Color superconductivity
Encyclopedia
Color superconductivity is a phenomenon predicted to occur in quark matter
if the baryon
density is sufficiently high (well above nuclear density) and the temperature is not too high (well below 1012 kelvin). Color superconducting phases are to be contrasted with the normal phase of quark matter, which is just a weakly interacting Fermi liquid
of quarks.
In theoretical terms, a color superconducting phase is a state in which the quarks near the Fermi surface
become correlated in Cooper pairs, which condense. In phenomenological terms, a color superconducting phase breaks some of the symmetries of the underlying theory, and has a very different spectrum of excitations and very different transport properties from the normal phase.
of electrons, and below a critical temperature, an attractive phonon
-mediated interaction between the electrons near the Fermi surface causes them to pair up and form a condensate of Cooper pairs, which via the Anderson-Higgs mechanism
makes the photon
massive, leading to the characteristic behaviors of a superconductor; infinite conductivity and the exclusion of magnetic fields (Meissner effect
). The crucial ingredients for this to occur are:
These ingredients are also present in sufficiently dense quark matter, leading physicists to expect that something similar will happen in that context:
The fact that a Cooper pair of quarks carries a net color charge, as well as a net electric charge, means that the gluons (which mediate the strong interaction just as photons mediate electromagnetism) become massive in a phase with a condensate of quark Cooper pairs, so such a phase is called a "color superconductor". Actually, in many color superconducting phases the photon itself does not become massive, but mixes with one of the gluons to yield a new massless "rotated photon". This is an MeV-scale echo of the mixing of the hypercharge
and W3 bosons that originally yielded the photon at the TeV scale of electroweak symmetry breaking.
matter comes in many varieties, each of which is a separate phase of
matter. This is because quarks, unlike electrons, come in many
species. There are three different colors (red, green, blue) and in
the core of a compact star we expect three different flavors (up,
down, strange), making nine species in all.
Thus in forming the Cooper pairs there is a
9x9 color-flavor matrix of possible pairing patterns. The
differences between these patterns are very physically significant:
different patterns break different symmetries of the underlying theory, leading to different excitation spectra and different transport properties.
It is very hard to predict which pairing patterns will be favored in nature. In principle this question could be decided by a QCD calculation, since QCD is the theory that fully describes the strong interaction. In the limit of infinite density, where the strong interaction becomes weak because of asymptotic freedom
, controlled calculations can be performed, and it is known that the favored phase in three-flavor quark matter is the color-flavor-locked
phase. But at the densities that exist in nature these calculations are unreliable, and the only known alternative is the brute-force computational approach of lattice QCD
, which unfortunately has a technical difficulty (the "sign problem") that renders it useless for calculations at high quark density and low temperature.
Physicists are currently following the following lines of
research on color superconductivity:
(often called a "neutron star
", a term which prejudges the question of its actual makeup). There are many open questions here:
and D. F. Kurdgelaidze of Moscow State University
, in 1969. However, their insight was not pursued until the development of QCD as the theory of the strong interaction in the early 1970s. In 1977 Stephen Frautschi, a professor at Caltech, and his graduate student Bertrand Barrois realized that QCD predicts Cooper pairing in high density quark matter, and coined the term "color superconductivity". Barrois was able to get part of his work published in the journal Nuclear Physics, but that journal rejected the longer manuscript based on his thesis, which impressively anticipated later results such as the exp(-1/g) dependence of the quark condensate on the QCD coupling g. Barrois then left academic physics. At around the same time the subject was also treated by David Bailin and Alexander Love at Sussex University, who studied various pairing patterns in detail, but did not give much attention to the phenomenology of color superconductivity in real-world quark matter.
Apart from papers by Masaharu Iwaskai and T. Iwado of Kochi University
in 1995,
there was little activity until 1998, when there was a major upsurge of interest in dense quark matter and color superconductivity, sparked by the simultaneously published work of two groups, one at the Institute for Advanced Study
in Princeton and the other at SUNY Stony Brook
.
These physicists pointed out that the strength of the strong interaction makes the phenomenon much more significant than had previously been suggested. These and other groups went on to investigate the complexity of the many possible phases of color superconducting quark matter, and perform accurate calculations in the well-controlled limit of infinite density. Since then, interest in the topic has steadily grown, with current research (as of 2007) focusing on the detailed mapping of a plausible phase diagram for dense quark matter, and the search for observable signatures of the occurrence of these forms of matter in compact stars.
QCD matter
Quark matter or QCD matter refers to any of a number of theorized phases of matter whose degrees of freedom include quarks and gluons. These theoretical phases would occur at extremely high temperatures and densities, billions of times higher than can be produced in equilibrium in laboratories...
if the baryon
Baryon
A baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...
density is sufficiently high (well above nuclear density) and the temperature is not too high (well below 1012 kelvin). Color superconducting phases are to be contrasted with the normal phase of quark matter, which is just a weakly interacting Fermi liquid
Fermi liquid
Fermi liquid theory is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low temperatures. The interaction between the particles of the many-body system does not need to be small...
of quarks.
