Type of Thesis
Understanding the behavior of the high-Tc superconductors is among the most important open questions in physics where many conventional field theoretical methods fail due to strong interactions of electrons. Recent advancements in string theory and holographic dualities that map d+1 dimensional quantum field theories in strongly coupled regimes to d+2 dimensional weakly curved classical general relativity proved to be useful for understanding the high-Tc superconductivity behavior. It is shown that the general properties of so-called holographic superconductors of the field theory side can be extracted by investigating the hair of the charged scalar field around the black hole in the Anti-de Sitter background. In this thesis, I numerically construct the gravitational duals of local electrically charged defects, modeled by various spherically symmetric chemical potential profiles in the boundary, when the charged scalar instabilities are presents at finite temperatures, in order to model local holographic superconductivity behavior. My research investigates the behavior of the superconducting order parameter and the critical temperature Tc under the presence of such defects, and compare it with the global holographic superconductors. Also, my research investigates the physics of hovering black holes, which these types of systems are known to include.
Firat, Atakan Hilmi, "Local Holographic Superconductors and Hovering Black Holes" (2019). Undergraduate Honors Theses. 1841.