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Topic: Cooper pairs

	Cooper Pairs and the BCS Theory of Superconductivity
		Cooper Pairs and the BCS Theory of Superconductivity
		This pair condensation is the basis for the BCS theory of superconductivity.
		The condensation of Cooper pairs is the foundation of the BCS theory of superconductivity.
	hyperphysics.phy-astr.gsu.edu /hbase/solids/coop.html (509 words)

	Splitting Up Cooper Pairs (Site not responding. Last check: 2007-10-03)
		Pairs of single nanotubes might be used in future experiments to separate the entangled electron pairs in superconductors.
		Entangled pairs of particles, in which measuring the state of one simultaneously determines the state of the other, are a central part of proposed schemes for quantum cryptography and teleportation.
		Cooper pairs, which exist naturally in an entangled state, are an obvious choice.
	focus.aps.org /v9/st33.html (581 words)

	exotic superconductivity - Quantum Physics - tribe.net
		Cooper had discovered that electrons in a superconductor don't act as individual particles, but as pairs, now called "Cooper pairs." When electrical voltage is applied to a superconductor, all Cooper pairs move as a single entity, establishing an electrical current.
		They discovered that electrons in a Cooper pair, no matter how far apart they are, have either conventional "singlet" or unconventional "triplet" internal rotation, or "spin" in quantum physics jargon.
		Lebed has now discovered that super-strong magnetic fields create exotic Cooper pairs that behave according to the weird, non-intuitive laws of quantum mechanics: the electron pairs are both rotating and non-rotating at the same time.
	quantumphysics.tribe.net /thread/3942f119-6c05-48b7-b8cb-d99259291179 (1645 words)

	Cooper pairs (Site not responding. Last check: 2007-10-03)
		Cooper pairs - a central mechanism in the BCS theory of superconductivity: the electrons in the lattice, because of lattice effects, may form bound systems despite their mutual repulsion and fermionic exclusiveness.
		Members of a pair are not necessarily (and in general will not be) physically near each other - they are related in momentum space.
		Consisting of two half-integer spin fermions, the Cooper pairs are composite bosons, and they subsequently may undergo Bose-Einstein condensation, resulting in, for example, superconductivity.
	www.nonlocal.com /hbar/cooperpairs.html (104 words)

	Experiment confirms existence of new electronic state in superconductors
		Quantum mechanics demands that the phase of two pairs moving in opposite directions be different by exactly zero or 180 degrees." If the clocks of two Cooper pairs moving in opposite directions have the same time, the symmetry of the pairs is designated as even parity.
		On the other hand, if the clocks for two pairs moving in the opposite directions are six hours apart--a phase difference of 180 degrees--the symmetry of the Cooper pairs is designated as odd-parity symmetry.
		The basic idea of the experiment is to measure the dependence of the phase of the Cooper-pair wave function on the direction in which the Cooper pair moves, using the phenomenon of wave interference.
	www.eurekalert.org /pub_releases/2004-11/ps-ece110504.php (1166 words)

	Cooper, Leon (Niels) (Site not responding. Last check: 2007-10-03)
		Cooper was born in New York, where he attended Columbia University, specializing in quantum field theory - the interaction of particles and fields in subatomic systems.
		Although the electrons in the pair are only weakly bound to each other, Bardeen, Cooper, and Schrieffer were able to show that they all form a single quantum state with a single momentum.
		Cooper pairs cannot be formed above the critical temperature, and superconductivity breaks down.
	www.cartage.org.lb /en/themes/Biographies/MainBiographies/C/Cooper/1.html (273 words)

	Superconductivity - BCS Theory
		The formation of Cooper pairs is supported by the fact that BCS and the Ginzburg-Landau theories predict the charge and mass of the supercurrent 'particle' to be 2e and 2M
		Mathematically, because the Cooper pair is more stable than a single electron within the lattice, it experiences less resistance (although the superconducting state cannot be made up entirely of Cooper pairs as this would lead to the collapse of the state).
		Physically, the Cooper pair is more resistant to vibrations within the lattice as the attraction to its partner will keep it 'on course' - therefore, Cooper pairs move through the lattice relatively unaffected by thermal vibrations (electron-phonon interactions) below the critical temperature.
	www.chm.bris.ac.uk /webprojects2000/igrant/bcstheory.html (457 words)

	Leon N. Cooper Biography \| World of Scientific Discovery
		Cooper was born in New York City on February 28, 1930.
		Cooper realized that the movement of a free electron through a metal has a tendency to attract positive ions toward itself.
		The BCS theory postulates next that the phenomenon of Cooper pairs may be extended to all of the conducting electrons in the metal.
	www.bookrags.com /biography/leon-n-cooper-wsd (428 words)

