductors involve more complex mechanisms. | Not all superconductors are fully explained by simple electron–phonon coupling. High-temperature superconductors, heavy-fermion superconductors, and unconventional superconductors involve more complex mechanisms. | ||
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== Quantum gases and mechanical systems == | == Quantum gases and mechanical systems == | ||
Macroscopic quantum behaviour is not limited to superconductors and superfluid helium. Dilute atomic gases cooled to nanokelvin temperatures can form | Macroscopic quantum behaviour is not limited to superconductors and superfluid helium. Dilute atomic gases cooled to nanokelvin temperatures can form Bose–Einstein condensatess, in which many atoms occupy a single quantum state.<ref>{{cite journal|author1=Anderson, M.H.|author2=Ensher, J.R.|author3=Matthews, M.R.|author4=Wieman, C.E.|author5=Cornell, E.A.|title=Observation of Bose–Einstein Condensation in a Dilute Atomic Vapor|journal=Science|volume=269|pages=198–201|year=1995|doi=10.1126/science.269.5221.198|pmid=17789847|issue=5221|bibcode=1995Sci...269..198A|doi-access=free}}</ref> | ||
Macroscopic quantum states have also been demonstrated in engineered mechanical systems. In quantum optomechanics and circuit electromechanics, mechanical resonators can be cooled close to their quantum ground state and controlled at the level of individual phonons.<ref>{{Cite journal |last1=Aspelmeyer |first1=Markus |last2=Kippenberg |first2=Tobias J. |last3=Marquardt |first3=Florian |title=Cavity optomechanics |journal=Reviews of Modern Physics |volume=86 |issue=4 |pages=1391–1452 |year=2014 |doi=10.1103/RevModPhys.86.1391 |arxiv=1303.0733 |bibcode=2014RvMP...86.1391A}}</ref><ref>{{Cite journal |first1=A. D. |last1=O’Connell |first2=M. |last2=Hofheinz |first3=M. |last3=Ansmann |first4=R. C. |last4=Bialczak |first5=M. |last5=Lenander |first6=E. |last6=Lucero |first7=M. |last7=Neeley |first8=D. |last8=Sank |first9=H. |last9=Wang |first10=M. |last10=Weides |first11=J. |last11=Wenner |first12=John M.|last12=Martinis |first13=A. N. |last13=Cleland |title=Quantum ground state and single-phonon control of a mechanical resonator |journal=Nature |volume=464 |issue=7289|pages=697–703 |year=2010 |doi=10.1038/nature08967 |bibcode=2010Natur.464..697O |pmid=20237473}}</ref> | Macroscopic quantum states have also been demonstrated in engineered mechanical systems. In quantum optomechanics and circuit electromechanics, mechanical resonators can be cooled close to their quantum ground state and controlled at the level of individual phonons.<ref>{{Cite journal |last1=Aspelmeyer |first1=Markus |last2=Kippenberg |first2=Tobias J. |last3=Marquardt |first3=Florian |title=Cavity optomechanics |journal=Reviews of Modern Physics |volume=86 |issue=4 |pages=1391–1452 |year=2014 |doi=10.1103/RevModPhys.86.1391 |arxiv=1303.0733 |bibcode=2014RvMP...86.1391A}}</ref><ref>{{Cite journal |first1=A. D. |last1=O’Connell |first2=M. |last2=Hofheinz |first3=M. |last3=Ansmann |first4=R. C. |last4=Bialczak |first5=M. |last5=Lenander |first6=E. |last6=Lucero |first7=M. |last7=Neeley |first8=D. |last8=Sank |first9=H. |last9=Wang |first10=M. |last10=Weides |first11=J. |last11=Wenner |first12=John M.|last12=Martinis |first13=A. N. |last13=Cleland |title=Quantum ground state and single-phonon control of a mechanical resonator |journal=Nature |volume=464 |issue=7289|pages=697–703 |year=2010 |doi=10.1038/nature08967 |bibcode=2010Natur.464..697O |pmid=20237473}}</ref> | ||
Revision as of 08:17, 20 May 2026
Quantum superconductivity is the study of superconductivity as a macroscopic quantum phenomenon. In a superconductor, electrical resistance vanishes and magnetic fields are expelled from the interior by the Meissner effect. These effects arise because electrons form a coherent quantum state, often described as a charged quantum fluid.
