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Correlated quantum matters are rife with multiple symmetry-broken phases that can be tuned using different perturbations, leading to a rich phase diagram. First, I will introduce the strong correlation regime of the standard tJ model in which different translational symmetry broken states are stabilized. Here unidirectional bond density wave states coexisting with charge and pairing modulations can have lower energy than the uniform superconducting (SC) state over an extensive doping range. The finite momentum orders melt upon increasing doping to a vestigial nematic order which only breaks the rotational symmetry of the system. The pairing modulations from such model calculations can arise from a simple coexistence of SC with charge density wave (CDW) order. Furthermore, it can also indicate the presence of exotic pair-density wave states. I provide a few predictions from the Josephson junction setup that distinguishes between the simple coexistence of orders and the presence of pair density wave states. However, such hybrid metal-SC configurations are often prone to superconducting proximity effects. Therefore, I explore the proximity effects of charge density wave on metal using the attractive Hubbard model. The periodic charge modulations develop in a metal due to the tunneling of finite momentum particle-hole pairs from the CDW region, leading to a CDW proximity effect similar to superconductivity. |