With the discovery of strong-coupling physics and superconductivity in moir\'e superlattices, it is essential to have an understanding of strong-coupling driven superconductivity in systems with trigonal symmetry. The simplest lattice model with trigonal symmetry is the triangular lattice Hubbard model. Although the triangular lattice spin model is a heavily studied model in the context of frustration, studies of the hole-doped triangular lattice Hubbard model are rare. Here, we use density matrix renormalization group to investigate the dominant superconducting channels in the hole-doped triangular lattice Hubbard model over a range of repulsive interaction strengths. We find a clear transition from
p-wave superconductivity at a moderate on-site repulsion strength (
U/t=2) at filling above 1/4 ($n\ensuremath{\sim}0.65$) to
d-wave superconductivity at a strong on-site repulsion strength (
U/t=10) at filling below 1/4 ($n\ensuremath{\sim}0.4$). The unusual tunability that moir\'e superlattices offer in controlling
U/t would open up the opportunity to realize this transition between
d-wave and
p-wave superconductivity.
The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while
B1g (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) and
B2g (
dxy) pairing dominates in the absence of repulsive longer-range Coulomb interactions
VNN, the latter induces pairing in other symmetry channels, including, e.g.,
A2g (
g-wave), nodal
A1g (extended
s-wave), or nodal
Eu (
p-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction,
VNN<0, on the superconducting gap structure. Depending on the electronic filling, such an attraction boosts
Eu (
p-wave) spin-triplet or
B1g (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) spin-singlet ordering.
The search for superconductivity with unconventional pairing symmetry has been a central focus in the study of strongly correlated electron systems. In this work, we report a numerically exact study of the spin-triplet pairing in a two-dimensional Hubbard model with repulsive interactions, employing the determinant quantum Monte Carlo method. The model includes next-nearest-neighbor and third-nearest-neighbor hopping terms and maintains spin balance. By tuning the fermion filling close to a type-II Van Hove singularity (VHS) in the model, we numerically investigate the ordering tendencies of several possible pairing channels with different symmetries. Our numerical results provide clear evidence of the spin-triplet
p-wave pairing instability approaching low temperatures, as revealed by the vertex contribution to the pairing susceptibility. This signature becomes increasingly pronounced as the interaction strength increases in the weak to intermediate regime. We further find that, near the type-II VHS, the dominant spin-spin correlations in the system are ferromagnetic, suggesting its close relation to the spin-triplet pairing instability. Our findings offer a reliable approach to realize spin-triplet
p-wave superfluidity in the repulsive Hubbard model from an unbiased numerical perspective.
Inspired by recent advances in the fabrication of surface superlattices, and in particular the triangular lattice made of tin (Sn) atoms on silicon, we study an extended Hubbard model on a triangular lattice. The observations of magnetism in these systems justify the inclusion of a strong on-site repulsion, and the observation of superconductivity suggests including an effective, nearest-neighbor attractive interaction. The attractive interaction mimics the effect of strong on-site repulsion near half filling, which can be seen in strong-coupling vertex calculations such as the Eliashberg method. With this extended Hubbard model on a triangular lattice with its geometrical frustration, we find a rich phase diagram of various magnetic orders and pairing functions, within the framework of self-consistent mean field theory. We uncover the competition between magnetism and unconventional superconductivity, and their coexistence for triplet pairings. We follow the Fermi surface of the system as the system is doped away from half filling and find nesting vectors and a Lifshitz transition, which provide an intuitive understanding of the phase transitions between the many orders we consider.
Many theoretical approaches find
d-wave superconductivity in the prototypical one-band Hubbard model for high-temperature superconductors. At strong coupling ($U\ensuremath{\ge}W$, where
U is the on-site repulsion and
W=8t the bandwidth) pairing is controlled by the exchange energy
J=4t2/U. One may then surmise, ignoring retardation effects, that near-neighbor Coulomb repulsion
V will destroy superconductivity when it becomes larger than
J, a condition that is easily satisfied in cuprates, for example. Using cellular dynamical mean-field theory with an exact diagonalization solver for the extended Hubbard model, we show that pairing at strong coupling is preserved, even when $V\ensuremath{\gg}J$, as long as $V\ensuremath{\lesssim}U/2$. While at weak coupling
V always reduces the spin fluctuations and hence
d-wave pairing, at strong coupling, in the underdoped regime, the increase of $J=4{t}^{2}/(U\ensuremath{-}V)$ caused by
V increases binding at low frequency while the pair-breaking effect of
V is pushed to high frequency. These two effects compensate in the underdoped regime, in the presence of a pseudogap. While the pseudogap competes with superconductivity, the proximity to the Mott transition that leads to the pseudogap, and retardation effects, protect
d-wave superconductivity from
V.
Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange (
J) and correlated hopping (
K) interaction. Detailed numerical analysis of
s-,
p-, and
d-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (
t) and next-nearest- (
t2) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the
d-wave and the extended
s-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the
tt2 ratio, giving in particular for
t2=0 s-wave (
d-wave) pairing as most favorable in the low (high) density limit, but increasing
t2 can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects
s-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.