	Tracking the Strange Behavior of Quasiparticles
		In superconductors, pairs of electrons known as Cooper pairs condense in a "superfluid" that carries electrical current without resistance.
		Unlike conventional superconductors, in which Cooper pairs are bound in spatially symmetric s-wave states, the pairs in high-Tc superconductors occupy d-wave states, with orbitals shaped rather like crossed dumbbells.
		Very little energy is needed to break a Cooper pair into quasiparticles if their momenta are oriented at 45 degrees to a cuprate's copper-oxygen bonds.
	www.lbl.gov /Science-Articles/Archive/MSD-tracking-quasiparticles.html (1571 words)

	Magnetic Field Creates Bizarre Superconducting Effects
		What this triumvirate of researchers had discovered is that electrons in a superconductor don't act as individual particles, but as pairs, now known as "Cooper pairs." When electrical voltage is applied to a superconductor, all Cooper pairs move as a single entity, establishing an electrical current.
		Electrons in such Cooper pairs are believed to have either conventional "singlet" or unconventional "triplet" internal rotation (spin).
		He and co-researcher Omjyoti Dutta say that time-reversal symmetry is broken because of the simultaneous rotating and non-rotating average spins of exotic Cooper pairs.
	www.scienceagogo.com /news/20060717005040data_trunc_sys.shtml (1419 words)

	National Synchrotron Light Source
		The Bardeen, Cooper, and Schrieffer (BCS) theory of superconductivity showed that, in a classical superconductor, zero electrical resistance is a consequence of electrons pairing themselves.
		These "Cooper pairs" have a typical binding energy (2Δ) that leads to a gap for unpaired electrons at the Fermi energy.
		We utilized the laser pulses to break pairs (pump) in several conventional superconductors, including Pb, Nb, and NbN, and the far-infrared light from beamlines U12IR and U10A to probe the changes in the optical response of the superconductor, which strongly depends on the number of Cooper pairs.
	www.nsls.bnl.gov /newsroom/science/2006/01-Lobo.htm (796 words)

	Press Release: The 1972 Nobel Prize in Physics
		The new theory demonstrated that the interaction between the electrons and the lattice leads to the formation of bound pairs of electrons, which are often called Cooper-pairs.
		The different pairs are strongly coupled to each other which leads to a complex collective pattern in which a considerable fraction of the total number of conduction electrons are coupled together to form the superconducting state.
		The theory developed by Bardeen, Cooper and Schrieffer together with extensions and refinements of the theory, which were developed by many authors soon after the key discovery, was indeed very successful in explaining in considerable detail the properties of superconductors.
	nobelprize.org /nobel_prizes/physics/laureates/1972/press.html (488 words)

	5 BCS Theory
		Determining exactly how many Cooper pairs are formed is a difficult task because it involves comparing the relative energy loss from the formation of an additional Cooper pair (see equation 47) with the energy gain from creating holes in the Fermi sea.
		Numerous Cooper pairs form until the energy is minimized, resulting in a system with a net energy lower than the normal ground state.
		The steepness of the transition to superconductivity (see Onnes' original data in figure 3) is because of the steepness of the transition from numerous Cooper pairs to zero Cooper pairs.
	iguanaworks.net /~bluey/MyWritings/SC/node6.html (2394 words)

	ILL : ANNUAL REPORT 2001
		The Cooper pairs are able to share the same quantum state because their quantum mechanical properties are different to those of the constituent electrons.
		In the first superconductors to be discovered, such as mercury and lead, the Cooper pairs form with the spins of the constituent electrons aligned in an anti-parallel “singlet state”, the total spin of the pair S = 0.
		In particular, the quantum state of the Cooper pair and attractive interaction that allows the Cooper pair to form are different.
	www.ill.fr /AR-01/p-28.htm (1146 words)

	ScienceWeek
		The essential aspect of BCS theory is the grouping of electrons in superconductors in pairs ("Cooper pairs"), with the motions of all the Cooper pairs within a single superconductor correlated, i.e., the population of Cooper-pair electrons constituting a system that functions essentially as a single entity.
		(In quantum mechanical terms, each Cooper pair consists of electrons of opposite spins, thus forming a spin-zero single boson, and the population of bosons form a Bose-Einstein condensate described by a single wave function.) Application of an electric voltage to the superconductor causes all Cooper pairs to move, the movement constituting a current.
		When the voltage is removed, current continues to flow indefinitely because the Cooper pairs (as members of a coherent condensate) are not scattered by the atomic lattice.
	scienceweek.com /2004/sc040416-2.htm (2036 words)

