Since its discovery, superconductivity has received significant attention, with renewed interest following the discovery of high-temperature superconductors (HTSCs) such as cuprates. The t–J model, combined with the Gutzwiller approximation, has been used to study HTSCs. While much research has focused on homogeneous systems, less attention has been given inhomogeneous ones - especially the possible coexistence of superconductivity and antiferromagnetism in them. The coexistence could be of interest for applications within superconducting spintronics.The focus of the present thesis is [110] edges of HTSCs. It is shown that these edges attract quasiparticles, increasing the local occupation and thereby strengthening local correlation, which in turn reduces the weight of the zero-energy Andreev bound states typically present at [110] edges. Furthermore, the s-wave order parameter, predicted in some models to form at the edge, is here seen to vanish or be suppressed. Finally, it is demonstrated that the charging of the edges enables antiferromagnetic order to emerge at the edges at higher average dopings than in homogeneous systems.
Since its discovery, superconductivity has received significant attention, with renewed interest following the discovery of high-temperature superconductors (HTSCs) such as cuprates. The t–J model, combined with the Gutzwiller approximation, has been used to study HTSCs. While much research has focused on homogeneous systems, less attention has been given inhomogeneous ones - especially the possible coexistence of superconductivity and antiferromagnetism in them. The coexistence could be of interest for applications within superconducting spintronics.The focus of the present thesis is [110] edges of HTSCs. It is shown that these edges attract quasiparticles, increasing the local occupation and thereby strengthening local correlation, which in turn reduces the weight of the zero-energy Andreev bound states typically present at [110] edges. Furthermore, the s-wave order parameter, predicted in some models to form at the edge, is here seen to vanish or be suppressed. Finally, it is demonstrated that the charging of the edges enables antiferromagnetic order to emerge at the edges at higher average dopings than in homogeneous systems.
We report results of a study of strongly correlated d -wave superconducting slabs within a t - model solved using the statistically consistent Gutzwiller approach. For different dopings, we model slabs cut at 45 ∘ relative to the main crystallographic a b axes, i.e., [110] orientation, and conclude that quasiparticle charge is drawn to the edges. Thus, the correlations are locally strengthened, and a region near the edge is closer to the Mott- insulating state with reduced hopping amplitudes on the links. Superconductivity is locally weakened near the edges in the correlated state, and the spectral weight of zero-energy Andreev bound states is substantially reduced compared to weak coupling theory. The renormalization of the edge states leaves no room for an extended s -wave component to form for hole dopings ranging from strongly underdoped to slightly overdoped.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.
The ground state of two-dimensional t – J model including superconductivity and antiferromagnetism is studied using a new type of analytic estimation of the effect of strong correlation. The method is an extension of the Gutzwiller approximation which gives renormalization of parameters, t and J , due to the Gutzwiller projection operator excluding double occupancies. It is shown that the essential point of the renormalization is its dependence on the expectation values of superconductivity and antiferromagnetic moment. In special the renormalization factor is anisotropic in spin space, which leads to a reliable estimate of antiferromagnetic order parameters in the phase diagram, in contrast to the conventional slave-boson mean-field theory. The obtained phase diagram shows the coexistence of antiferromagnetism and d x 2 - y 2 -wave superconductivity for the doping rate, δ, less than 10%. At half-filling, the renormalization of the J -term represents some aspects of quantum spin nature. For the finite doping case, there are two kinds of superconducting order parameters. The variational order parameter of the d-wave superconductivity increases as the doping rate decreases, which will correspond to the experimentally observed superconducting gap. In contrast, the actual expectation value of superconducting order parameter is proportional to δ in underdoped region and has a maximum near δ=0.11, which probably determines T c . We also speculate that the ground-state antiferromagnetic order, being destroyed at finite temperatures, gives the energy and temperature scale of the pseudogap. Applications to the inhomogeneous systems such as the vortex state and stripe state are discussed.
