Abstract We investigate chiral d -wave superconductivity in the honeycomb-lattice t-J - U model within Renormalized Mean-Field Theory (RMFT). By incorporating Gutzwiller renormalization factors, the effects of strong correlations and the suppression of double occupancy are treated self-consistently. In the nearest-neighbor chiral d + id pairing state of the honeycomb lattice, we analyzed the evolution of the pairing amplitude, the quasiparticle spectrum, and the superfluid weight with respect to the doping concentration, the local Coulomb repulsion energy ( U ), and the antiferromagnetic exchange interaction ( J ). The pairing amplitude exhibits a dome-like doping dependence. As U increases, the dome broadens and the optimal doping shifts toward higher carrier concentration due to the renormalization of the effective kinetic energy. We further determine the critical exchange interaction required to obtain a self-consistent pairing solution and show that strong correlations reduce this threshold over a wide doping range. Finally, from the calculated superfluid weight, we estimate the phase-ordering temperature scale associated with the self-consistent chiral d-wave solution.Our research results have clarified how the correlation effect influences the chirality d-wave pairing and the superfluid weight in the honeycomb lattice system.
Abstract We investigate chiral d -wave superconductivity in the honeycomb-lattice t-J - U model within Renormalized Mean-Field Theory (RMFT). By incorporating Gutzwiller renormalization factors, the effects of strong correlations and the suppression of double occupancy are treated self-consistently. In the nearest-neighbor chiral d + id pairing state of the honeycomb lattice, we analyzed the evolution of the pairing amplitude, the quasiparticle spectrum, and the superfluid weight with respect to the doping concentration, the local Coulomb repulsion energy ( U ), and the antiferromagnetic exchange interaction ( J ). The pairing amplitude exhibits a dome-like doping dependence. As U increases, the dome broadens and the optimal doping shifts toward higher carrier concentration due to the renormalization of the effective kinetic energy. We further determine the critical exchange interaction required to obtain a self-consistent pairing solution and show that strong correlations reduce this threshold over a wide doping range. Finally, from the calculated superfluid weight, we estimate the phase-ordering temperature scale associated with the self-consistent chiral d-wave solution.Our research results have clarified how the correlation effect influences the chirality d-wave pairing and the superfluid weight in the honeycomb lattice system.
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.
A microscopic theory of the electronic spectrum and of superconductivity within the t-J model on the honeycomb lattice is developed. We derive the equations for the normal and anomalous Green functions in terms of the Hubbard operators by applying the projection technique. Superconducting pairing of d + id-type mediated by the antiferromagnetic exchange is found. The superconducting T-c as a function of hole doping exhibits a two-peak structure related to the van Hove singularities of the density of states for the two-band t-J model. At half-filling and for large enough values of the exchange coupling, gapless superconductivity may occur. For small doping the coexistence of antiferromagnetic order and superconductivity is suggested. It is shown that the s-wave pairing is prohibited, since it violates the constraint of no-double-occupancy.
In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.
A microscopic theory of the electronic spectrum and of superconductivity within the t-J model on the honeycomb lattice is developed. We derive the equations for the normal and anomalous Green functions in terms of the Hubbard operators by applying the projection technique. Superconducting pairing of d + id′-type mediated by the antiferromagnetic exchange is found. The superconducting Tc as a function of hole doping exhibits a two-peak structure related to the van Hove singularities of the density of states for the two-band t-J model. At half-filling and for large enough values of the exchange coupling, gapless superconductivity may occur. For small doping the coexistence of antiferromagnetic order and superconductivity is suggested. It is shown that the s-wave pairing is prohibited, since it violates the constraint of no-double-occupancy.
Antiferromagnetism, charge density wave, and d-wave superconductivity in the t-J-U-V model of correlated electrons: Role of direct Coulomb interactions
We study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase and show it appears only above some critical values of V and in a limited hole doping range δ. The effect of the term V on SC and AF phases is that a strong interaction suppresses SC altogether, whereas the AF order is not significantly influenced by its presence. Calculations for the case of pure SC phase have been also carried out within an extended approach, the extended approach, the diagrammatic expansion for the Gutzwiller wave function (DE-GWF) in order to analyze influence of the higher-order correlations onto this phase beyond the renormalized mean field approach. In the Appendices we discuss, the specific ambiguity of the choice of the Gutzwiller renormalization factors within the SGA when either AF or CDW orders are considered.
In view of quite recent experimental activities on magnetic and superconducting properties of honeycomb and hexagonal lattice based materials, in this thesis we have used field-theoretic and many-body methods to investigate magnetic and superconducting properties of the large-U Hubbard model on the honeycomb lattice at half-filling and in the hole-doped regime. Within the framework of a functional-integral approach, we obtain the Lagrangian density associated with the charge (Grassmann fields) and spin [SU(2) gauge fields] degrees of freedom. The Hamiltonian related to the charge degrees of freedom is exactly diagonalized. In the strong-coupling regime, we derive a perturbative low-energy theory suitable to describe the (quantum) magnetic and superconducting phases at half-filling and in the hole-doped regime. At half-filling, we deal with the underlying spin degrees of freedom of the quantum antiferromagnetic (AF) Heisenberg model by employing a second-order spin-wave analysis, in which case we have calculated the ground-state energy and the staggered magnetization; the results are in very good agreement with previous studies. Further, in the continuum, we derive a nonlinear σ-model with a topological Hopf term that describes the AF-VBS (valence bond solid) competition. In the challenging hole-doped regime, our approach allows the derivation of a t-J Hamiltonian, and the analysis of the role played by charge and spin quantum fluctuations on the ground-state energy and, particularly, on the breakdown of the AF order at a critical hole doping; the results are benchmarked against recent Grassmann tensor product state simulations. In addition, we have performed an extensive study of the electronic structure of the doped system for each competing phase: AF, ferromagnetic (FM), and (spin-singlet pairing) s-, dx₂₋ʏ₂ – and idxʏ -wave superconducting (SC) state induced by purely electronic effects. In this context, an energetic analysis of the ground state of these phases reveal that the AF order prevails for low hole doping, while a dominantly chiral dx₂₋ʏ₂ + idxʏ superconducting state was found in the vicinity of the Van Hove singularity (high hole doping). We also stress that a thermodynamic analysis of the superconducting phase shows that the critical temperature is directly related to the exchange constant J = 4t²/U, in which t denotes the hopping amplitude and U the on-site Coulomb repulsion of the Hubbard model (purely electronic origin). Remarkably, the competition between the AF and dx₂₋ʏ₂ + idxʏ SC phases takes place by the occurrence of a first-order transition accompanied by a spatial phase separation of the referred phases.