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.
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.
We use unrestricted Hartree-Fock, density matrix renormalization group, and variational projected entangled-pair state calculations to investigate the ground-state phase diagram of the triangular-lattice Hubbard model at “half doping” relative to single occupancy, i.e., at fillings of ( 1 ± 1 2 ) electrons per site. The electron-doped case has a nested Fermi surface in the noninteracting limit, and hence a weak-coupling instability toward density-wave orders whose wave vectors are determined by Fermi-surface nesting conditions. We find that at moderate-to-strong interaction strengths, other spatially modulated orders arise, with wave vectors distinct from the nesting vectors. In particular, we identify a series of closely competing, itinerant long-wavelength magnetically ordered states, yielding to uniform ferromagnetic order at the largest interaction strengths. For half-hole doping and a similar range of interaction strengths, our data indicate that magnetic orders are most likely absent.
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.
Several new classes of compounds can be modeled in first approximation by electrons on the triangular lattice that interact through on-site repulsion U as well as nearest-neighbor repulsion V. This extended Hubbard model on a triangular lattice has been studied mostly in the strong coupling limit for only a few types of instabilities. Using the extended two-particle self-consistent approach (ETPSC), that is valid at weak to intermediate coupling, we present an unbiased study of the density and interaction dependent crossover diagram for spin- and charge-density wave instabilities of the normal state at arbitrary wave vector. When U dominates over V and electron filling is large, instabilities are chiefly in the spin sector and are controlled mostly by Fermi surface properties. Increasing V eventually leads to charge instabilities. In the latter case, it is mostly the wave vector dependence of the vertex that determines the wave vector of the instability rather than Fermi surface properties. At small filling, nontrivial instabilities appear only beyond the weak coupling limit. There again, charge-density wave instabilities are favored over a wide range of dopings by large V at wave vectors corresponding to $\sqrt{(3)}\ifmmode\times\else\texttimes\fi{}\sqrt{(3)}$ superlattice in real space. Commensurate fillings do not play a special role for this instability. Increasing U leads to competition with ferromagnetism. At negative values of U or V, neglecting superconducting fluctuations, one finds that charge instabilities are favored. In general, the crossover diagram presents a rich variety of instabilities. We also show that thermal charge-density wave fluctuations in the renormalized-classical regime can open a pseudogap in the single-particle spectral weight, just as spin or superconducting fluctuations.
In this thesis we try to understand the unconventional superconducting mechanism on cuprates and organic superconductors (or sodium cobaltates) which can be modeled by a two-dimensional square- and triangular-lattice Hubbard model respectively. The formation of the superconducting dome requires explanations of feasible scenarios. Generally speaking, pairing strength is provided by magnetic fl_x001D_uctuations in the strongly correlated region and the structure of the Fermi surface in this region will favor superconducting pairings with a certain type of symmetry. For the cuprate physics, a superconducting dome composed of d-wave pairings has been identified experimentally. We study the Hubbard model on square lattices and _x001C_find that the pairing strength is originated from anti-ferromagnetic instabilities, and the nearly nested Fermi surface with the square symmetry further supports the d-wave pairing. Moreover, our results show there is a quantum critical point (QCP) beneath the superconducting dome. The QCP is a zero-temperature instability which separates the Fermi liquid and pseudogap regions and exhibits the quantum _x001D_fluctuations which may lead to a high superconducting transition temperature. Above the QCP, a V-shape marginal Fermi liquid region associated with the quantum critical phenomena is also identi_x001C_fied. Using next-nearest-neighbor hopping, chemical potential, and temperature as control parameters, there is a line of Lifshitz transition associated with the change of topology of the Fermi surface. Along the Lifshitz line with t'<=0, the marginal Fermi liquid region prevails, the peak of density of states crosses the Fermi level, and the bare d-wave pairing susceptibility shows a universal scaling with the exponent consistent with theoretical proposals. For the triangular-lattice Hubbard model in the strongly correlated region, we _x001C_find a d+id superconducting pairing on the hole-doped side of the phase diagram. Here the pairing strength comes from the instabilities of the anti-ferromagnetic order (120-degree-spin structure), and the nested hexagon-deformed Fermi surface with the triangular symmetry further boosts the d+id symmetry. Due to the strong competition between electronic interactions and geometric frustrations, the superconductivity and other novel features of the system equal to or above half fi_x001C_lling requires future studies. The numerical tool we apply to study these systems is the dynamical cluster approximation with continuous-time quantum Monte Carlo as the solver. Our approach includes nonlocal correlations embedded in a mean _x001C_field host and is a most up-to-date and reliable approach in dealing with the above mentioned strongly correlated systems valid in the thermodynamic limit. Our _x001C_findings shine light on future investigations of the nature
The ${120}^{\ensuremath{\circ}}$ antiferromagnetism (AFM) is widely believed as the magnetic ground state of the triangular systems because of the geometrical frustration. The emergence of novel magnetism, such as the row-wise AFM in Mn/Cu(111) and Sn/Si(111), reveals the importance of the longer-range hopping on magnetic competitions in realistic material systems. By utilizing advanced many-body techniques, we systematically studied the isotropic triangular Hubbard model with second nearest-neighbor hopping ${t}^{\ensuremath{'}}$, including both the single- and the two-particle responses. We found that both electronic and magnetic phase transitions show a clear dependence on ${t}^{\ensuremath{'}}/t$. Consequently, we observed a remarkable reentrance of the metal-insulator transition and a crossover between the ${120}^{\ensuremath{\circ}}$- and the row-wise AFM. The Fermi surface (FS) shows two distinct structures with the nesting vectors consistent with the magnetic correlations. When ${t}^{\ensuremath{'}}$ evolvs from 0 to 1, the correlated Fermi surface demonstrates a Lifschitz transition between the two nesting structures, and exotic phases like the featureless insulating state can be realized. Our work sheds light on the engineering of electronic and magnetic correlations of correlated triangular surfaces via longer-range hopping. The rich phase diagram and the high degree of tunability make the triangular lattice with longer-range hopping a more realistic platform to study the emergent magnetic competitions.
Abstract Using a mean-field theory based upon Hartree—Fock approximation, we theoretically investigate the competition between the metallic conductivity, spin order and charge order phases in a two-dimensional half-filled extended Hubbard model on anisotropic triangular lattice. Bond order, double occupancy, spin and charge structure factor are calculated, and the phase diagram of the extended Hubbard model is presented. It is found that the interplay of strong interaction and geometric frustration leads to exotic phases, the charge fluctuation is enhanced and three kinds of charge orders appear with the introduction of the nearest-neighbor interaction. Moreover, for different frustrations, it is also found that the antiferromagnetic insulating phase and nonmagnetic insulating phase are rapidly suppressed, and eventually disappeared as the ratio between the nearest-neighbor interaction and on-site interaction increases. This indicates that spin order is also sensitive to the nearest-neighbor interaction. Finally, the single-site entanglement is calculated and it is found that a clear discontinuous of the single-site entanglement appears at the critical points of the phase transition.