This thesis deals with different aspects of high temperature superconductivity in hole-doped cuprates. We assume the t - J model to describe the CuO2 planes of cuprates and we use a spin-charge gauge approach with spin-charge separation to describe holes in terms of a spinless fermion carrying the charge (holon) and a neutral boson carrying spin 1/2 (spinon), coupled by a slave-particle gauge field. In this framework we consider the effects of the presence of a finite density of incoherent holon pairs in the normal state as a precursor of superconductivity. We show that it is possible to take such pairs into account through a strongly direction dependent spectral weight for holons, which suppresses quasi-particles starting from the anti-nodal directions, and a wave function renormalization for the slave particle gauge field. In this way we prove that, when temperature is reduced, the formation of holon pairs causes both the deviation from linearity of the resistivity and the deviation from the constant value of the Knight shift. Moreover we point out the need for a negative next-nearest-neighbor hopping term ((t - t' - J model) to get a good continuum limit and to evaluate the Knight shift. These results are obtained through a Green's function, which follows naturally from the formalism and analytically interpolates between a Fermi liquid-like behavior and a d-wave superconductor when the coherence length of the holon pair order parameter is increased. The system preserves a finite Fermi surface until the superconducting transition, where it reduces to four nodes. Finally when, at lower temperatures, both the holon pairs and the RVB spinon pairs condense we enter the superconducting phase. In this phase we study the magnetic excitations showing how to extend to spin waves the hourglass-shape dispersion, found for spinons near the antiferromagnetic vector, if a suitable local mechanism of attraction between spinon and anti-spinon is assumed. The resulting spin wave Green's function, whose imaginary part is directly comparable with experiments, generates the hourglass with a finite gap between the two branches. Since the U(1) slave-particle gauge field gains mass in the superconducting phase via Anderson-Higgs mechanism, we propose the necessary mechanism of attraction comes from the unbroken Z2 subgroup of the U(1) gauge group.
We present a. study of the superconducting properties of models containing the Hubbard rnpulsion term. This strnng on-site repulsion is considered as a key ingTedient of the high tempera.turn superconductivity. Though the fact that for the normal, lovv temperature superconductors, rnpulsion destroys superconducting order, it is argued in the present thesis, that for the pairing of the d-·wave symmetry in the strongly correlated electronic systems its effect is to enhance and may be to cause superconductivity. Various methods such as Variational Monte Carlo, Gutzwiller Approximation, Time Dependent Hartree-Fock and Fixed Node Approximation have been used to investigate t - U - W model, t - U - J - V and pure Hubbard models. In this thesis, by considering correlations contribution to the BCS condensation energy due to the Hubbard U it is shown that the latter lowers the total energy of a d-wave superconductor in the weak coupling limit, thus enforcing the stability of such superconductor. This effect appears to be mainly due to the enhancement of the spin fluctuations near the nesting vector Q = ( π, π). It is then studied the crossover from weak to strong coupling regimes in t - U - J - V model by increasing U. Remarkably in this model an order of magnitude growth of the superconducting order parameter is found and explained as being due to the Hubbard repulsion. vVe fi.nd also, that the pairings, originally induced by spin or charge fluctuations upon increase of U are differently renormalized, being the former enhanced, while the latter suppressed. In the fi.nal part of the thesis the superconductivity in the pure Hubbard model is carefully studied by means of Variational Monte Carlo and related numerical methods aimed to improve variational results. VVe observe the onset of strong coupling superconductivity at U/t ~ 7 within the Fixed Node Approximation in the systems of large size and compare our results for small clusters with those of Lanczos diagonalization. We show that Variational Monte Carlo, though overestimating the quasiparticle weight (ZvMc > Zexact) succeeds in reproducing the correct pairing between quasiparticles.
Using Gutzwiller-projected wave functions, I estimate the ground-state energy of the $t\text{\ensuremath{-}}J$ model for several variational states relevant for high-temperature cuprate superconductors. The results indicate that both the superconducting state and the staggered-flux normal state (proposed for vortex cores) are unstable at low doping towards antiferromagnetism and towards phase separation. While phase separation in the underdoped superconducting state may be relevant for the stripe formation mechanism, the results for the normal state suggest that similar charge inhomogeneities may also appear in vortex cores up to relatively high doping values.