Tunneling studies of strongly correlated materials provide information about the nature of electronic correlations, which is vital for investigation of emergent materials at the microscopic level. In particular, scanning tunneling spectroscopy/microscopy (STS/STM) studies have made major contributions to understanding cuprate superconductors (66), yet there is a sense that huge STM data arrays contain much more precious information to be extracted and analyzed. One of the most pressing questions in the field is how to improve the data analysis, so as to
extract more information from STM data. A dominant trend in STM data analysis has been to interpret the data within a particular microscopic model, while using only basic data analysis tools. To decrease the reliance of the STM data interpretation on particular microscopic models, further advances in data analysis methods are necessary.
In Chapter 2 of this Thesis, we discuss how one can extract information about the phase of the order parameter from STM data. We show that symmetrized and anti-symmetrized correlators of local density of states give rise to observable coherence factor effects. In Chapter 3, we apply this framework to analyze the recent scanning tunneling experiments on an underdoped cuprate superconductor calcium sodium oxychloride by T. Hanaguri et al. (60). In Chapter 4, we
propose a model for nodal quasiparticle scattering in a disordered vortex lattice.
Recently, scanning tunneling studies of a Kondo lattice material U Ru2S i2 became possible (117). If it proves possible to apply scanning tunneling spectroscopy to Kondo lattice materials, then remarkable new opportunities in the ongoing investigation may emerge.
In Chapter 5, we examine the effect of co-tunneling to develop a theory of tunneling into a Kondo lattice. We find that the interference between the direct tunneling and the co-tunneling channels leads to a novel asymmetric lineshape, which has two peaks and a gap. The presence of the peaks suggests that the interference is more dramatic in the case of Kondo lattice than in the single impurity case, because of the coherence. These features should be observed in future tunneling experiments on Kondo lattice materials.Ph.D.Includes bibliographical references (p. 67-74)by Marianna Maltsev
