Intertwined vestigial order in quantum materials: Nematicity and beyond

Rafael M. Fernandes, Peter P. Orth, Jörg Schmalian

Research output: Contribution to journalReview articlepeer-review

107 Scopus citations


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 languageEnglish (US)
Pages (from-to)133-154
Number of pages22
JournalAnnual Review of Condensed Matter Physics
Issue number1
StatePublished - Mar 10 2019

Bibliographical note

Publisher Copyright:
© 2019 by Annual Reviews.


  • Composite order
  • Electronic liquid-crystalline phases
  • Frustrated magnetism
  • Intertwined phases
  • Strongly correlated electronic systems
  • Unconventional superconductivity


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