论文标题
在三维安德森金属绝缘体过渡的超导率
Superconductivity at the three-dimensional Anderson metal-insulator transition
论文作者
论文摘要
我们通过在存在随机电位的三维晶格中以三维晶格的数值来求解Anderson过渡周围的无序弱耦合超导体。随着疾病接近过渡，订单参数的空间平均值被适度增强，但在绝缘区域急剧下降。顺序参数的空间分布对疾病强度敏感：对于过渡以下的中间疾病，我们已经观察到具有指数尾巴的高度不对称分布。在过渡周围，它通过对数正态分布和抛物线奇异性光谱进行了很好的描述。这些特征是多重措施的典型特征。我们定量地确定通过对频谱区域中水平统计的分析，在频谱区域的水平统计数据中进行的关键疾病，这有助于形成顺序参数。有趣的是，过渡时的光谱相关性与安德森过渡中非相互作用无序系统中发现的光谱相关性相似。渗透分析表明，临界疾病可能发生相干性丧失。
We study a disordered weakly-coupled superconductor around the Anderson transition by solving numerically the Bogoliubov-de Gennes (BdG) equations in a three dimensional lattice of size up to $20\times20\times20$ in the presence of a random potential. The spatial average of the order parameter is moderately enhanced as disorder approaches the transition but decreases sharply in the insulating region. The spatial distribution of the order parameter is sensitive to the disorder strength: for intermediate disorders below the transition, we already observe a highly asymmetric distribution with an exponential tail. Around the transition, it is well described by a log-normal distribution and a parabolic singularity spectrum. These features are typical of a multifractal measure. We determine quantitatively the critical disorder at which the insulator transition occurs by an analysis of level statistics in the spectral region that contributes to the formation of the order parameter. Interestingly, spectral correlations at the transition are similar to those found in non-interacting disordered systems at the Anderson transition. A percolation analysis suggests that the loss of phase coherence may occur around the critical disorder.
