Cooper instability and superconductivity of the Penrose lattice
Cooper instability and superconductivity of the Penrose lattice
复制标题
彭罗斯晶格的库珀不稳定性和超导性
DOI：
10.1007/s11433-021-1877-5
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Fan Yang
中科院分区：
文献类型：
--
作者：
Yu;Juan;Yongyou Zhang;Ye Cao;Weiqiang Chen;Fan Yang
最近在Al-Zn-Mg准晶中观察到了体超导电性。为了解决SC在QC上的几个基本问题，我们使用一个有吸引力的Hubbard模型对Penrose格进行了系统的研究。第一个问题是QC的库珀不稳定性，即，在无穷小的吸引力作用下没有费米面。从充满费米海外的两电子问题出发，分析证明了只要费米能级上态密度不为零，无限小的Hubbard吸引就能导致库珀不稳定性.调查结果为SC进行QC提供了依据。我们的数值计算结果表明，库珀配对总是发生在两个时间反转态之间，满足安德森定理。在这个定理上，我们在零温度和有限温度下进行了平均场（MF）研究。MF研究表明，任意弱的吸引力都可以导致一个配对序，由此产生的配对态可以用Bardeen-Cooper-Schrieffer理论很好地描述，热力学行为与实验结果吻合较好.第二个问题是没有平移对称的QC上的超流密度。我们的研究结果表明，虽然系统的正常态位于金属-绝缘体转变的临界点，但配对态具有真实的超临界，具有有限的超流密度，这可以通过Meissner效应得到验证.这一发现与实验结果一致。本研究还揭示了彭罗斯格点上的SC的性质对所有的量子化学都是普适的。
Bulk superconductivity (SC) has recently been observed in the Al-Zn-Mg quasicrystal (QC). To settle several fundamental issues of the SC on the QC, we use an attractive Hubbard model to perform a systematic study on the Penrose lattice. The first issue is the Cooper instability of the QC, i.e., no Fermi surface under an infinitesimal attractive interaction. Starting from the two-electron problem outside a filled Fermi sea, we analytically prove that an infinitesimal Hubbard attraction can lead to the Cooper instability as long as the density of the state is nonzero at the Fermi level. The findings provide a basis for the SC on the QC. Our numerical results show that the Cooper pairing always takes place between two time-reversal states, satisfying Anderson’s theorem. On this theorem, we perform a mean-field (MF) study at zero and finite temperatures. The MF study shows that an arbitrarily weak attraction can lead to a pairing order, with the resulting pairing state being well described by the Bardeen-Cooper-Schrieffer theory and the thermal dynamic behaviors being well consistent with the experimental results. The second issue is about the superfluid density on the QC without translational symmetry. Our findings clarify that although the normal state of the system locates at the critical point of the metal-insulator transition, the pairing state exhibits a real SC, carrying finite superfluid density that can be verified by the Meissner effect. This finding is consistent with the experiment results. This study also reveals that the properties of the SC on the Penrose lattice are universal for all QCs.