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In condensed matter physics, a Cooper pair or BCS pair is a pair of electrons (or other charge, but it also attracts the positive ions that make up the rigid lattice of the metal. This attraction distorts the ion lattice, moving the ions slightly toward the electron, increasing the positive charge density of the lattice in the vicinity. This positive charge can attract other electrons. 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 rigorous quantum mechanical explanation shows that the effect is due to electron–phonon interactions. The energy of the pairing interaction is quite weak, of the order of 10−3eV, and thermal energy can easily break the pairs. So only at low temperatures, in metal and other substrates, are a significant number of the electrons 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 nanometers apart. This distance is usually greater than the average interelectron distance, so many Cooper pairs can occupy the same space.〔 cite book | last = Feynman | first = Richard P. |author2=Leighton, Robert |author3=Sands, Matthew | title = Lectures on Physics, Vol.3 | publisher = Addison–Wesley | year = 1965 | pages = 21–7, 8 | isbn = 0-201-02118-8 }}〕 Electrons have , so they are fermions, but a Cooper pair is a composite boson 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 BCS theory is also applicable to other fermion systems, such as helium-3. Indeed, Cooper pairing is responsible for the superfluidity of helium-3 at low temperatures. It has also been recently demonstrated that a Cooper pair can comprise two bosons.〔(Cooper Pairs of Bosons )〕 Here the pairing is supported by entanglement in an optical lattice. == Relationship to superconductivity == The tendency for all the Cooper pairs in a body to 'condense' into the same ground quantum state is responsible for the peculiar properties of superconductivity. Cooper originally considered only the case of an isolated pair's formation in a metal. When one considers the more realistic state of many electronic pair formations, as is elucidated 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.〔 cite web are energetically favored, and electrons go in and out of those states preferentially. This is a fine distinction that John Bardeen makes: :''"The idea of paired electrons, though not fully accurate, captures the sense of it." 〔J. Bardeen, "Electron-Phonon Interactions and Superconductivity", in Cooperative Phenomena, eds. H. Haken and M. Wagner (Springer-Verlag, Berlin, Heidelberg, New York, 1973), p. 67.〕'' The mathematical description of the second-order coherence involved here is given by Yang.〔C. N. Yang, "Off-Diagonal Long-Range Order." ''Rev. Mod. Phys.'' 34, 694 (1962)〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cooper pair」の詳細全文を読む スポンサード リンク
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