Intertwined vestigial order in quantum materials: nematicity and beyond
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A hallmark of the phase diagrams of quantum materials is the existence of multiple electronic ordered states, which, in many cases, are not independent competing phases, but instead display a complex intertwinement. In this review, we focus on a particular realization of intertwined orders: a primary phase characterized by a multi-component order parameter and a fluctuation-driven vestigial phase characterized by a composite order parameter. This concept has been widely employed to elucidate nematicity in iron-based and cuprate superconductors. Here we present a group-theoretical framework that extends this notion to a variety of phases, providing a classification of vestigial orders of unconventional superconductors and density waves. Electronic states with scalar and vector chiral order, spin-nematic order, Ising-nematic order, time-reversal symmetry-breaking order, and algebraic vestigial order emerge from one underlying principle. The formalism provides a framework to understand the complexity of quantum materials based on symmetry, largely without resorting to microscopic models.
This is a manuscript of an article published as Fernandes, Rafael M., Peter P. Orth, and Jörg Schmalian. "Intertwined vestigial order in quantum materials: nematicity and beyond." Annual Review of Condensed Matter Physics 10 (2019): 133-154. DOI: 10.1146/annurev-conmatphys-031218-013200.