In theoretical terms, a color superconducting phase is a state in which the quarks near the Fermi surface
Fermi surface
In condensed matter physics, the Fermi surface is an abstract boundary useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline...
become correlated in Cooper pairs, which condense. In phenomenological terms, a color superconducting phase breaks some of the symmetries of the underlying theory, and has a very different spectrum of excitations and very different transport properties from the normal phase.
Analogy with superconducting metals
It is well known that at low temperature many metals become superconductors. A metal can be viewed as a Fermi liquidFermi liquid
Fermi liquid theory is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low temperatures. The interaction between the particles of the many-body system does not need to be small...
of electrons, and below a critical temperature, an attractive phonon
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
-mediated interaction between the electrons near the Fermi surface causes them to pair up and form a condensate of Cooper pairs, which via the Anderson-Higgs mechanism
Higgs mechanism
In particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....
makes the photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
massive, leading to the characteristic behaviors of a superconductor; infinite conductivity and the exclusion of magnetic fields (Meissner effect
Meissner effect
The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin...
). The crucial ingredients for this to occur are:
- a liquid of charged fermions.
- an attractive interaction between the fermions
- low temperature (below the critical temperature)
These ingredients are also present in sufficiently dense quark matter, leading physicists to expect that something similar will happen in that context:
- quarks carry both electric charge and color charge;
- the strong interactionStrong interactionIn particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
between two quarks is powerfully attractive; - the critical temperature is expected to be given by the QCD scale, which is of order 100 MeV, or 1012 kelvin, the temperature of the universe a few minutes after the big bangBig BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
, so quark matter that we may currently observe in compact stars or other natural settings will be below this temperature.
The fact that a Cooper pair of quarks carries a net color charge, as well as a net electric charge, means that the gluons (which mediate the strong interaction just as photons mediate electromagnetism) become massive in a phase with a condensate of quark Cooper pairs, so such a phase is called a "color superconductor". Actually, in many color superconducting phases the photon itself does not become massive, but mixes with one of the gluons to yield a new massless "rotated photon". This is an MeV-scale echo of the mixing of the hypercharge
Hypercharge
In particle physics, the hypercharge Y of a particle is related to the strong interaction, and is distinct from the similarly named weak hypercharge, which has an analogous role in the electroweak interaction...
and W3 bosons that originally yielded the photon at the TeV scale of electroweak symmetry breaking.
Diversity of color superconducting phases
Unlike an electrical superconductor, color-superconducting quarkmatter comes in many varieties, each of which is a separate phase of
matter. This is because quarks, unlike electrons, come in many
species. There are three different colors (red, green, blue) and in
the core of a compact star we expect three different flavors (up,
down, strange), making nine species in all.
Thus in forming the Cooper pairs there is a
9x9 color-flavor matrix of possible pairing patterns. The
differences between these patterns are very physically significant:
different patterns break different symmetries of the underlying theory, leading to different excitation spectra and different transport properties.
It is very hard to predict which pairing patterns will be favored in nature. In principle this question could be decided by a QCD calculation, since QCD is the theory that fully describes the strong interaction. In the limit of infinite density, where the strong interaction becomes weak because of asymptotic freedom
Asymptotic freedom
In physics, asymptotic freedom is a property of some gauge theories that causes interactions between particles to become arbitrarily weak at energy scales that become arbitrarily large, or, equivalently, at length scales that become arbitrarily small .Asymptotic freedom is a feature of quantum...
, controlled calculations can be performed, and it is known that the favored phase in three-flavor quark matter is the color-flavor-locked
Color-flavor locking
Color–flavor locking is a phenomenon that is expected to occur in ultra-high-density quark matter. The quarks form Cooper pairs, whose color properties are correlated with their flavor properties in a symmetric pattern...
phase. But at the densities that exist in nature these calculations are unreliable, and the only known alternative is the brute-force computational approach of lattice QCD
Lattice QCD
Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time....
, which unfortunately has a technical difficulty (the "sign problem") that renders it useless for calculations at high quark density and low temperature.
Physicists are currently following the following lines of
research on color superconductivity:
- Performing calculations in the infinite density limit, to get some idea of the behavior at one edge of the phase diagram.
- Performing calculations of the phase structure down to medium density using a highly simplified model of QCD, the Nambu-Jona-LasinioNambu-Jona-Lasinio modelIn quantum field theory, the Nambu–Jona-Lasinio model is a theory of nucleons and mesons constructed from interacting Dirac fermions with chiral symmetry which parallels the construction of Cooper pairs from electrons in the BCS theory of superconductivity...
(NJL) model, which is not a controlled approximation, but is expected to yield semi-quantitative insights. - Writing down an effective theory for the excitations of a given phase, and using it to calculate the physical properties of that phase.
- Performing astrophysical calculations, using NJL models or effective theories, to see if there are observable signatures by which one could confirm or rule out the presence of specific color superconducting phases in nature (i.e. in compact stars: see next section).
