Title: Visualizing nematicity in the pnictides with scanning tunneling spectroscopy
Description: The origin of the nematic phase in the iron-based superconductors is still unknown, and an understanding of its microscopic mechanism could have important implications on the unconventional superconductivity in these materials. This thesis describes a series of experiments using scanning tunneling microscopy (STM) and spectroscopy (STS) to visualize the nematic electronic structure in NaFe1-xCoxAs as a function of energy, temperature, strain, and doping. We first start with background material on the iron-based superconductors and the iron pnictides in particular. We then extensively explore the physical details of NaFe1-xCoxAs which is the main material of study in this thesis. Additional attention is paid to the electronic structure due to its relation to quasiparticle interference (QPI) measurements made with STS. The theoretical underpinnings of STM and STS are then derived as well as further details of QPI. Many of the experiments described in this thesis were performed on a custom-built, low temperature STM which the author helped build.

We describe the design of this system and report on benchmarking tests that were used to characterize the system's performance. Both pristine, undoped NaFeAs and LiFeAs were measured by STM, and we compare and contrast these two materials which come from the same structural family. The electronic local density of states (LDOS) of NaFeAs was measured at various temperatures in all three phases of the material (tetragonal paramagnetic, orthorhombic paramagnetic, and orthorhombic spin density wave (SDW)). The electronic structure in the SDW phase is highly anisotropic. QPI signals in this phase are found to be well-explained by comparison to a joint density of states (JDOS) model using the reconstructed bandstructure fit to angle-resolved photoemission spectroscopy data. The electronic anisotropy is found to persist into the nominally tetragonal phase. This persistence arises from built-in crystallographic strain coupling to high amplitude, unidirectional, antiferroic fluctuations. These fluctuations renormalize the bare Green's function which gives rise to anisotropic scattering.

We then describe the construction of a novel device created for variable-strain STS. Antiphase domains in NaFeAs are visualized and found to change in size as a function of unidirectional strain. These domains are tracked as a function of temperature and found to disappear at exactly the nematic transition temperature proving that this is the temperature at which long-range order is lost. By measuring Co-doped samples, we find that the domains disappear before optimal doping in an underdoped sample with superconducting transition temperature of 18 K. However, the electronic structure remains anisotropic implying that nematic fluctuations persist. These fluctuations are found even in overdoped samples and disappear with superconductivity at heavy doping.