On the Microscopic Model for Strange Metal

Abstract

High-temperature superconductors, particularly cuprates, have long intrigued both theoretical and experimental researchers. Despite recent progress in phenomenological explanations, such as the application of the AdS/CMT, the exact physical mechanism underlying high-temperature superconductivity remains elusive. This thesis investigates a physical model of the strange metal phase, a hallmark of high-temperature superconducting systems, with the aim of gaining insights into the nature of high-Tc superconductivity. One key feature of the strange metal phase is its momentum-dependent power law behavior, which deviates from the predictions of conventional Fermi-liquid theory, posing a significant theoretical challenge. Inspired by the work of M. Khodas, et al. on one-dimensional Luttinger liquids[1], which demonstrated momentum-dependent power law, this thesis explores an alternative approach for extending these results to higher dimensions. While the original work relies on techniques such as bosonization, which are difficult to generalize to two-dimensional systems like cuprates, we propose a novel approach utilizing path-integral formalism and the Hubbard-Stratonovichtransformation, serving as ananalog to bosonization in two dimensions. By incorporating a linearization scheme, we successfully reproduce the momentum-dependent power law behavior in one-dimensional systems, validating the robustness of our method. Building on this success, we extend our framework to two-dimensional systems, laying the groundwork for future studies. We anticipate that this generalization will elucidate the momentum-dependent power law behavior in two-dimensional strange metals, advancing our understanding of the mechanisms driving high-temperature superconductivity.