This work is a series of reports on progress in the description of electron-electron and electron-lattice interactions in transition-metal oxides, with an emphasis to the class of high-Tc superconducting cuprates. Combinations of numerical and analytical approaches were devised and developed to study large-scale models, which distinguish cation and anion sites of the realistic lattice structure. The many results range from incremental deviation to significant difference compared to those of the widely-accepted simple models without such distinction. A previously proposed numerical scheme and a perturbation approach were adapted to study the one-dimensional breathing-mode model, which describes a charge carrier interacting with vibrating anions. The effort yielded the first accurate benchmark result for all parameters values of the model. Based on a physical insight about the spin-1/2 Heisenberg antiferromagnet on a two-dimensional square lattice, an octapartite approach was devised to model the low-energy states. The efficiency of the resulting numerical approach was showcased with the explicit solution to a record-breaking 64-spin torus. A spin-polaron model was derived to model holes injected into cuprate's quasi two-dimensional copper-oxygen layer. Total-spin-resolved exact diagonalization was performed for a single fermionic hole in a record-breaking cluster with 32 copper and 64 oxygen sites. The solutions revealed important physics missed by previous studies. The octapartite approach was then developed to solve the spin-polaron model with two extra holes in the same cluster. The accuracy and efficiency of the method were established. Enhanced singlet correlation between two holes was observed. The preliminary results justify the need for an in-depth study.
This work is a series of reports on progress in the description of electron-electron and electron-lattice interactions in transition-metal oxides, with an emphasis to the class of high-Tc superconducting cuprates. Combinations of numerical and analytical approaches were devised and developed to study large-scale models, which distinguish cation and anion sites of the realistic lattice structure. The many results range from incremental deviation to significant difference compared to those of the widely-accepted simple models without such distinction. A previously proposed numerical scheme and a perturbation approach were adapted to study the one-dimensional breathing-mode model, which describes a charge carrier interacting with vibrating anions. The effort yielded the first accurate benchmark result for all parameters values of the model. Based on a physical insight about the spin-1/2 Heisenberg antiferromagnet on a two-dimensional square lattice, an octapartite approach was devised to model the low-energy states. The efficiency of the resulting numerical approach was showcased with the explicit solution to a record-breaking 64-spin torus. A spin-polaron model was derived to model holes injected into cuprate's quasi two-dimensional copper-oxygen layer. Total-spin-resolved exact diagonalization was performed for a single fermionic hole in a record-breaking cluster with 32 copper and 64 oxygen sites. The solutions revealed important physics missed by previous studies. The octapartite approach was then developed to solve the spin-polaron model with two extra holes in the same cluster. The accuracy and efficiency of the method were established. Enhanced singlet correlation between two holes was observed. The preliminary results justify the need for an in-depth study.
We extend the methods recently introduced [Phys. Rev. Lett. 106, 036401 (2011)] to investigate correlations between two spin-polarons in a quasi-two-dimensional CuO2 layer. The low-energy wave functions for two doped holes introduced in a half filled CuO2 plane with 32 copper and 64 oxygen sites are calculated explicitly using an efficient yet accurate truncation scheme to model the antiferromagnet background. The energetics and wave functions show that the charges form three spin-polarons and the spin is carried by a disturbance around the three spin-polaron core. The low-energy band results from the competition between the kinetic energy and a local attractive potential, which favors ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ states. Last, we point out features that are expected to be robust for larger systems.
In this dissertation we investigate superconductivity in strongly correlated systems, with a specific focus on copper oxides, known as cuprates. These materials exhibit a variety of emerging phases as we vary parameters such as temperature, doping, and pressure. In addition to the superconducting phase, other phases, such as the pseudogap, remain poorly understood. The pseudogap phase is characterized by a suppression of spectral weight in certain directions in momentum space. Understanding this phase is fundamental to understanding superconductivity, as it is believed that there are signatures of the superconducting phase in the pseudogap phase. The Hubbard model is used to describe strongly correlated systems, as it well describes the competition between the kinetic energy and the Coulomb interaction of electrons. It is believed that much can be learned about cuprates considering the Hubbard model in two spatial dimensions, corresponding to the planes of copper and oxygen, in the presence of doping, arising from the other atoms. However, the model does not have an exact solution in two dimensions, requiring the use of a numerical method for its resolution. In previous work by the group, the model was solved numerically without considering superconductivity via extensions of Dynamical Mean Field Theory (DMFT). This technique maps the Hubbard model onto the Anderson impurity problem, simplifying the resolution. The results obtained revealed two distinct metallic phases, conventional and pseudogap, as the system doping varied. The objective of this dissertation is to verify whether the different metallic phases mentioned above give rise to different superconducting phases. For this, an electron pair formation term was added to the Hamiltonian and new numerical DMFT results were obtained. These results are difficult to understand; to analyze them, we use a phenomenological model that describes electron dynamics at low energies. We built a code that simultaneously adjusts the DMFT curves for the real and imaginary parts of the normal and anomalous self-energies to the phenomenological model for each doping value, allowing the analysis of the model parameters starting from the different metallic regions. Our preliminary results show fluctuations in these parameters when we vary the doping, suggesting that it would be desirable to obtain more accurate DMFT results, which is in progress, so that new adjustments to the phenomenological model can be made.
