Cooper instability and superconductivity on the Penrose lattice

Bulk SC has recently been observed in the Al-Zn-Mg QC. To settle the several fundamental issues on the SC on the QC, we perform a systematic study on an attractive Hubbard model on the Penrose lattice. The first issue is the Cooper instability under an infinitesimal attractive interaction on the QC without a Fermi surface. We start from the two-electron problem outside the filled Fermi-sea, where we analytically prove that an infinitesimal Hubbard attraction can lead to the Cooper instability as long as the density of state is nonzero at the Fermi level, which provides the basis for the SC on the QC. Our numerical results yield that the Cooper pairing always takes place between a time-reversal partner, satisfying the Anderson's theorem. On this basis, we perform a MF study on the system, at both the zero and finite temperatures. The MF study also shows that an arbitrarily weak attraction can lead to the pairing order, with the resulting pairing state well described by the BCS theory, and the thermal dynamic behaviors well consistent with experiment results. The second issue is about the superfluid density on the QC without translational symmetry. It's clarified that although the normal state of the system locates at the critical point of the metal-insulator transition, the pairing state exhibits real SC, carrying finite superfluid density that can be verified by the Meissner effect. Further more, our study reveals a fundamental difference between the SC on the periodic lattice and that on the QC: while the paramagnetic superfluid density in the former case vanishes at zero temperature, that in the latter case is nonzero due to the lack of translational symmetry, reflecting the consumption of superfluid density from the scattering by the non-periodic structure. These properties of the SC on the Penrose lattice revealed here are universal for all QCs.Comment: 10 pages, 6 figures, plus appendi

Making Chiral Topological Superconductivities from Non-topological Superconductivities Through the Twist

In this paper, we propose a general scheme to realize chiral TSCs through the "twistronics". Suppose we have a $D_n$-symmetric monolayer superconductor, which carries non-topological SC with pairing angular momentum $L=n/2$. Here we propose that we can obtain chiral TSC with the same $L$, by stacking two such monolayers with the largest twist angle $\pi/n$, forming a Moireless quasi-crystal (QC) structure, dubbed as the twist-bilayer QC (TB-QC) here. The chiral TSC in the TB-QC is driven by the interlay Josephson coupling between the pairing order parameters of the two layers. An argument based on the universal Ginzburg-Landau theory is provided to understand this proposal. One known example which fits our proposal is the $d+id$-chiral TSC in the 45$^\circ$-twisted bilayer cuprates. Here, based on the microscopic framework developed previously to treat with the electron-electron interactions in the TB-QC, we demonstrate the application of our proposal to a new example, i.e., the $f+if$-chiral TSC obtained by twisting two properly-doped honeycomb-Hubbard-model monolayers by the angle 30$^\circ$. This example is related to the newly synthesized 30$^\circ$-twisted bilayer graphene.Comment: 7 pages, 5 figure

Impacts of international oil price fluctuations on China’s PM2.5 concentrations: a wavelet analysis

In the past few years, China’s air quality, particularly PM2.5 concentrations, has received extensive attention. China is increasingly dependent on imported oil, and the international oil price fluctuations influence the air quality by two paths. A rise in oil prices puts pressure on the economy and reduces energy consumption, which could improve air quality. However, the substitution effect by high oil prices tends to increase the use of environmentally unfriendly energies, which worsens air quality. In this study, the authors employ wavelet analysis to determine how international oil price fluctuations affect PM2.5 concentrations in China. The authors process a sample of 12 typical Chinese cities, which are discretely distributed in the northeast, north, east, central, south, and southwest of China. The results show that in most cities international crude oil prices are positively correlated to the PM2.5 concentrations in the short term (1–4 months) and that the fluctuations in oil prices are usually ahead of the changes of PM2.5 concentrations. It is more pronounced in industrially developed cities such as in Shanghai. An extension of the study to include the country data yields more consistent findings. Empirical analysis indicates that, in the short run, the substitution effect caused by oil price fluctuations exerts a stronger impact on PM2.5 concentrations