In
condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions between the...
, a
Cooper pair is the name given to electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist
Leon CooperLeon N Cooper is an American physicist and Nobel Prize laureate, who with John Bardeen and John Robert Schrieffer, developed the BCS theory of superconductivity. He is also the namesake of the Cooper pair.-Biography:...
. Cooper showed that an arbitrarily small attraction between electrons in a metal can cause a paired state of electrons to have a lower energy than the
Fermi energyThe Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature...
, which implies that the pair is bound. In normal
superconductorsSuperconductivity is a phenomenon occurring in certain materials generally at very low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field . It was discovered by Heike Kamerlingh Onnes in 1911. Like ferromagnetism and atomic spectral...
, this attraction is due to the
electronAn electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...
–
phononIn physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's...
interaction. The Cooper pair state is responsible for superconductivity, as described in the
BCS theoryBCS theory is the first microscopic theory of superconductivity, proposed by Bardeen, Cooper, and Schrieffer in 1957 since the discovery of superconductivity in 1911. It describes superconductivity as a microscopic effect caused by a condensation of pairs of electrons into a boson-like...
developed by
John BardeenJohn Bardeen, Ph.D. was an American physicist and electrical engineer, who won the Nobel Prize in Physics twice: first in 1956 with William Shockley and Walter Brattain for the invention of the transistor; and again in 1972 with Leon Neil Cooper and John Robert Schrieffer for a fundamental theory...
, John Schrieffer and
Leon CooperLeon N Cooper is an American physicist and Nobel Prize laureate, who with John Bardeen and John Robert Schrieffer, developed the BCS theory of superconductivity. He is also the namesake of the Cooper pair.-Biography:...
for which they shared the 1972
Nobel PrizeThe Nobel Prize is a Sweden-based international monetary prize. The award was established by the 1895 will and estate of Swedish chemist and inventor Alfred Nobel. It was first awarded in Physics, Chemistry, Physiology or Medicine, Literature, and Peace in 1901...
.
The reason for the pairing can be seen from a simplified explanation. An electron in a metal normally behaves as a free particle. The electron is repelled from other electrons due to their negative
charge-In mathematics, science, and technology:* Charge , the air and/or fuel mixture being fed to an internal combustion engine* Charge , the susceptibility of a body to one of the fundamental forces...
, but it also attracts the positive
ionAn ion is an atom or molecule where the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge...
s that make up the rigid lattice of the metal. This attraction can distort the positively charged ion lattice in such a way as to attract other electrons (electron–
phononIn physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's...
interactions). At long distances this attraction between electrons due to the displaced ions can overcome the electrons' repulsion due to their negative charge, and cause them to pair-up.
The energy of the pairing interaction is quite weak, of the order of 10
−3eV, and thermal energy can easily break the pairs up. So only at low temperatures are a significant number of the electrons in a metal in Cooper pairs. The electrons in a pair are not necessarily close together; because the interaction is long range, paired electrons may still be many hundreds of
nanometersA nanometre is a unit of length in the metric system, equal to one billionth of a meter....
apart. This distance is usually greater than the average interelectron distance, so many Cooper pairs can occupy the same space. Electrons have spin-
{{Mergefrom|Spin–charge separation|discuss=Talk:Spin–charge separation#Merge?|date=August 2009}}
In
condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions between the...
, a
Cooper pair is the name given to electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist
Leon CooperLeon N Cooper is an American physicist and Nobel Prize laureate, who with John Bardeen and John Robert Schrieffer, developed the BCS theory of superconductivity. He is also the namesake of the Cooper pair.-Biography:...
. Cooper showed that an arbitrarily small attraction between electrons in a metal can cause a paired state of electrons to have a lower energy than the
Fermi energyThe Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature...
, which implies that the pair is bound. In normal
superconductorsSuperconductivity is a phenomenon occurring in certain materials generally at very low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field . It was discovered by Heike Kamerlingh Onnes in 1911. Like ferromagnetism and atomic spectral...
, this attraction is due to the
electronAn electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...
–
phononIn physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's...
interaction. The Cooper pair state is responsible for superconductivity, as described in the
BCS theoryBCS theory is the first microscopic theory of superconductivity, proposed by Bardeen, Cooper, and Schrieffer in 1957 since the discovery of superconductivity in 1911. It describes superconductivity as a microscopic effect caused by a condensation of pairs of electrons into a boson-like...
developed by
John BardeenJohn Bardeen, Ph.D. was an American physicist and electrical engineer, who won the Nobel Prize in Physics twice: first in 1956 with William Shockley and Walter Brattain for the invention of the transistor; and again in 1972 with Leon Neil Cooper and John Robert Schrieffer for a fundamental theory...
