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arXiv cond-mat/0103431cond-mat.supr-con
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MgB2中的双带型超导不稳定性

Two-Band-Type Superconducting Instability in MgB2

Kunihiko Yamaji

摘要:

利用紧束缚方法计算了$_2$中的$π$带,将两个不等价的硼$p_z$轨道上的Hubbard在位库仑相互作用转化为$π$带算符的表达式.对于波矢{ \bf q}平行于$\hat{z}$的散射过程,我们发现其散射过程的形式较为简单,包括带内库仑散射、带间成对散射等,并具有较大的常耦合常数。这使得可以得到一个简单的表达式的两个$π$ -带之间的带间对散射的振幅,发散,如果它的带间极化函数变得足够大,后者进行了近似评估,并发现在MgB $_2$的能带结构大大增强。这些结果导致发散的带间对散射,这意味着两个带型超导不稳定性增强$T_c$。在每个能带中加入一个辅助BCS吸引相互作用,给出了半定量的能隙方程,导出了$T_c$和同位素指数$α$。目前的不稳定性被断言是高$T_c$的MgB $_2$的起源。

英文摘要:

Using the tight-binding method for the $π$-bands in MgB$_2$, the Hubbard on-site Coulomb interaction on two inequivalent boron $p_z$-orbitals is transformed into expressions in terms of $π$-band operators. For scattering processes relevant to the problemin which a wave vector {\bf q} is parallel to $\hat{z}$, it is found to take a relatively simple form consisting of intra-band Coulomb scattering, interband pair scattering etc. with large constant coupling constants. This allows to get a simple expression for the amplitude of interband pair scattering between two $π$-bands, which diverges if the interband polarization function in it becomes large enough.The latter was approximately evaluated and found to be largely enhanced in the band structure in MgB$_2$. These results lead to a divergent interband pair scattering, meaning two-band-type superconducting instability with enhanced $T_c$. Adding a subsidiary BCS attractive interaction in each band into consideration, a semi-quantitative gap equation is given, and $T_c$ and isotope exponent $α$ are derived. The present instability is asserted to be the origin of high $T_c$ in MgB$_2$.

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