退火复杂网络上的超导体-绝缘体转变
Supercondutor-Insulator Transition on Annealed Complex Networks
摘要：
铜氧化合物具有多相结构的复杂性，这一复杂性一直阻碍着人们对高温超导机理的研究。Fratini等人最近报道了一种电子尺度不变性的指纹，通过扫描微区X射线衍射检测掺杂剂的结构尺度不变性。为了揭示这些材料的临界现象，在这里，我们提出了一个程式化的模型捕捉的超导绝缘体过渡的本质特征的高度动态的，异质颗粒材料：退火复杂网络上的无序量子横向伊辛模型（DQTIM）。我们证明了当网络对幂律分布所描述的期望度的高度异质性进行编码时，当期望度分布的幂律指数γ小于3时，即γ<3，超传导相开始的临界温度发散到无穷大。此外，我们研究的情况下，其中的临界态的电子背景是由一个外部参数g，确定指数截止的幂律期望度分布的特征在于指数γ触发。我们发现当g=g_c时，超导-绝缘体转变的临界温度有一个极大值γ>3，当γ<3时，临界温度发散。
英文摘要：
Cuprates show multiphase complexity that has hindered physicists search for the mechanism of high T_c for many years. A fingerprint of electronic scale invariance has been reported recently by Fratini et al. by detecting the structural scale invariance of dopants using scanning micro x-ray diffraction. In order to shed light on critical phenomena on these materials, here we propose a stylized model capturing the essential characteristics of the superconducting-isulator transition of a highly dynamical, heterogenous granular material: the Disordered Quantum Tranverse Ising Model (DQTIM) on Annealed Complex Network. We show that when the networks encode for high heterogeneity of the expected degrees described by a power law distribution, the critical temperature for the onset of the supercoducting phase diverges to infinity as the power-law exponent γof the expected degree distribution is less than 3, i.e. γ<3. Moreover we investigate the case in which the critical state of the electronic background is triggered by an external parameter g that determines an exponential cutoff in the power law expected degree distribution characterized by an exponent γ. We find that for g=g_c the critical temperature for the superconduting-insulator transition has a maximum is γ>3 and diverges if γ<3.
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