SU(2) color superconductivity

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Several hundred metals, compounds, alloys and ceramics possess the property of superconductivity at low temperatures. The SU(2) color quark matter adjoins the list of superconducting systems. Although it is a mathematical abstraction, its properties are believed to be closely related to the SU(3) color quark matter, which exists in nature when ordinary matter is compressed at supranuclear densities above ~ 0.5 1039 nucleon/cm3.

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Superconductors in Lab

Superconducting materials are characterized by the loss of resistance and two parameters: a critical temperature Tc and a critical magnetic field which brings the superconductor to its normal state. In 1911, H. Kamerlingh Onnes discovered the superconductivity of mercury at a temperature below 4 K. Later, other substances with superconductivity at temperatures up to 30 K were found. Superconductors prevent the penetration of the external magnetic field into the sample when the magnetic field strength is less than the critical value. This effect was called the Meissner effect. High-temperature superconductivity was discovered in the 1980s. Of the known compounds, the highest critical temperature Tс = 135 K belongs to HgBa2Ca2Cu3O8+x.

Low-temperature superconductivity has found a theoretical explanation in the model of Bardeen, Cooper, and Schrieffer (BCS theory). [1] The physical basis of the model is the phenomenon of Cooper pairing of electrons. Since a pair of electrons carries an integer spin, the correlated states of the electrons can form a Bose–Einstein condensate. An equivalent formalism was developed by Bogoliubov [2] and Valatin . [3]

Cooper pairing of nucleons takes place in ordinary nuclei. The effect manifests itself in the Bethe–Weizsacker mass formula, the last pairing term of which describes the correlation energy of two nucleons. Because of the pairing, the binding energy of even-even nuclei systematically exceeds the binding energy of odd-even and odd-odd nuclei.

Superfluidity in neutron stars

The superfluid phase of neutron matter exists in neutron stars. The superfluidity is described by the BCS model with a realistic nucleon-nucleon interaction potential. By increasing the density of nuclear matter above the saturation density, quark matter is formed. It is expected that dense quark matter at low temperatures is a color superconductor. [4] [5] [6] In the case of the SU(3) color group, a Bose–Einstein condensate of the quark Cooper pairs carries an open color. To meet the requirement of confinement, a Bose–Einstein condensate of colorless 6-quark states is considered, [5] or the projected BCS theory is used. [7] [8]

Superconductivity with dense two-color QCD

The BCS formalism is applicable without modifications to the description of quark matter with color group SU(2), where Cooper pairs are colorless. The Nambu–Jona-Lasinio model predicts the existence of the superconducting phase of SU(2) color quark matter at high densities . [9] This physical picture is confirmed in the Polyakov–Nambu–Jona-Lasinio model, [10] and also in lattice QCD models [11] , [12] in which the properties of cold quark matter can be described based on the first principles of quantum chromodynamics. The possibility of modeling on the lattices of two-color QCD at finite chemical potentials for even numbers of the quark flavors is associated with the positive-definiteness of the integral measure and the absence of a sign problem.

See also

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In physics, theBardeen–Cooper–Schrieffer (BCS) 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.

<span class="mw-page-title-main">Quantum chromodynamics</span> Theory of the strong nuclear interactions

In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carriers of the theory, just as photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years.

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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.

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<span class="mw-page-title-main">Effective field theory</span> Type of approximation to an underlying physical theory

In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective field theory includes the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale or energy scale, while ignoring substructure and degrees of freedom at shorter distances. Intuitively, one averages over the behavior of the underlying theory at shorter length scales to derive what is hoped to be a simplified model at longer length scales. Effective field theories typically work best when there is a large separation between length scale of interest and the length scale of the underlying dynamics. Effective field theories have found use in particle physics, statistical mechanics, condensed matter physics, general relativity, and hydrodynamics. They simplify calculations, and allow treatment of dissipation and radiation effects.

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<span class="mw-page-title-main">Lattice QCD</span> Quantum chromodynamics on a lattice

Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum QCD is recovered.

