Exploring Strongly Interacting Gapless States: Cuprates, Pair Density Waves, and Fluctuating Superconductivity.

We study the physical property of pair density wave (PDW) and fluctuating PDW, and use it to build an effective theory of the strongly interacting pseudogap phase in cuprate high temperature superconductors. In Chapter2, we study how Fulde-Ferrell state, the simplest form of PDW, responds to incident light. The collective motion of the condensate plays a key role; gauge invariance guides us to the correct result. From Chapter 3 to Chapter 7, we construct a pseudogap metallic state by considering quantum fluctuating PDW. We analyze a recent scanning tunneling microscope (STM) discovery of period-8 density waves in the vortex halo of the d-wave superconductor. We put it in the context of the broader pseudogap phenomenology, and compare the experimental results with various PDW-driven models and a charge density wave (CDW) driven model. We propose experiments to distinguish these different models. We present the Bogoliubov bands of PDW. We discuss fluctuating PDW from the general perspective of fluctuating superconductivity. We discuss how Bogoliubov bands evolve when the superconducting order parameter is fluctuating. We compare theoretical predictions with existing experiments on angle-resolved photoemission spectroscopy (ARPES), infrared conductivity, diamagnetism, and lattice symmetry breaking. The material presented here is based on Ref.[38,40,41].