The three-band model relevant to high-temperature copper-oxide superconductors is solved using single-site dynamical mean field theory and a tight-binding parametrization of the copper and oxygen bands. For a band filling of one hole per unit cell the metal/charge-transfer-insulator phase diagram is determined. The electron spectral function, optical conductivity, and quasiparticle mass enhancement are computed as functions of electron and hole doping for parameters such that at one hole per cell the paramagnetic phase is insulating and for parameters such that at one hole per unit cell the paramagnetic phase is metallic. The optical conductivity is computed using the Peierls phase approximation for the optical matrix elements. The calculation includes the physics of ``Zhang-Rice singlets.'' The effects of antiferromagnetism on the magnitude of the gap and the relation between correlation strength and doping-induced changes in state density are determined. Three-band and one-band models are compared. The two models are found to yield quantitatively consistent results for all energies less than about 4 eV including energies in the vicinity of the charge-transfer gap. Parameters on the insulating side of the metal/charge-transfer insulator phase boundary lead to gaps which are too large and near-gap conductivities which are too small relative to data. The results place the cuprates clearly in the intermediate correlation regime, on the paramagnetic metal side of the metal/charge-transfer insulator phase boundary.
Polaronic features of dopant-induced charge carriers are manifest in recent experiments on ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$SrxCuO4+y and ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$NixCuO4+y. To study the formation of hole (bi)polarons in such systems exhibiting strong Coulomb interactions, the Holstein t-J model is examined by means of a variational diagonalization technqiue for a wide range of phonon frequencies and electron-phonon (EP) couplings on finite square lattices, up to 18 effective sites in size. Including static displacement field, polaron, and squeezing effects, our approach allows for the description of nearly free polarons in the weak-coupling limit as well as for adiabatic Holstein polarons and nonadiabatic Lang-Firsov polarons in the case of strong EP interactions. At low doping levels and low phonon frequencies we demonstrate that antiferromagnetic spin correlations and EP interactions reinforce each other to the effect of lowering the threshold for polaronic self-localization in a strongly distorted lattice. This is contrasted with the nonadiabatic regime, where we observe the formation of Lang-Firsov polarons with moderate polaronic mass enhancement in a nearly undistorted lattice. In the case of two doped holes, the hole binding energy is analyzed in detail and we find that hole binding is enhanced as a dynamical (static) effect of a rather weak (extremely strong) EP interaction for delocalized (self-trapped) polarons. At quarter-filling we notice, in the adiabatic regime, a sequence of transitions as the EP coupling increases from nearly free mobile polarons to a polaronic superlattice and finally to a charge-separated state. The ordering of polarons disappears at higher phonon frequencies.
Solid state physics, a very broad field in natural science, aims to explain physical properties of materials modeled as a many-body ensemble of the order of ∼ 10^23 interacting particles. For interacting metallic systems, one of the most powerful tools for unraveling the consequences of the collective interaction is the Fermi liquid theory. While still being an approximation, it excellently models many materials especially in the low-temperature and low-energy regime by treating themany-body problem as being equivalent to effectively non-interacting ”particles”, which is done by introducing the concept of quasiparticles. During the last few decades, several exotic phases of matter have been discovered, which originate from strong Coulomb interactions between the electrons, whose description is beyond the Fermi liquid theory. This thesis addresses the question of the validity of Fermi liquid theory once a single hole is introduced into an antiferromagnet with completely localized spins due to the strong interactions. Here, the most-studied case concerns the so-called 2D t − J model, which hosts a well-defined quasiparticle, the spin polaron. Focusing on a more tractable case, the t − Jz model without quantum spin fluctuations, we study the stability of the spin polaron solution once the nextnearest neighbor hopping t′ is introduced into the system. We focus on observations at the Γ-point and the X-point of systems with fixed Jz = 0.4t and varying t′ ∈ [−0.5t, 0.5t]. The model is numerically solved using exact diagonalization on finite-size lattices of up to 32 sites. A study of the quasiparticle weight under finite-size scaling reveals an “anomalous” regime at the Γ-point fort′ ≤ −0.3t, indicated by a vanishing quasiparticle weight. In order to characterize the low-energy dynamics within this “anomalous” regime, we investigated the spin correlation centered around the hole, as well as the magnon number distribution of a single-doped 20-site system. Based on the results, we present a preliminary picture of the antiferromagnetic ground state doped with one hole within that “anomalous” regime (t′ ≤ −0.3t) that deviates from the standard spin polaron as the cloud of magnetic fluctuations, typically localized around the hole, delocalizes over the whole finite-size lattice. Consequently, such systems show a weakly suppressed antiferromagnetic configuration under single-hole doping.
We derive and investigate numerically a minimal yet detailed spin-polaron model that describes lightly doped CuO2 layers. The low-energy physics of a hole is studied by total-spin-resolved exact diagonalization on clusters of up to 32 CuO2 unit cells, revealing features missed by previous studies. In particular, spin-polaron states with total spin 3/2 are the lowest eigenstates in some regions of the Brillouin zone. In these regions, and also at other points, the quasiparticle weight is identically zero indicating orthogonal states to those represented in the one electron Green's function. This highlights the importance of the proper treatment of spin fluctuations in the many-body background.