For Quantitative Estimation of Superconducting Temperature in Strongly Correlated Electron Systems

人们认为，超导转变温度是由下列两个相互竞争的效应决定的。有效质量的重整化决定了费米液态中准粒子的带宽。电子之间的库仑相互作用增强了电子的有效质量。这种增强来自于电子能带中色散的减少。重整化因子z决定了能量标度。例如，重电子的电子质量是自由电子的1000倍。另一方面，铜酸盐中的电子质量增加了约10倍，准粒子的带宽减小了1/10~1000K。超导能隙是在这些准粒子带中产生的，并通过准粒子质量z的倒数重整化。也就是说，超导转变温度与波函数重整化因子z成比例降低。因此，强电子相互作用降低了转变温度。准粒子间相互作用的动量依赖性决定了超导的对称性和转变温度，各向同性排斥力被禁带函数的符号变化抵消，而准粒子相互作用的各向异性部分决定了超导态的对称性和转变温度。在这种情况下，强相互作用提高了超导转变温度，这两种效应相互竞争。前者由包含各向同性部分的总相互作用决定，而后者由准粒子相互作用的主要各向异性动量相关部分决定。因此，我们可以定量地解释相变温度。在强关联电子系统中。

It is made dear that the superconducting transition temperature is determined by the following competing two effects.1. Renormalization of effective mass determines the band width of quasiparticles in Fermi liquid statesThe Coulomb interaction between electrons enhances the effective mass of electrons. The enhancement arises from the reduction of dispersion in electron bands. The renormalization factor z determines energy scale. For example, heavy electrons possesses 1000times large electron mass compared with free electron. Therefore the band width of quasiparticles is reduced by the factor of 1/1000 and takes the value around 10K On the other hand, the electron mass in cuprates is enhanced around 10 times and the band width of quasiparticles is reduced by 1/10 to 1000K. The superconducting gaps are created in these quasiparticle bands and renormalized by the inverse of quasiparticle mass, z. That is, the superconducting transition temperature is reduced in proportion to the wavefunction renormalization factor z. Thus the strong electron interaction reduces the transition temperature.2 . The momentum dependence of interaction between quasiparticles determines the symmetry and transition temperature of superconductivity.The isotropic repulsive force is canceled out by the sign change of gap function and the anisotropic parts of quasiparticle interaction determine the symmetry and transition temperature of superconducting state. In this case strong interaction increases the superconducting transition temperatureThe above two effects compete with each other. The former is determined by total interaction including isotropic part, while the latter is determined by dominant anisotropic momentum dependent part of quasiparticle interaction. As a result we can explain the transition temperature quantitatively. In strongly correlated electron systems.