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We study the physical property of pair density wave (PDW) and fluctuatingPDW, and use it to build an effective theory of the strongly interactingpseudogap phase in cuprate high temperature superconductors. In Chapter2, westudy how Fulde-Ferrell state, the simplest form of PDW, responds to incidentlight. The collective motion of the condensate plays a key role; gaugeinvariance guides us to the correct result. From Chapter 3 to Chapter 7, weconstruct a pseudogap metallic state by considering quantum fluctuating PDW. Weanalyze a recent scanning tunneling microscope (STM) discovery of period-8density waves in the vortex halo of the d-wave superconductor. We put it in thecontext of the broader pseudogap phenomenology, and compare the experimentalresults with various PDW-driven models and a charge density wave (CDW) drivenmodel. We propose experiments to distinguish these different models. We presentthe Bogoliubov bands of PDW. We discuss fluctuating PDW from the generalperspective of fluctuating superconductivity. We discuss how Bogoliubov bandsevolve when the superconducting order parameter is fluctuating. We comparetheoretical predictions with existing experiments on angle-resolvedphotoemission spectroscopy (ARPES), infrared conductivity, diamagnetism, andlattice symmetry breaking. The material presented here is based onRef.[38,40,41].

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