, John Schrieffer and
Leon CooperLeon N Cooper is an American physicist and Nobel Prize laureate, who with John Bardeen and John Robert Schrieffer, developed the BCS theory of superconductivity. He is also the namesake of the Cooper pair.-Biography:...
for which they shared the 1972
Nobel PrizeThe Nobel Prize is a Sweden-based international monetary prize. The award was established by the 1895 will and estate of Swedish chemist and inventor Alfred Nobel. It was first awarded in Physics, Chemistry, Physiology or Medicine, Literature, and Peace in 1901...
.
The reason for the pairing can be seen from a simplified explanation. An electron in a metal normally behaves as a free particle. The electron is repelled from other electrons due to their negative
charge-In mathematics, science, and technology:* Charge , the air and/or fuel mixture being fed to an internal combustion engine* Charge , the susceptibility of a body to one of the fundamental forces...
, but it also attracts the positive
ionAn ion is an atom or molecule where the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge...
s that make up the rigid lattice of the metal. This attraction can distort the positively charged ion lattice in such a way as to attract other electrons (electron–
phononIn physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's...
interactions). At long distances this attraction between electrons due to the displaced ions can overcome the electrons' repulsion due to their negative charge, and cause them to pair-up.
The energy of the pairing interaction is quite weak, of the order of 10
−3eV, and thermal energy can easily break the pairs up. So only at low temperatures are a significant number of the electrons in a metal in Cooper pairs. The electrons in a pair are not necessarily close together; because the interaction is long range, paired electrons may still be many hundreds of
nanometersA nanometre is a unit of length in the metric system, equal to one billionth of a meter....
apart. This distance is usually greater than the average interelectron distance, so many Cooper pairs can occupy the same space. Electrons have spin-
{{Mergefrom|Spin–charge separation|discuss=Talk:Spin–charge separation#Merge?|date=August 2009}}
In
condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions between the...
, a
Cooper pair is the name given to electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist
Leon CooperLeon N Cooper is an American physicist and Nobel Prize laureate, who with John Bardeen and John Robert Schrieffer, developed the BCS theory of superconductivity. He is also the namesake of the Cooper pair.-Biography:...
. Cooper showed that an arbitrarily small attraction between electrons in a metal can cause a paired state of electrons to have a lower energy than the
Fermi energyThe Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature...
, which implies that the pair is bound. In normal
superconductorsSuperconductivity is a phenomenon occurring in certain materials generally at very low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field . It was discovered by Heike Kamerlingh Onnes in 1911. Like ferromagnetism and atomic spectral...
, this attraction is due to the
electronAn electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. An electron has a mass that is approximately 1836 times less than that of the proton. The intrinsic angular momentum of the electron is a half integer...
–
phononIn physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's...
interaction. The Cooper pair state is responsible for superconductivity, as described in the
BCS theoryBCS theory is the first microscopic theory of superconductivity, proposed by Bardeen, Cooper, and Schrieffer in 1957 since the discovery of superconductivity in 1911. It describes superconductivity as a microscopic effect caused by a condensation of pairs of electrons into a boson-like...
developed by
John BardeenJohn Bardeen, Ph.D. was an American physicist and electrical engineer, who won the Nobel Prize in Physics twice: first in 1956 with William Shockley and Walter Brattain for the invention of the transistor; and again in 1972 with Leon Neil Cooper and John Robert Schrieffer for a fundamental theory...
, John Schrieffer and
Leon CooperLeon N Cooper is an American physicist and Nobel Prize laureate, who with John Bardeen and John Robert Schrieffer, developed the BCS theory of superconductivity. He is also the namesake of the Cooper pair.-Biography:...
for which they shared the 1972
Nobel PrizeThe Nobel Prize is a Sweden-based international monetary prize. The award was established by the 1895 will and estate of Swedish chemist and inventor Alfred Nobel. It was first awarded in Physics, Chemistry, Physiology or Medicine, Literature, and Peace in 1901...
.
The reason for the pairing can be seen from a simplified explanation. An electron in a metal normally behaves as a free particle. The electron is repelled from other electrons due to their negative
charge-In mathematics, science, and technology:* Charge , the air and/or fuel mixture being fed to an internal combustion engine* Charge , the susceptibility of a body to one of the fundamental forces...
, but it also attracts the positive
ionAn ion is an atom or molecule where the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge...
s that make up the rigid lattice of the metal. This attraction can distort the positively charged ion lattice in such a way as to attract other electrons (electron–
phononIn physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. The study of phonons is an important part of solid state physics, because phonons play a major role in many of the physical properties of solids, including a material's...
interactions). At long distances this attraction between electrons due to the displaced ions can overcome the electrons' repulsion due to their negative charge, and cause them to pair-up.
