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
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
In a recent publication [Chen et al., Phys. Rev. B 86, 165136 (2012)], we identified a line of Lifshitz transition points separating the Fermi liquid and pseudogap regions in the hole-doped two-dimensional Hubbard model. Here, we extend the study to further determine the superconducting transition temperature in the phase diagram. By means of large-scale dynamical cluster quantum Monte Carlo simulations, we are able to identify the evolution of the d-wave superconducting dome in the hole-dope side of the phase diagram, with next-nearest-neighbor hopping (${t}^{\ensuremath{'}}$), chemical potential, and temperature as control parameters. To obtain the superconducting transition temperature Tc, we employ two-particle measurements of the pairing susceptibilities. As ${t}^{\ensuremath{'}}$ goes from positive to negative values, we find the d-wave projected irreducible pairing vertex function is enhanced, and the curvature of its doping dependence changes from convex to concave, which fixes the position of the maximum superconducting temperature at the same filling ($n\ensuremath{\approx}0.85$) and constraints the dome from precisely following the Lifshitz line. We furthermore decompose the irreducible vertex function into fully irreducible, charge and spin components via the parquet equations, and consistently find that the spin component dominates the pairing vertex function in the doping range where the dome is located. Our investigations deepen the understanding of the phase diagram of the two-dimensional Hubbard model and, more importantly, pose new questions to the field. For example, we found as ${t}^{\ensuremath{'}}$ goes from positive to negative values, the curvature of the pairing strength as a function of doping changes from convex to concave, and the nature of the dominant fluctuations changes from charge degree of freedom to spin degree of freedom. The study of these issues will lead to further understanding of the phase diagram of the two-dimensional Hubbard model and also the physics of the hole-doped cuprate high-temperature superconductors.
Many properties of the two-dimensional Hubbard model have been explored for the model parameters appropriate for strongly correlated electronic systems, especially cuprate superconductors.Most of the calculations are done using a well-established dynamical cluster quantum Monte Carlo method.Using this method, we investigate the effect of long-range hoppings on superconductivity with and without the presence of phonons on small clusters.The superconducting transition temperature, T c , is found to generally decrease with a negative next nearest neighbor hopping, t ′ .In the presence of the Holstein phonons, a finite t ′ enhances T c in the under-doped region for the hole-doped system, consistent with band structure calculations and experiment.The validity of the spin-susceptibility-mediated pairing in this model is studied and found to yield symmetries other than d-wave when a finite t ′ is considered.A new numerical algorithm for solving the embedded cluster problems is introduced, and used to calculate the thermodynamic properties of the model on larger clusters, especially those associated with the quantum critical behavior at finite doping.Our results suggest that the quantum critical point (QCP) which separates the Fermi liquid and pseudogap regions, is the second order terminus of the line of first order phase separation transition in the limit when a positive t ′ goes to zero.For small t ′ , the superconducting dome is centered at the QCP, suggesting that charge fluctuations might have a role in the pairing mechanism in this model.I am very thankful to University of Cincinnati for providing me with the opportunity to pursue my education and the support I received during my program.Part of this thesis is a result of my work as a researcher at Louisiana State University.I am also thankful to them for their support.I would like to thank my adviser, Mark Jarrell, who taught me how to be an effective researcher, provided me with the opportunities to interact with other professionals and fully supported me financially for most of the duration of the
In this thesis, symmetry and related transformation laws under a suitable unitary transformation are used in the study of the superconducting and magnetic properties of strongly correlated electronic systems. Such a study profits from a recently found global SO(3)×SO(3)×U(1) = [SO(4)×U(1)]/Z2 symmetry in the Hubbard model on a bipartite lattice. The introduction of the square-lattice quantum liquid relies on a general description of the Hubbard model consistent with its exact global SO(3) × SO(3) × U(1) symmetry. Such a quantum liquid is expected to play the same role for many-electron problems with short-range interactions on a square lattice, as a Fermi liquid for three-dimensional isotropic metals. It refers to the Hubbard model on the square