arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1002.0859cond-mat.supr-con
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局域化阈值附近的分形超导

Fractal superconductivity near localization threshold

M. V. Feigel'man, L. B. Ioffe, V. E. Kravtsov, E. Cuevas

摘要:

我们开发了一个半定量的理论,电子配对和由此产生的超导体中的“不良导体”,其中费米能$E_F$是位于该地区的本地化的国家不是那么远的安德森迁移率边缘$E_c$。我们回顾了现有的理论和实验数据,并认为这一模型描述了一大类无序薄膜。我们的理论分析是基于配对相关性的分析处理,描述的基础上,精确的单粒子本征态的3D安德森模型,我们结合本征函数相关性的数值数据。临界波函数的相关性的分形性质被证明是至关重要的这些系统的物理。我们确定了三个不同的阶段:“临界”超导态形成在$E_F=E_c$,超导态具有较强的赝能隙,实现由于配对的弱局域化的电子和绝缘状态实现在$E_F$更深的局域带内。临界超导相的特征是相变温度相对于BCS结果的提高,超导序参量和局域态密度的空间分布不均匀。赝能隙态的主要新特征是存在两个独立的能量标度:超导能隙$Δ$,这是由于多体关联和一个新的“赝能隙”能量标度$Δ_P$,它表征了局域电子对的典型结合能,并导致绝缘行为的电阻率作为温度的函数高于$T_c$。“赝隙超导体”的双能隙性质导致了许多不寻常的物理性质。

英文摘要:

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk "poor conductors" in which Fermi energy $E_F$ is located in the region of localized states not so far from the Anderson mobility edge $E_c$. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model. Our theoretical analysis is based on the analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems. We identify three distinct phases: 'critical' superconductive state formed at $E_F=E_c$, superconducting state with a strong pseudogap, realized due to pairing of weakly localized electrons and insulating state realized at $E_F$ still deeper inside localized band. The 'critical' superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gaped state is the presence of two independent energy scales: superconducting gap $Δ$, that is due to many-body correlations and a new "pseudogap" energy scale $Δ_P$ which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive $T_c$. Two gap nature of the "pseudo-gaped superconductor" is shown to lead to a number of unusual physical properties.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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