We consider a correlated wavefunction including particle-hole pairing at half a reciprocal lattice vector for itinerant electrons hopping on a square lattice in two dimensions and subject both to on-site and nearest-neighbor repulsion. We find, within mean field theory, that in a suitable range of parameters there is a tendency toward a novel form of ordering characterized by discrete symmetry breaking and a gap at the magnetic zone boundary, which supports hole-like semiconductor behavior near half filling despite an apparently normal Fermi surface. The effective quasiparticle couplings to phonons includes a significant d-wave piece, which plausibly leads to an especially robust tendency toward superconductivity.
We consider a correlated wavefunction including particle-hole pairing at half a reciprocal lattice vector for itinerant electrons hopping on a square lattice in two dimensions and subject both to on-site and nearest-neighbor repulsion. We find, within mean field theory, that in a suitable range of parameters there is a tendency toward a novel form of ordering characterized by discrete symmetry breaking and a gap at the magnetic zone boundary, which supports hole-like semiconductor behavior near half filling despite an apparently normal Fermi surface. The effective quasiparticle couplings to phonons includes a significant d-wave piece, which plausibly leads to an especially robust tendency toward superconductivity.
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=0s-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.
We examine the phase diagram of the extended Hubbard model on a square lattice, for both attractive and repulsive nearest-neighbor interactions, using CDMFT+HFD, a combination of Cluster Dynamical Mean Field theory (CDMFT) and a Hartree-Fock mean-field decoupling of the inter-cluster extended interaction. For attractive non-local interactions, this model exhibits a region of phase separation near half-filling, in the vicinity of which we find islands of d-wave superconductivity, decaying rapidly as a function of doping, with disconnected regions of extended s-wave order at smaller (higher) electron densities. On the other hand, when the extended interaction is repulsive, a Mott insulating state at half-filling is destabilized by hole doping, in the strong-coupling limit, in favor of d-wave superconductivity. At the particle-hole invariant chemical potential, we find a first-order phase transition from antiferromagnetism (AF) to d-wave superconductivity as a function of the attractive nearest-neighbor interaction, along with a deviation of the density from the half-filled limit. A repulsive extended interaction instead favors charge-density wave (CDW) order at half-filling.
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 extendeds-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 In3Cu2VO9. Our findings are also relevant to the understanding of exotic superfluidity with cold atoms.
An elaborate variational wave function is used for studying superconductivity in the (repulsive) two-dimensional Hubbard model, including both nearest- and next-nearest-neighbor hoppings. A marked asymmetry is found between the ``localized'' hole-doped region and the more itinerant electron-doped region. Superconductivity with d-wave symmetry turns out to be restricted to densities where the Fermi surface crosses the magnetic zone boundary. A concomitant peak in the magnetic structure factor at $(\ensuremath{\pi},\ensuremath{\pi})$ clearly points to a magnetic mechanism.
We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (U) and nearest-neighbor (V) interactions, at weak couplings. We show that the charge-density wave phase that is known to occur at half filling when 4V>U gives way to a dxy-wave superconducting instability away from half filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive V and a range of on-site repulsive interaction U. In addition, when nesting is further suppressed and in the presence of a nearest-neighbor attraction, a triplet time-reversal breaking (px+ipy)-wave pairing instability emerges, competing with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the (px+ipy)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while dxy pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.
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.