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.
|Original language||English (US)|
|Number of pages||22|
|Journal||Annual Review of Condensed Matter Physics|
|State||Published - Mar 10 2019|
Bibliographical notePublisher Copyright:
© 2019 by Annual Reviews.
- Composite order
- Electronic liquid-crystalline phases
- Frustrated magnetism
- Intertwined phases
- Strongly correlated electronic systems
- Unconventional superconductivity