Narrow Results

By using the determined quantum Monte Carlo method, we explore the evolution of the pairing correlation depending on doping and frustration in the two-dimensional Hubbard model on an anisotropic triangular lattice. In the full frustrated system where the nearest hoping term $t$ is equal to the next nearest hoping $t^{\prime }$, the $d_{xy}$-wave pairing dominates over $d_{x^2-y^2}$ as the electron filling $〈n〉>1.20$. The $d_{x^2-y^2}$ superconducting pairing tends to be dominated as the frustration $t^{\prime }∕t$ decreases, and the decreasing electron fillings also push the system into a possible $d_{x^2-y^2}$ superconducting state. Our intensive nonbiased numerical results reveal the competition between $d_{x^2-y^2}$ and $d_{xy}$ superconducting pairing states, clarifying the different pairing symmetries in the $\kappa$-(BEDT-TTF)${}_{2}X$ family of organic charge transfer salts.

A constrained path quantum Monte Carlo simulation is performed to investigate the superconducting pairing correlation in doped staggered-flux Hubbard model on a square lattice, which is an interesting platform to host Dirac fermions. For various electron fillings and interaction strengths, the $d_{xy}$ pairing dominates over other pairing forms since its long-range correlation is larger over mostly distances. We deepen our study by including the nearest-neighbor interaction $V$ and found the $d_{xy}$ pairing correlation is slightly suppressed by increasing $V$.

Experimental studies of the pairing state of cuprate superconductors reveal asymmetric behaviors of the hole-doped (p-type) and electron-doped (n-type) cuprates. The pairing symmetry, pseudogap phenomenon, low-energy spin excitations and the spatial homogeneity of the superconducting order parameter appear to be non-universal among the cuprates, which may be attributed to competing orders. We propose that the non-universal pseudogap and nano-scale variations in the quasiparticle spectra may be the result of a charge nematic (CN) phase stabilized by disorder in highly two-dimensional (2D) p-type cuprates. The CN phase is accompanied by gapped spin excitations and competes with superconductivity (SC). In contrast, gapless spin excitations may be responsible for the absence of pseudogap and the presence of excess sub-gap spectral weight in the momentum-independent quasiparticle spectra of n-type cuprates. The physical implications and further verifications for these conjectures are discussed.

In this paper, we discuss the mathematical structure of the s-wave superconducting gap and other quantitative characteristics of superconducting systems. In particular, we evaluate and discuss integrals inherent in fundamental equations describing superconducting systems. The results presented here extend the approach formulated by Abrikosov and Maki, which was restricted to the first-order expansion. A few infinite families of integrals are derived and allow us to express the fundamental equations by means of analytic formulas. They can be then exploited in order to find some quantitative characteristics of superconducting systems by the method of successive approximations. We show that the results can be applied to some modern formalisms in order to study high-T_c superconductors and other superconducting materials of the new generation.

The effect of nonmagnetic Zn impurity on superconductivity in iron-based superconductors is reviewed. Zn impurity can severely suppress the antiferromagnetic (AFM) order of Fe ions in the parent compound LaFeAsO. In the 1111 type F-doped LaFeAs(O, F) system, the superconducting transition temperature (T_c) increases in the underdoped regime, remains unchanged in the optimally-doped regime, and is severely suppressed in the overdoped regime in the presence of Zn impurity. The results suggest a switch of the symmetry of the superconducting order parameters from a s-wave to s±- or d-wave states as the charge carrier doping increases in this system. To our surprise, Zn impurity strongly suppresses T_c in the Co-doped LaFeAsO and BaFe₂As₂ systems despite of the Co doping level. The absence of universal Zn impurity effect implies that the pairing symmetry of the iron-based superconductors may be dependent on the details of the electronic structure.

Certain significant fallacies are involved in discussions of the high-$T_c$ mechanism unsolved for over 30 years in cuprate superconductors. These fallacies are explored with the aim of unraveling this mechanism. Moreover, using polarized electronic Raman scattering in inhomogeneous underdoped cuprate superconductors, the intrinsic nonlinear Raman spectrum is obtained by subtracting the pseudogap characteristic of a nonlinear from the linear Raman spectrum measured in the ${\mathrm{\text{B}}}_{2\mathrm{\text{g}}}$ mode of the node area below the critical temperature. The intrinsic nonlinear behavior implies the existence of the nodal superconducting gap denying $d_{x^2-y^2}$-wave pairing symmetry. An origin of the nodal superconducting gap is discussed.

Unconventional superconductivity on a honeycomb lattice has received increasing interest since the discovery of graphene primarily due to the similarities between materials with a honeycomb lattice and cuprate superconductors. Many theoretical studies have been conducted on superconductivity on a honeycomb lattice, however, a consistent picture is still lacking. In this paper, we have extended the theory of kinetic-energy-driven superconductivity, which has been developed to investigate unconventional superconductivity in cuprate superconductors, to explore superconductivity on a honeycomb lattice within the t-J model. Our results demonstrate that the charge-carrier pair gap parameter with $d_{x^2-y^2}+\mathrm{\text{i}}{d}_{xy}$-wave symmetry exhibits a dome-like shape as a function of doping, with superconductivity emerging at a certain doping concentration and disappearing at high doping levels, similar to what has been observed in cuprate and cobaltate superconductors. Furthermore, the charge-carrier pair gap parameter decreases with increasing the value of $J∕t$ (the ratio between the antiferromagnetic exchange coupling constant and the nearest-neighbor hopping integral), and approaches zero when $J∕t$ reaches a sufficiently large value. This indicates that the antiferromagnetic order will suppress the superconducting state and a sufficiently strong exchange coupling will completely destroy the superconductivity. Taking into account our present results together with the corresponding results of cuprate and cobaltate superconductors, it appears that the dome-like shape of the doping dependence of the charge-carrier pair gap parameter may be a common feature in doped Mott insulators.