The energy of the pairing interaction is quite weak, of the order of 10
−3eV, and thermal energy can easily break the pairs up. So only at low temperatures are a significant number of the electrons in a metal in Cooper pairs. The electrons in a pair are not necessarily close together; because the interaction is long range, paired electrons may still be many hundreds of
nanometersA nanometre is a unit of length in the metric system, equal to one billionth of a meter....
apart. This distance is usually greater than the average interelectron distance, so many Cooper pairs can occupy the same space. Electrons have spin-{{frac, so they are
fermionIn particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. In contrast to bosons, which have Bose-Einstein statistics, only one fermion can occupy a quantum state at a given time; this is the Pauli Exclusion Principle. Thus, if more than one...
s, but a Cooper pair is a composite
bosonIn particle physics, bosons are particles which obey Bose–Einstein statistics; they are named after Satyendra Nath Bose and Albert Einstein. In contrast to fermions, which obey Fermi-Dirac statistics, several bosons can occupy the same quantum state. Thus, bosons with the same energy can occupy the...
as its total spin is integer (0 or 1). This means the wave functions are symmetric under particle interchange, and they are allowed to be in the same state. The tendency for all the Cooper pairs in a body to 'condense' into the same ground quantum state, or zero point is thought to be responsible for the peculiar properties of superconductivity.
Recently it has been shown that Cooper pairs can also be composed by two bosons. Here the pairing is supported by entanglement in an optical lattice.
Relationship to superconductivity
Cooper originally just considered the case of an isolated pair forming in a metal. When one considers the more realistic state consisting of many electrons forming pairs as is done in the full BCS Theory one finds that the pairing opens a gap in the continuous spectrum of allowed energy states of the electrons, meaning that all excitations of the system must possess some minimum amount of energy. This
gap to excitations leads to superconductivity, since small excitations such as scattering of electrons are forbidden.
The gap appears due to many-body effects between electrons feeling the attraction.
Herbert FröhlichHerbert Fröhlich was a German-born British physicist and a Fellow of the Royal Society....
was first to suggest that the electrons might act as pairs coupled by lattice vibrations in the material. This was indicated by the
isotopeIsotopes are different types of atoms of the same chemical element, each having a different number of neutrons. Correspondingly, isotopes differ in mass number but not in atomic number. The difference in the number of nucleons comes from a difference how many neutrons are in the atomic nucleus...
effect observed in superconductors. The isotope effect showed that materials with heavier ions (different
nuclear isotopesIsotopes are different types of atoms of the same chemical element, each having a different number of neutrons. Correspondingly, isotopes differ in mass number but not in atomic number. The difference in the number of nucleons comes from a difference how many neutrons are in the atomic nucleus...
) had lower superconducting transition temperatures. This can be explained nicely by the theory of Cooper pairing; since heavier ions are harder to move they would be less able to attract the electrons resulting in a smaller binding energy for Cooper pairs.
The pair are still Cooperic if and
The theory of Cooper pairs is quite general and does not depend on the specific electron-phonon interaction. Condensed matter theorists have proposed pairing mechanisms based on other attractive interactions such as electron–
excitonAn exciton is a bound state of an electron and an imaginary particle called an electron hole in an insulator or semiconductor, and such is a Coulomb-correlated electron-hole pair. It is an elementary excitation, or a quasiparticle of a solid. In current research, the bound electron and hole pairs ...
interactions or electron–
plasmonIn physics, a plasmon is a quantum of plasma oscillation. The plasmon is the quasiparticle resulting from the quantization of plasma oscillations just as photons and phonons are quantizations of light and sound waves, respectively. Thus, plasmons are collective oscillations of the free electron...
interactions. Currently, none of these alternate pairing interactions has been observed in any material.
See also
- Color–flavor locking
- Superinsulator
A superinsulator is a material that at low temperatures under certain conditions has an infinite resistance and no current will pass through it. The superinsulating state has many parallels to the superconducting state, and can be destroyed by increased temperature, magnetic fields and voltage.The...
- lone pair
A lone pair is a electron pair without bonding or sharing with other atoms. They are found in the outermost electron shell of an atom, so lone pairs are a subset of a molecule's valence electrons...
- electron pair
In chemistry, an electron pair consists of two electrons that occupy the same orbital but have opposite spins.Because electrons are fermions, the Pauli exclusion principle forbids these particles from having exactly the same quantum numbers. Therefore the only way to occupy the same orbital, i.e....
- superconductivity
Superconductivity is a phenomenon occurring in certain materials generally at very low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field . It was discovered by Heike Kamerlingh Onnes in 1911. Like ferromagnetism and atomic spectral...
- superfluidity
{{DEFAULTSORT:Cooper Pair}}