Intertwined vestigial order in quantum materials: nematicity and beyond

TL;DR

This paper reviews the concept of intertwined vestigial orders in quantum materials, focusing on a group-theoretical framework that classifies various emergent phases like nematicity and chiral orders based on symmetry principles.

Contribution

It introduces a comprehensive symmetry-based classification scheme for vestigial orders in unconventional superconductors and density-waves, extending the understanding of intertwined phases beyond specific microscopic models.

Findings

Classifies multiple vestigial orders using group theory.

Provides a unified framework for understanding complex quantum phases.

Connects various orders to a common symmetry principle.

Abstract

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.