	Cooper pair - Search Results - MSN Encarta (Site not responding. Last check: 2007-10-03)
		Cooper pair - Search Results - MSN Encarta
		Cooper, Leon N., born in 1930, American physicist, professor, and Nobel Prize winner.
		Cooper contributed significantly to the development of a...
	ca.encarta.msn.com /Cooper+pair.html (110 words)

	ScienceDaily: Physicist Discovers Exotic Superconductivity
		This fanciful illustration depicts a) how the two electrons in a conventional, or singlet, Cooper pair (Alice-Alice) keep their same symmetry when reflected in a mirror, and b) how the two electrons in an unconventional, or triplet, Cooper pair (Alice-cat) reverse their signs when reflected in a mirror.
		The newly discovered 'exotic' Cooper pair is the quantum mechanical sum of singlet and triplet Cooper pairs, said UA physicist Andrei Lebed.
		UCSD Physicist Pushes Ahead In Describing The "Pairing Glue" In Novel Superconducting Materials (September 27, 1999) -- Dimitri Basov of the Department of Physics at the University of California, San Diego, along with collaborators J.P. Carbotte of McMaster University and E. Schachinger of the University of Graz, has...
	www.sciencedaily.com /releases/2006/08/060817101658.htm (2173 words)

	Wikinfo \| BCS theory
		In many superconductors, the attractive interaction between electrons (necessary for pairing) is brought about indirectly by the interaction between the electrons and the vibrating crystal lattice (the phonons).
		BCS theory was developed in 1957 by John Bardeen, Leon Cooper, and Robert Schrieffer, who received the Nobel Prize for Physics in 1972 as a result.
		Since the electrons are bound into Cooper pairs, a finite amount of energy is needed to break these apart into two independent electrons.
	www.wikinfo.org /wiki.php?title=Cooper_pair (750 words)

	CSC Logo - IEEE Technical Council on Superconductivity
		By considering phonon interaction of a pair of electrons with opposite spins and with equal and opposite momenta, Cooper was able to postulate pairs of electrons with zero net spin that in a many body formalism could undergo a Bose-Einstein condensation, with an energy gap.
		In 1957, Bardeen, Cooper, and Schrieffer developed a microscopic theory of superconductivity in which pairs of electrons with anti-parallel spins and opposite momenta, known as Cooper pairs, are attracted to each other via the exchange of lattice vibrations, phonons.
		When the energy of the many body system comprising these Cooper Pairs is computed, they found that a temperature dependent energy gap is produced at the Fermi surface of a material that becomes superconducting.
	www.ewh.ieee.org /tc/csc/logostory.html (2519 words)

	Cooper pair - Wikipedia, the free encyclopedia
		Cooper pairs result from interactions between conduction band electrons and the ion lattice in which they move, such as the Pierels effect or Jahn-Teller distortion.
		Generally, the pairing is quite weak, meaning the paired electrons may be many hundreds of nanometers apart.
		The boson-like behavior of such electron pairs was further investigated by Leon Cooper and hence they are called "Cooper pairs".
	en.wikipedia.org /wiki/Cooper_pairs (479 words)

	High density quark matter and color superconductivity (Site not responding. Last check: 2007-10-03)
		The reason why we expect quarks to behave like electrons, forming Cooper pairs which produce a superconducting state, is that the mechanism that causes the pairing is very general.
		The resultant Cooper pairing is rather fragile, and easily disrupted by thermal fluctuations, hence metals only become superconducting at very low temperatures.
		The condensate of Cooper pairs of electrons is charged, and as a result the photon, which couples to electric charge, becomes massive.
	www.physics.wustl.edu /~alford/high_density.html (1495 words)

	Entanglement, Cooper Pairs And Superconductivity
		Technically, the quantum mechanical wavefunction of each Cooper pairs have to be identical in order to maximize the energy reduction due to attractive interactions (that is, the binding energy of a Cooper pair is greatest when all pairs are in the same state).
		Scattering of a Cooper pair would change its wavefunction; this would necessarily require all pairs to change as well (their binding energy would drop).
		Cooper pairs are pairs of coupled electrons that have the interesting property that they can act like bosons instead of a pair of fermions.
	www.physicsforums.com /showthread.php?threadid=8994 (1037 words)

	NetLogo User Community Models: josephson-cooperative
		The physical reason is that the two superconductors are so close together that the wavefunctions of the Cooper pairs of the films overlap and the system behaves as a single "weak" superconductor.
		The circuit is assumed to be current biased (using a dc and an rf bias) and the voltage V across the junction is proportional to the time derivative of the phase phi.
		A current of Cooper pairs is now tunneling across the junction, but the voltage remains zero because the junction is acting like a single superconductor and the current can flow with no electrical resistance and hence no voltage drop.
	ccl.northwestern.edu /netlogo/models/community/josephson-cooperative (2641 words)

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