Vestigial electronic orders in quantum materials
A hallmark of the phase diagrams of quantum materials is the existence of multiple electronic ordered states. In many cases, they cannot be simply described as independent competing phases, but instead display a complex intertwinement. In this talk, I will present a framework to describe intertwined phases in terms of a primary and a vestigial phase. While the former is characterized by a multi-component order parameter, the fluctuation-driven vestigial state is characterized by a composite order parameter formed by higher-order, symmetry-breaking combinations of the primary order parameter. Exotic electronic states with scalar and vector chiral order, spin-nematic order, Potts-nematic order, time-reversal symmetry-breaking order, and charge 4e superconductivity emerge from this simple underlying principle. I will present a rich variety of possible phase diagrams involving the primary and vestigial orders, and discuss possible realizations of these exotic composite orders in different quantum materials, such as high-temperature superconductors and twisted moiré systems.