Intertwined vestigial order in quantum materials: Nematicity and beyond

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

Research output: Contribution to journalReview articlepeer-review

47 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

Funding Information:
We thank C. Batista, E. Berg, P. Chandra, G.W. Chern, A. Chubukov, M. Christensen, P. Coleman, I. Eremin, R. Flint, E. Fradkin, M. Hecker, B. Jeevanesan, J. Kang, S. Kivelson, I. Mazin, J. Venderbos, and X. Wang for fruitful discussions and collaborations on topics reviewed in this work. R.M.F. is supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under Award DE-SC0012336. P.P.O. acknowledges support from Iowa State University Startup Funds. J.S. is supported by the Helmholtz Program Science and Technology of Nanosystems at the Karlsruhe Institute of Technology (KIT) and was funded in part by the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4302.


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

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