Superconductivity is one of the best-known examples of a macroscopic quantum phenomenon, together with superfluidity, the Josephson effect, the quantum Hall effect, and Bose–Einstein condensatess. Such systems show quantum behaviour not merely at the atomic scale but across macroscopic distances.[1][2]
Magnetic flux lines penetrating a type-II superconductor. The field enters in quantized vortex lines while superconductivity remains between the lower and upper critical fields.
Macroscopic quantum state
A superconducting state is described by a macroscopic wave function,
where is the amplitude and is the phase. When a quantum state is occupied by a very large number of particles, the wave function describes not only probability but also a macroscopic density and phase-coherent flow.[3][4]
The particle-flow density can be related to the phase of the wave function. For a condensate, the velocity is
where is the particle mass, is the charge, and is the magnetic vector potential.[5]
This equation shows the central idea: a classical observable such as flow velocity is controlled by the phase of a quantum wave function.
Relation to superfluidity
Superconductivity is closely related to superfluidity, but it is not the same phenomenon. Superfluidity is frictionless mass flow, while superconductivity is resistance-free charge flow.
In superfluid helium, the particles are neutral, so . The velocity of the superfluid is then determined only by the phase gradient:
Because the wave function must be single-valued, circulation is quantized:
This leads to quantized vortices in rotating superfluids. Superconductors show a closely related phenomenon, but because the condensate is charged, magnetic flux becomes quantized.
For this reason, superconductivity is often described as a charged superfluid.
Cooper pairs
In conventional superconductors, the particles forming the macroscopic quantum state are Cooper pairss. A Cooper pair consists of two electrons bound together by an effective attraction mediated by lattice vibrations, or phonons.
Although electrons are fermions, a Cooper pair behaves as a composite boson. The paired electrons can therefore occupy a collective quantum state. This coherent state is responsible for zero electrical resistance and the Meissner effect.
For a Cooper pair,
and
where is the electron mass and is the elementary charge.[6]
Flux quantization
Because the superconducting wave function is single-valued, magnetic flux in a superconducting loop is quantized. The basic flux quantum is
This value is extremely small, yet it is fundamental in superconducting circuits, vortex physics, and precision measurement.
Flux quantization is one of the clearest macroscopic manifestations of quantum mechanics. It shows that a superconducting ring behaves as a single coherent quantum object.
Type-I and Type-II superconductors
Superconductors are commonly divided into two types.
Type-I superconductors expel magnetic fields completely below a critical magnetic field. When the applied field exceeds this critical value, superconductivity is destroyed abruptly.
Type-II superconductors have two critical fields. Between the lower critical field and the upper critical field , magnetic flux penetrates the superconductor in quantized vortex tubes. The material remains superconducting around these vortices.
This mixed state was explained by Alexei Abrikosov using Ginzburg–Landau theory. In a type-II superconductor, the vortices can form an ordered triangular lattice, now called the Abrikosov vortex lattice.[7][8]
Josephson effect
The Josephson effect occurs when two superconductors are separated by a thin insulating barrier or weak link. Even without a voltage, a supercurrent can tunnel through the barrier.
The DC Josephson relation is
where is the phase difference between the two superconductors.[9]
If a voltage is applied, the phase difference changes in time:
This gives an alternating supercurrent with frequency
Josephson junctions are essential in superconducting electronics, SQUIDss, voltage standards, and superconducting quantum circuits.
SQUIDs
A SQUIDs is a superconducting quantum interference device. It usually consists of a superconducting loop interrupted by one or more Josephson junctions. Because the total flux through the loop is quantized, the current through the SQUID depends sensitively on the applied magnetic field.
This makes SQUIDs among the most sensitive magnetometers known. They are used in physics, materials science, geophysics, and biomedical measurements.
