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Motivated by recent research works on the flat-band correlated electron systems, we construct a plaquette-Lieb lattice, which exhibits nearly flat bands close to the Fermi level around half-filling, when the inter-plaquette hopping integral is much smaller than the intra-plaquette one. A detailed comparison study with the well-known checkerboard lattice indicates that there exist significant differences for the pairing property between the two lattices, and the nearly flat bands on the plaquette-Lieb lattice strongly enhance the $d$-wave pairing correlation for repulsive on-site Hubbard interaction and $s$-wave pairing correlation for attractive on-site Hubbard interaction. Our study not only provides a new lattice with nearly flat bands, but also deepens the understanding of electronic structure on superconductivity.

To gain a deeper understanding of the high-temperature superconductivity in doped cuprates, the constrained-path quantum Monte Carlo method was used to explore the superconducting pairing correlation function and effective pairing interaction in the three-band Hubbard model. Our main observation was that in the low doping region, compared to other symmetries, $d$-wave superconducting pairing dominates. The Coulomb interaction $U$ suppresses $d$-wave pairing correlation, while the effective pairing interaction is both enhanced by the increasing $U$ and the nearest attraction. These results are used to understand the superconducting state in copper oxide high-temperature superconductors.

We investigate the tensor and pairing correlations in ¹¹Li based on the ⁹Li+n+n model. For ⁹Li, we perform the configuration mixing with the shell model type wave function to introduce the core polarization caused by the tensor and pairing correlations. For ¹¹Li, we perform the coupled ⁹Li+n+n calculation, in which the couplings between the correlations in ⁹Li and the motion of the last two neutrons emerge Pauli-blocking for the p² configuration of ¹¹Li and increases the s² component to develop the halo structure.

The $\nu 1h_{11/2}$ band in ¹⁰⁰Pd is investigated by the cranking covariant density functional theory (CDFT) with the particle-number-conservation shell-model-like approach (SLAP) to treat the pairing correlations. The experimental $B(E2)$, moments of inertia, and the total angular momentum are well reproduced by our calculation. The deformations for neutrons, protons, and the whole nucleus behave in a similar way with the decreasing of $\beta$ and the tiny change of $\gamma$ with increasing rotational frequency $\hslash \omega$ from 0.2 to 0.6MeV. The features of the antimagnetic rotation (AMR) are identified by above calculation results. To conclude, the configuration of AMR for ${}^{100}$Pd given by the cranking CDFT-SLAP is $\pi$($1g_{9/2}$)${}^{-4}\otimes \nu [1h_{11/2}{(1g_{7/2})}^3]$. Furthermore, the configuration of $\pi$($1g_{9/2}$)${}^{-4}\otimes \nu [1h_{11/2}{(1g_{7/2})}^{2}2d_{5/2}]$, which presents the experimental result of low spins, is also presented.

The hot nucleus ${}^{162}\mathrm{\text{Dy}}$ is investigated using covariant density functional theory, where the shell-model-like approach treats the pairing correlation. Lee–Yang’s theorem is applied to classify the pairing phase transition by analyzing the distribution of zeros of the partition function in the complex temperature plane. The distribution of zeros of the partition function converges with increasing particle numbers and illustrates the characteristics of the phase transition. In our calculations, we determine the first-order of the phase transition near the critical temperature. Different seniority states show the pairing phase transition from a superfluid to a normal phase, ranging from fully paired states to completely unpaired states.

Two- and three-body correlations in weakly bound states and continuum states of the Borromean systems such as ⁶He and ¹¹Li are discussed. In these systems, a two-neutron decay channel comes down to the lowest threshold, and the pairing correlation between valence neutrons is very important together with couplings with continuum states. In addition to those correlations, the tensor correlation is investigated for the halo structure and its excited states. Concerning the problem how to observe the correlation in the halo state experimentally, the final interaction between ⁴He and n is shown to dominate the Coulomb-breakup cross section of ⁶He.

The pairing correcting energies at high spins in ¹⁶¹Lu and ¹³⁸Nd are studied by comparing the results of the cranked-Nilsson-Strutinsky (CNS) and cranked-Nilsson-Strutinsky-Bogoliubov (CNSB) models. It is concluded that the Coriolis effect rather than the rotational alignment effect plays a major role in the reduction of the pairing correlations in the high spin region. Then we proposed an average pairing correction method which not only better reproduces the experimental data comparing with the CNS model but also enables a clean-cut tracing of the configurations thus the full-spin-range discussion on the various rotating bands.

The proton density distribution of ⁴⁶Ar is calculated in the framework of the Skyrme-Hartree-Fock (SHF) approach with the SLy5, SLy5+T and SLy5+T_w interactions. It is shown that the tensor force in the SLy5+T_w interaction favors its bubble structure due to the inversion between the single-proton states 2s_1/2 and 1d_3/2. However, the SLy5+T interaction can not lead to any 2s_1/2-1d_3/2 inversion, consequently no bubble structure can be found. In addition, a detailed discussion on the competition between tensor force and pairing correlation on the bubble formation is performed within the Skyrme-Hartree-Fock-Bogoliubov (SHFB) approach.

Nuclear pairing gaps of normally deformed nuclei are investigated by using the particle-number conserving formalism for the cranked shell model, in which the blocking effects are treated exactly. Both rotational frequency ω-dependence and seniority ν-dependence of the pairing gap are investigated.

We systematically investigate the E1 strength distributions of even-even nuclei (Z = 8 – 20 isotopes) using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory that can describe the dynamics of superfluid nuclei. Especially, we focus on the low-lying E1 strength that is often called pygmy dipole resonance and investigate the neutron-number dependence of the strength in neutron-rich nuclei. The evolution of the low-lying E1 strength is determined by several factors including the neutron-shell effects, the deformation and the pairing.