Superconductivity Cooper pairs

Since it is commonly accepted that superconducting Cooper pairs form in the Cu(2) sheets in the lattice from holes of the Cu3d02p hybrid band, and the Cu(2) sheet and the rare earth sheet are neighbors, overlap or even charge transfer may take place between them depending on the size of the rare earth cation. Charge transfer is plausible because unlike... 

Having identified methods to deposit conductive polymer and molecular metal systems onto cuprate superconductor structures without damage to either material, it becomes important now to consider the electronic interactions that occur when the two conductors are in contact with one another. Of particular importance is the interaction that occurs between the polymer-derived charge carriers and the superconducting Cooper pairs. Important background information related to this area can be obtained from the well-documented behavior of the more classical metal/superconductor and semicon-ductor/superconductor systems. Thus, prior to considering experimental data and theoretical treatments for organic conductor proximity effects, we review previous studies of proximity effects in the more classical systems. 

When a normal metal and a superconductor are in intimate contact with each other, there can be a leakage of the superconducting Cooper pairs from the superconductor to the normal metal and quasiparticle (normal electron) leakage from the metal to the superconductor. This effect is known as the superconducting proximity effect and is an important phenomenon that can be used in practical applications such as in electronic devices and as a tool to better understand superconductivity [64J. The proximity effect can occur over distances that are quite large compared to molecular dimensions. Cooper pairs typically extend into normal metals for distances on the order of 100 nm and, in some cases, considerably further. 

In a superconducting metal, some of the electrons are paired into the so-called cooper pairs which are all in the same zero entropy state and do not carry heat. Heat is carried only by unpaired electrons which are in energy states separated from cooper pairs by an energy gap AE(T). The number of unpaired electrons varies as exp(—AE/kBT). Hence ... 

If transition temperatures other than those allowed by superconducting pure metals are required, two metallic layers can be deposited to form a bi-layer TES. In most cases, only one of the two metals is a superconductor. In this case, the Cooper pairs diffuse from... 

While, in the BCS theory, such attractive force for electron Cooper pair is provided by phonons, for dense quark matter, where phonons are absent, the gluon exchange interaction provides the attraction, as one-gluon exchange interaction is attractive in the color anti-triplet channel1 One therefore expects that color anti-triplet Cooper pairs will form and quark matter is color superconducting, which is indeed shown more than 20 years ago [13, 14],... 

For large enough asymmetries the homogeneous state becomes unstable towards formation of either the LOFF phase - a superconducting state with nonzero center-of-mass momentum of the Cooper pairs, or the DFS phase - a superconducting state which requires a quadrapole deformation of Fermi surfaces. A combined treatment of these phases in non-relativistic systems shows that while the LOFF phase corresponds to a local minimum, the DFS phase has energy lower that the LOFF phase. These phases break either the rotational, the translational or both symmetries. 

In a superconducting system, when one increases the temperature at a given chemical potential, thermal motion will eventually break up the quark Cooper pairs. In the weakly interacting Bardeen-Copper-Schrieffer (BCS) theory, the transition between the superconducting and normal phases is usually of second order. The ratio of the critical temperature TcBCS to the zero temperature value of the gap AbGS is a universal value [18]... 

From BCS theory it is known, that in order to form Cooper pairs at T = 0 in a dense Fermi system, the difference in the chemical potentials of the Fermions to be paired should not exceed the size of the gap. As previous calculations within this type of models have shown [24], there is a critical chemical potential for the occurrence of quark matter pf > 300 MeV and values of the gap in the region A < 150 MeV have been found. Therefore it is natural to consider the problem of the color superconducting (2SC) phase with the assumption, that quark matter is symmetric or very close to being symmetric (pu pd). 

The opening of a band gap at in the superconducting state can also be interpreted within this framework. The charge carriers of a superconducting state are not individual electrons as in the normal metallic state but electrons coupled in pairs, the so-called Cooper pairs, having opposite wave vectors. Hence, Cooper pairs are described by product functions (p k)(p —k)). Following the discussion given above. 

In 1957, Bardeen, Cooper, and Schrieffer published their theory of superconductivity, known as the BCS theory. It predicts that under certain conditions, the attraction between two conduction electrons due to a succession of phonon interactions can slightly exceed the repulsion that they exert directly on one another due to the Coulomb interaction of their like charges. The two electrons are thus weakly bound together forming a so-called Cooper pair. It is these Cooper pairs that are responsible for superconductivity. In conventional superconductors, these electrons are paired so that their spin and orbital angular momenta cancel. They are described by a wave function, known as an order parameter. In this case the order parameter has symmetry similar to that of the wave function of s electrons and represents a singlet state. 

The theoretical grounds for existence of 2D-SIT which was suggested in [9, 10] appealed to the boson-vortex duality model. It considered the superconducting phase as a condensate of Cooper pairs with localized vortices and the insulating phase as a condensate of vortices with localized Cooper pairs. The theory described only vicinity of the SIT and predicted existence of some critical region on the (T, B)-plane where the behavior of the system was... 

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