Theoretical studies of strong correlations in cuprates

Abstract

This thesis presents work that has been done to describe the high temperature superconducting cuprates by going beyond first principles calculations using the Hubbard model with (pi,pi) antiferromagnetic and BCS superconducting order. The unique approach here is to fit the Hubbard model to either first principles or experimental band structure and obtain electronic structure properties by self consisting the antiferromagnetic and superconducting gaps as well as self consistently computing self energy corrections. The self energy corrections are determined through the QPGW model which correctly describes the cuprates as having intermediate coupling of electrons. These methods of modeling cuprates are used to describe the experimental results of spectroscopies such as photoemission and scanning tunneling spectroscopy. The first topic presented here studies the one, three, and four band versions of the Hubbard model. It is shown that, in the three and four band model, by fitting the tight binding parameters to first principles calculations and the antiferromagnetic gap to experimental gap measurements, cuprates should be described as charge transfer insulators instead of Mott insulators which is predicted by one band models. The one, three, and four band models with parameters fit to experiment predict a negative electronic compressibility. This phenomenon is shown to be due to a dramatic decrease in the Hubbard U with increased electron doping away from half filling. Switching focus to hole doped cuprates, the addition of superconducting order reveals a property known as Fermi surface free superconductivity. Fermi surface free superconductivity drives a topological transition from open to closed Fermi surfaces in the hole doped cuprates. STM measurements of the local density of states on hole doped cuprates show a gap filling rather than a gap closing with increased doping. A model of nanoscale phase separation in conjunction with a Coulomb gap which describes stripe pinning by impurities is shown to successfully model this gap filling. In a recent STM study, unusual features were observed in the quasiparticle interference spectra of single layered bismuth cuprates, within the superconducting gap at the antinodes. To describe these feature a realistic model of quasiparticle interference is employed with self energy corrections which show quasiparticle weight being pushed into the antinodal regions when in the superconducting state. Overall, it is shown that the Hubbard model can be an effective tool in describing the cuprates and spectroscopies performed on them especially when using realistic bands from experiments or first principles along with self consistent order parameters and self energy corrections.