lattice in the subspace spanned by the ground state, and the excited states generated by application onto it of one- and two-electron operators. For such a square-lattice quantum liquid only the charge c fermions and spin-neutral two-spinon s1 fermions play an active role. Part of the studies of this thesis use an effective superconductivity theory according to which, for zero spin density m = 0 and the range 0 < x < x∗ of finite hole concentrations of a short-range spin ordered phase, the ground state of the square-lattice quantum liquid of c and s1 fermions with residual interactions is superconducting. (For U/4t > ui ≈ 3/4 the critical hole concentration x∗ increases continuously upon increasing the U/4t value from x∗ = 1/√2 ≈ 0.225 at U/4t = ui to x∗ = 1/ ≈ 0.318 for U/4t → ∞.) Superconductivity emerges naturally from the effects of the residual interactions of the c and s1 fermions and as a side product of the short-range spin correlations. The phase of the c fermion pairs reads = 0 + 1 where the fluctuations of the phases 0 and 1 become large for x → 0 and x → x∗, respectively. For 0 < x < x∗ and x = 0, the symmetry of the action for the phase is a global superconducting U(1) symmetry and a local compact gauge symmetry, respectively. The former U(1) symmetry is identified with the U(1) symmetry of the Hubbard-model global SO(3) × SO(3) × U(1) = [SO(4) × U(1)]/Z2 symmetry. The amplitudes g = g0 g1, g0 = |heiθ0i|, and g1 = |heiθ1i|, their zero-temperature values ˘g ≈ (x/x∗)(1−x/x∗), ˘g0 ≈ (x/x∗), and ˘g1 ≈ (1−x/x∗) and the fluctuations of the phase , play an important role in the physics of the square-lattice quantum liquid. Together with the energy scale 2 0, which gives the maximum magnitude of the s1 fermion spinon pairing energy, they fully control the order parameters of both the short-range spin and long-range superconducting correlations. Indeed, for temperatures T < Tc, the short-range spin ordered phase has both a macroscopic quantum phase-coherent pair superconducting order so that |heiθi| > 0, and a short-range spin order, whereas for Tc < T < T∗ only the latter order prevails yet there remain c fermion pairing correlations such that |heiθ1i| > 0 but heiθ0i = 0. Here the critical temperature Tc and the crossover pseudogap temperature T∗ are fully controlled by the absolute value of the order parameters of the two above orders, respectively. However, the square-lattice quantum liquid alone does not describe quantitatively the unusual properties of the hole-doped cuprates. To fulfill such a goal we profit from a suitable theory according to which the interplay of electronic correlations described by the square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions with intrinsic disorder, is behind the unusual properties of the holedoped hight-temperature cuprate superconductors. By profiting from such an interplay, an excellent quantitative agreement with experiments for the physical quantities of several families of hole-doped cuprates is reached. That includes universal properties such as a dome-like critical-temperature hole-concentration dependence and normal-state linear-T resistivity near optimal doping, extending over a wide temperature window. The results confirm a coexisting two-gap scenario associated with an incoherent two-spinon pairing and a coherent twoc- fermion pairing, respectively. While most of our studies focus on the superconducting and magnetic properties of the square-lattice quantum liquid associated with the Hubbard model on the square lattice, the magnetic properties of a related model – the periodic Anderson model – are also addressed, on the cubic lattice.
Spin-triplet superconductivity is actively pursued in condensed matter physics due to the potential applications in topological quantum computations. The related pairing mechanism involving the interaction remains an important research topic. Here we propose a universal approach to obtain p-wave triplet superconductivity in the Hubbard models by simply changing the sign of the hopping amplitudes of the spin-down electrons, and apply it to three prototype two-dimensional lattices (honeycomb, square, and triangular). The parent Hamiltonian at half filling has long-range magnetic order, which is ferromagnetic in all three directions for the frustrated triangular lattices, and ferromagnetic (antiferromagnetic) in the xy plane (z direction) for the bipartite honeycomb and square lattices. The magnetic transitions occur at some critical interactions on honeycomb and triangular lattices, which are estimated by finite-size scalings. When the systems are doped, we find the triplet p-wave pairing is a dominating superconducting instability. We demonstrate its emergence is closely related to the strong ferromagnetic spin fluctuations induced by the doping. Our results provide an understanding of the microscopical triplet-pairing mechanism, and will be helpful in the search for spin-triplet superconducting materials.
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.