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<span class="mw-page-title-main">Superfluidity</span> Fluid which flows without losing kinetic energy

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<span class="mw-page-title-main">Light-front quantization applications</span> Quantization procedure in quantum field theory

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References

  1. ↑ Bardeen, J.; Cooper, L. N.; Schrieffer, J. R. (1957). "Microscopic Theory of Superconductivity". Physical Review. 106 (1): 162–164. Bibcode:1957PhRv..106..162B. doi: 10.1103/PhysRev.106.162 .
  2. ↑ Bogoljubov, N. N. (1958). "On a new method in the theory of superconductivity". Il Nuovo Cimento. 7 (6): 794–805. Bibcode:1958NCim....7..794B. doi:10.1007/bf02745585. S2CID   120718745.
  3. ↑ Valatin, J. G. (1958). "Comments on the theory of superconductivity". Il Nuovo Cimento. 7 (6): 843–857. Bibcode:1958NCim....7..843V. doi:10.1007/bf02745589. S2CID   123486856.
  4. ↑ Ivanenko, D. D.; Kurdgelaidze, D. F. (1969). "Remarks on quark stars". Lettere al Nuovo Cimento. 2: 13–16. Bibcode:1969NCimL...2...13I. doi:10.1007/BF02753988. S2CID   120712416.
  5. 1 2 Barrois, B. C. (1977). "Superconducting quark matter". Nuclear Physics B. 129 (3): 390–396. Bibcode:1977NuPhB.129..390B. doi:10.1016/0550-3213(77)90123-7.
  6. ↑ Rajagopal, K.; Wilczek, F. (2000). "The Condensed Matter Physics of QCD". At the Frontier of Particle Physics. 34: 2061–2151. arXiv: hep-ph/0011333 . doi:10.1142/9789812810458_0043. ISBN   978-981-02-4445-3. S2CID   13606600.
  7. ↑ Bayman, B. F. (1960). "A derivation of the pairing-correlation method". Nuclear Physics. 15: 33–38. Bibcode:1960NucPh..15...33B. doi:10.1016/0029-5582(60)90279-0.
  8. ↑ Amore, P.; Birse, M. C.; McGovern, J. A.; Walet, N. R. (2002). "Color superconductivity in finite systems". Physical Review D. 65 (7): 074005. arXiv: hep-ph/0110267 . Bibcode:2002PhRvD..65g4005A. doi:10.1103/PhysRevD.65.074005. S2CID   119105093.
  9. ↑ Kondratyuk, L. A.; Krivoruchenko, M. I. (1992). "Superconducting quark matter in SU(2) color group". Zeitschrift für Physik A. 344 (1): 99–115. Bibcode:1992ZPhyA.344...99K. doi:10.1007/BF01291027. S2CID   120467300.
  10. ↑ Strodthoff, N.; von Smekal, L. (2014). "Polyakov-quark-meson-diquark model for two-color QCD". Physics Letters B. 731: 350–357. arXiv: 1306.2897 . Bibcode:2014PhLB..731..350S. doi:10.1016/j.physletb.2014.03.008. S2CID   118559080.
  11. ↑ Hands, S.; Kim, S.; Skullerud, J.-I. (2006). "Deconfinement in dense two-color QCD". The European Physical Journal C. 48 (1): 193–206. arXiv: hep-lat/0604004 . Bibcode:2006EPJC...48..193H. doi:10.1140/epjc/s2006-02621-8. S2CID   6669937.
  12. ↑ Braguta, V. V.; Ilgenfritz, E.-M.; Kotov, A. Yu.; Molochkov, A. V.; Nikolaev, A. A. (2016). "Study of the phase diagram of dense two-color QCD within lattice simulation". Physical Review D. 94 (11): 114510. arXiv: 1605.04090 . Bibcode:2016PhRvD..94k4510B. doi:10.1103/PhysRevD.94.114510. S2CID   119138862.
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