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EXTENSIONS OF BCS THEORY

机译：BCS理论的扩展

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The simplest formulation of BCS theory involves a single electronic band approximated by a three dimensional electron gas with plane wave states occupied up the the Fermi energy, E_F , or momentum, k_F , with E_F= , where h is Planck's constant over 2rc and m is the electron mass. The effective interaction between two electrons of equal and opposite momentum, one with spin up and the other with spin down, is assumed to be a constant, i.e. independent of energy and direction of momentum, k, in a rim about the Fermi energy of width hop. Here kor) is the Debye energy, but for other superconductors, such as the high-To cuprates it might be replaced by a typical spin fluctuation energy kosF. If the pairing potential, V, is attractive then the Fermi sea is unstable to the formation of Cooper pairs. These have zero center of mass momentum, zero total spin, and the spatial part of the pair wave-function has s-wave symmetry. Thus, the total wave function changes sign on exchange of the two electrons, as it must for Fermions. This need not always be the case. In the cuprates, the spatial part has d-wave symmetry [1]. Futher, in the ruthenates [21, the spin arrangement is a triplet state instead and the spatial part of the wave-function is p-wave. There is also the possibility that the center of mass momentum of the pair is finite, as in the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state [3]. Thus, nature provides us with a rich array of possibilities, but for this short report we will describe mainly conventional superconductors [4,5].
机译：BCS理论的最简单表述涉及一个由三维电子气近似的单个电子带，其平面波状态占据了费米能量E_F或动量k_F，其中E_F =，其中h是2rc上的普朗克常数，m是电子质量。假设两个等速和相反动量的电子之间的有效相互作用是一个常数，即与能量和动量方向k无关，在围绕费米能的宽度上的一个边沿中跳。这里的kor是Debye能量，但是对于其他超导体，例如高To铜酸盐，可以用典型的自旋波动能量kosF代替。如果配对电位V很吸引人，那么费米海对于库珀对的形成就不稳定了。它们具有零质心动量，零总自旋，并且对波函数的空间部分具有s波对称性。因此，总波函数在两个电子交换时改变符号，这对费米子来说是必须的。并非总是如此。在铜酸盐中，空间部分具有d波对称性[1]。此外，在钌酸酯中[21]，自旋排列改为三重态，波函数的空间部分为p波。像Fulde-Ferrel-Larkin-Ovchinnikov（FFLO）状态一样，该对的重心动量中心也是有限的[3]。因此，自然为我们提供了丰富的可能性，但是对于这份简短的报告，我们将主要描述传统的超导体[4,5]。

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