Occurrence in nature
The only known place in the universe where the baryon density might possibly be high enough to produce quark matter, and the temperature is low enough for color superconductivity to occur, is the core of a compact starCompact star
In astronomy, the term compact star is used to refer collectively to white dwarfs, neutron stars, other exotic dense stars, and black holes. These objects are all small for their mass...
(often called a "neutron star
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...
", a term which prejudges the question of its actual makeup). There are many open questions here:
- We do not know the critical density at which there would be a phase transition from nuclear matter to some form of quark matter, so we do not know whether compact stars have quark matter cores or not.
- On the other extreme, it is conceivable that nuclear matter in bulk is actually metastable, and decays into quark matter (the "stable strange matterStrange matterStrange matter is a particular form of quark matter, usually thought of as a "liquid" of up, down, and strange quarks. It is to be contrasted with nuclear matter, which is a liquid of neutrons and protons , and with non-strange quark matter, which is a quark liquid containing only up and down quarks...
hypothesis"). In this case, compact stars would consist completely of quark matter all the way to their surface. - Assuming that compact stars do contain quark matter, we do not know whether that quark matter is in a color superconducting phase or not. At infinite density one expects color superconductivity, and the attractive nature of the dominant strong quark-quark interaction leads one to expect that it will survive down to lower densities, but there may be a transition to some strongly coupled phase (e.g. a Bose-Einstein condensate of spatially bound diquarks).
History
The first physicists to realize that Cooper pairing could occur in quark matter were D. D. IvanenkoDmitri Ivanenko
Dmitri Ivanenko , Professor of Moscow State University , made a great contribution to the physical science of the twentieth century, especially to nuclear physics, field theory , and gravitation theory.His outstanding achievements include:* the Fock-Ivanenko coefficients of parallel...
and D. F. Kurdgelaidze of Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
, in 1969. However, their insight was not pursued until the development of QCD as the theory of the strong interaction in the early 1970s. In 1977 Stephen Frautschi, a professor at Caltech, and his graduate student Bertrand Barrois realized that QCD predicts Cooper pairing in high density quark matter, and coined the term "color superconductivity". Barrois was able to get part of his work published in the journal Nuclear Physics, but that journal rejected the longer manuscript based on his thesis, which impressively anticipated later results such as the exp(-1/g) dependence of the quark condensate on the QCD coupling g. Barrois then left academic physics. At around the same time the subject was also treated by David Bailin and Alexander Love at Sussex University, who studied various pairing patterns in detail, but did not give much attention to the phenomenology of color superconductivity in real-world quark matter.
Apart from papers by Masaharu Iwaskai and T. Iwado of Kochi University
Kochi University
is a national university in Kōchi, Kōchi, Japan. The predecessor of the school was founded in 1922, and it was chartered as a university in 1949.-External links:*...
in 1995,
there was little activity until 1998, when there was a major upsurge of interest in dense quark matter and color superconductivity, sparked by the simultaneously published work of two groups, one at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton and the other at SUNY Stony Brook
State University of New York at Stony Brook
The State University of New York at Stony Brook, also known as Stony Brook University, is a public research university located in Stony Brook, New York, on the North Shore of Long Island, about east of Manhattan....
.
These physicists pointed out that the strength of the strong interaction makes the phenomenon much more significant than had previously been suggested. These and other groups went on to investigate the complexity of the many possible phases of color superconducting quark matter, and perform accurate calculations in the well-controlled limit of infinite density. Since then, interest in the topic has steadily grown, with current research (as of 2007) focusing on the detailed mapping of a plausible phase diagram for dense quark matter, and the search for observable signatures of the occurrence of these forms of matter in compact stars.
Further reading
- S. Hands, "The phase diagram of QCD", Contemp. Phys. 42, 209 (2001) arXiv.org:physics/0105022
- J. Cheyne, G. Cowan, M. Alford, "Superconducting quarks", PPARC Frontiers 21, 16 (2004)
External Links
- M. Alford, K. Rajagopal, T. Schäfer, A. Schmitt, "Color superconductivity in dense quark matter", Reviews of Modern Physics, 80, 1455 (2008);arXiv.org:0709.4635
- K. Rajagopal and F. Wilczek, "The condensed matter physics of QCD", arXiv.org:hep-ph/0011333
- M. Alford, "Color superconducting quark matter", Ann. Rev. Nucl. Part. Sci. 51, 131 (2001);arXiv.org:hep-ph/0102047
- G. Nardulli, "Effective description of QCD at very high densities", Riv. Nuovo Cim. 25N3, 1 (2002); arXiv.org: hep-ph/0202037
- T. Schäfer, "Quark matter", arxiv.org:hep-ph/0304281
- D. Rischke, "The quark-gluon plasma in equilibrium", Prog. Part. Nucl. Phys. 52, 197 (2004);arXiv.org:nucl-th/0305030
- S. Reddy, "Novel phases at high density and their roles in the structure and evolution of neutron stars", Acta Phys. Polon. B 33, 4101 (2002); arXiv.org:nucl-th/0211045
- I. Shovkovy, Two lectures on color superconductivity, Found.Phys. 35 (2005) 1309-1358 arXiv.org: nucl-th/0410091