NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The thesis deals with the theory of high temperature superconductivity from the standpoint of three-band Hubbard models. Chapter 1 of the thesis proposes a strongly coupled variational wavefunction that has the three-spin system of an oxygen hole and its two neighboring copper spins in a doublet and the background Cu spins in an eigenstate of the infinite range antiferromagnet. This wavefunction is expected to be a good "zeroth order" wavefunction in the superconducting regime of dopings. The three-spin polaron is stabilized by the hopping terms rather than the copper-oxygen antiferromagnetic coupling Jpd. Considering the effect of the copper-copper antiferromagnetic coupling Jdd, we show that the three-spin polaron cannot be pure Emery (Dg), but must have a non-negligible amount of doublet-u (Du) character for hopping stabilization. Finally, an estimate is made for the magnitude of the attractive coupling of oxygen holes. Chapter 2 presents an exact solution to a strongly coupled Hamiltonian for the motion of oxygen holes in a 1-D Cu-O lattice. The Hamiltonian separates into two pieces: one for the spin degrees of freedom of the copper and oxygen holes, and the other for the charge degrees of freedom of the oxygen holes. The spinon part becomes the Heisenberg antiferromagnet in 1-D that is soluble by the Bethe Ansatz. The holon piece is also soluble by a Bethe Ansatz with simple algebraic relations for the phase shifts. Finally, we show that the nearest neighbor Cu-Cu spin correlation increases linearly with doping and becomes positive at x [...] 0.70.
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The thesis deals with the theory of high temperature superconductivity from the standpoint of three-band Hubbard models. Chapter 1 of the thesis proposes a strongly coupled variational wavefunction that has the three-spin system of an oxygen hole and its two neighboring copper spins in a doublet and the background Cu spins in an eigenstate of the infinite range antiferromagnet. This wavefunction is expected to be a good "zeroth order" wavefunction in the superconducting regime of dopings. The three-spin polaron is stabilized by the hopping terms rather than the copper-oxygen antiferromagnetic coupling Jpd. Considering the effect of the copper-copper antiferromagnetic coupling Jdd, we show that the three-spin polaron cannot be pure Emery (Dg), but must have a non-negligible amount of doublet-u (Du) character for hopping stabilization. Finally, an estimate is made for the magnitude of the attractive coupling of oxygen holes. Chapter 2 presents an exact solution to a strongly coupled Hamiltonian for the motion of oxygen holes in a 1-D Cu-O lattice. The Hamiltonian separates into two pieces: one for the spin degrees of freedom of the copper and oxygen holes, and the other for the charge degrees of freedom of the oxygen holes. The spinon part becomes the Heisenberg antiferromagnet in 1-D that is soluble by the Bethe Ansatz. The holon piece is also soluble by a Bethe Ansatz with simple algebraic relations for the phase shifts. Finally, we show that the nearest neighbor Cu-Cu spin correlation increases linearly with doping and becomes positive at x [...] 0.70.
A Hamiltonian for the motion of oxygen holes strongly coupled to the Cu spins in a one-dimensional (1D) Cu-O lattice is solved exactly for all dopings. This Hamiltonian retains the dominant O-hole hopping term, that is, spin-exchange hopping of the hole spin with the intervening Cu spin and neglects the weaker non-spin-exchange hopping term. The excitations naturally separate into two independent quasiparticles: spinons and holons. It is this Hamiltonian that should be taken as the correct zeroth-order Hamiltonian from which perturbation theory should be applied. We show that the spinon spectrum is the spectrum of the 1D antiferromagnet incommensurate with the Cu lattice and the holons are spinless noninteracting fermions in a cosine band. The Cu-Cu spin correlation in the ground state increases linearly with doping from antiferromagnetic (-0.443) at x=0 to ferromagnetic (\ensuremath{\approxeq}0.19) at x=1.
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.
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.
Strong coupling diagram technique equations are derived for hole Green’s functions of the three-band Hubbard model, which describes Cu–O planes of high-[Formula: see text] cuprates. The equations are self-consistently solved in the approximation, in which the series for the irreducible part in powers of the oxygen–copper hopping constant is truncated to two lowest-order terms. For parameters used for hole-doped cuprates, the calculated energy spectrum consists of lower and upper Hubbard subbands of predominantly copper nature, oxygen bands with a small admixture of copper states and the Zhang–Rice states of mixed nature, which are located between the lower Hubbard subband and oxygen bands. The spectrum contains also pseudogaps near transition frequencies of Hubbard atoms on copper sites.
The one-dimensional three-band Hubbard Hamiltonian is shown to be equivalent to an effective Hamiltonian that has independent spinon and holon quasiparticle excitations plus a weak coupling of the two. The spinon description includes both copper sites and oxygen hole sites leading to a one-dimensional antiferromagnet incommensurate with the copper lattice. The holons are spinless noninteracting fermions in a simple cosine band. Because the oxygen sites are in the Hamiltonian, the quasiparticles are much simpler than in the exact solution of the t-J model for 2t = +/- J. If a similar description is correct for two dimensions, then the holons will attract in a p-wave potential.
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.