Using the numerical diagonalization method, we examine the one-dimensional t1–t2–J1–J2 model (zigzag-chain t–J model) which is an effective model for metallic CuO double chains in the superconductor Pr2Ba4Cu7O15-δ. Based on the Tomonaga–Luttinger liquid theory, we calculate the Luttinger liquid parameter Kρ as a function of the electron density n. It is found that superconductivity is realized in the parameter region, which is in accordance with experimental results. We show the phase diagram of a spin gap in the t2/|t1|–n plane by analyzing the expectation value of the twist operator Zσ in the spin sector. The spin gap appears in the region with a large t2/|t1|, where the phase boundary at half filling is consistent with that of the known frustrated quantum spin system. The analysis also suggests that the estimated value of the spin gap reaches ∼100 K in the realistic parameter region of Pr2Ba4Cu7O15-δ.
We investigate the properties of the nearest-neighbor singlet pairing and the emergence of
d-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the $t\ensuremath{-}{J}_{1}\ensuremath{-}{J}_{2}$ model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott-insulating state, we confirm the emergence of
d-wave superconductivity, in agreement with earlier works. We show that a small but finite
J2 spin coupling between next-nearest neighbors stabilizes
d-wave symmetry compared to the extended
s-wave scenario. At small hole doping, to minimize the energy and to gap the whole Fermi surface or all the Dirac points, the superconducting ground state is characterized by a
d+id singlet pairing assigned to one valley and a $d\ensuremath{-}id$ singlet pairing to the other, which then preserves time-reversal symmetry. The slightly doped situation is distinct from the heavily doped case (around 3/8 and 5/8 filling) supporting a pure chiral
d+id symmetry and breaking time-reversal symmetry. Then, we apply the functional renormalization group and study in more detail the competition between antiferromagnetism and superconductivity in the vicinity of half filling. We discuss possible applications to strongly correlated compounds with copper hexagonal planes such as In
3Cu
2VO
9. Our findings are also relevant to the understanding of exotic superfluidity with cold atoms.
To investigate the non-Fermi liquid behavior we consider the extended two-dimensional t-J model which includes additional hopping t''. In the regime t,J << t'' we were able to solve the model analytically. It has a very rich phase diagram including antiferromagnetic (AF) insulator and AF strange metal with different kinds of pseudospin-singlet superconducting pairings (p,d,g-waves). We also demonstrate a collective triplet excitation with energy below the superconducting gap