Superconductivity and phonons
In conventional superconductors, phonons provide the attractive interaction that binds electrons into Cooper pairs. This electron–phonon mechanism is central to BCS theory. The isotope effect, in which the superconducting critical temperature depends on ionic mass, provides evidence for the role of lattice vibrations in conventional superconductivity.
Not all superconductors are fully explained by simple electron–phonon coupling. High-temperature superconductors, heavy-fermion superconductors, and unconventional superconductors involve more complex mechanisms.
Quantum gases and mechanical systems
Macroscopic quantum behaviour is not limited to superconductors and superfluid helium. Dilute atomic gases cooled to nanokelvin temperatures can form Bose–Einstein condensatess, in which many atoms occupy a single quantum state.[10]
Macroscopic quantum states have also been demonstrated in engineered mechanical systems. In quantum optomechanics and circuit electromechanics, mechanical resonators can be cooled close to their quantum ground state and controlled at the level of individual phonons.[11][12]
Importance
Quantum superconductivity is important because it connects microscopic quantum mechanics to directly observable macroscopic effects. It provides examples of phase coherence, flux quantization, quantum tunneling, collective excitations, and topological defects in real materials.
Applications include superconducting magnets, magnetic sensors, quantum interference devices, particle accelerators, MRI systems, and superconducting qubits for quantum computing.
See also
Table of contents (198 articles)
Index
Full contents
References
- ↑ D.R. Tilley and J. Tilley, Superfluidity and Superconductivity, Adam Hilger, Bristol and New York, 1990
- ↑ Jaeger, Gregg (September 2014). "What in the (quantum) world is macroscopic?". American Journal of Physics 82 (9): 896–905. doi:10.1119/1.4878358. Bibcode: 2014AmJPh..82..896J.
- ↑ Fritz London, Superfluids, Wiley, 1954–1964.
- ↑ Gavroglu, K.; Goudaroulis, Y. (1988). "Understanding macroscopic quantum phenomena: The history of superfluidity 1941–1955". Annals of Science 45 (4): 367. doi:10.1080/00033798800200291.
- ↑ "The Feynman Lectures on Physics Vol. III Ch. 21: The Schrödinger Equation in a Classical Context: A Seminar on Superconductivity, Section 21-5: Superconductivity". https://feynmanlectures.caltech.edu/III_21.html.
- ↑ M. Tinkham (1975). Introduction to Superconductivity. McGraw-Hill.
- ↑ Landau, Lev Davidovich; Ginzburg, Vitaly L (1950). "On the theory of superconductivity". Zh. Eksp. Teor. Fiz. 20. https://cds.cern.ch/record/486430.
- ↑ Abrikosov, Alexei A. (2004-07-19). "Type H Superconductors and the Vortex Lattice". ChemPhysChem 5 (7): 924–929. doi:10.1002/cphc.200400138. PMID 15298378.
- ↑ B.D. Josephson (1962). "Possible new effects in superconductive tunneling". Phys. Lett. 1 (7): 251–253. doi:10.1016/0031-9163(62)91369-0. Bibcode: 1962PhL.....1..251J.
- ↑ Anderson, M.H.; Ensher, J.R.; Matthews, M.R.; Wieman, C.E.; Cornell, E.A. (1995). "Observation of Bose–Einstein Condensation in a Dilute Atomic Vapor". Science 269 (5221): 198–201. doi:10.1126/science.269.5221.198. PMID 17789847. Bibcode: 1995Sci...269..198A.
- ↑ Aspelmeyer, Markus; Kippenberg, Tobias J.; Marquardt, Florian (2014). "Cavity optomechanics". Reviews of Modern Physics 86 (4): 1391–1452. doi:10.1103/RevModPhys.86.1391. Bibcode: 2014RvMP...86.1391A.
- ↑ O’Connell, A. D.; Hofheinz, M.; Ansmann, M.; Bialczak, R. C.; Lenander, M.; Lucero, E.; Neeley, M.; Sank, D. et al. (2010). "Quantum ground state and single-phonon control of a mechanical resonator". Nature 464 (7289): 697–703. doi:10.1038/nature08967. PMID 20237473. Bibcode: 2010Natur.464..697O.
Source attribution: Physics:Quantum Superconductivity