Quantum Phase Transitions of Antiferromagnets and the Cuprate Superconductors

Elastocaloric determination of the phase diagram of Sr2RuO4

One of the main developments in unconventional superconductivity in the past two decades has been the discovery that most unconventional superconductors form phase diagrams that also contain other strongly correlated states. Many systems of interest are therefore close to more than one instability, and tuning between the resultant ordered phases is the subject of intense research¹. In recent years, uniaxial pressure applied using piezoelectric-based devices has been shown to be a particularly versatile new method of tuning^2,3, leading to experiments that have advanced our understanding of the fascinating unconventional superconductor Sr₂RuO₄ (refs. ^4–9). Here we map out its phase diagram using high-precision measurements of the elastocaloric effect in what we believe to be the first such study including both the normal and the superconducting states. We observe a strong entropy quench on entering the superconducting state, in excellent agreement with a model calculation for pairing at the Van Hove point, and obtain a quantitative estimate of the entropy change associated with entry to a magnetic state that is observed in proximity to the superconductivity. The phase diagram is intriguing both for its similarity to those seen in other families of unconventional superconductors and for extra features unique, so far, to Sr₂RuO₄.

The phase diagram of the unconventional superconductor Sr₂RuO₄ in both normal and superconducting states is mapped out using high-precision measurements of the elastocaloric effect, showing similarities to other unconventional superconductors as well as unique features.

Emergent gauge fields and the high-temperature superconductors

The quantum entanglement of many states of matter can be represented by electric and magnetic fields, much like those found in Maxwell's theory. These fields 'emerge' from the quantum structure of the many-electron state, rather than being fundamental degrees of freedom of the vacuum. I review basic aspects of the theory of emergent gauge fields in insulators in an intuitive manner. In metals, Fermi liquid (FL) theory relies on adiabatic continuity from the free electron state, and its central consequence is the existence of long-lived electron-like quasi-particles around a Fermi surface enclosing a volume determined by the total density of electrons, via the Luttinger theorem. However, long-range entanglement and emergent gauge fields can also be present in metals. I focus on the 'fractionalized Fermi liquid' (FL*) state, which also has long-lived electron-like quasi-particles around a Fermi surface; however, the Luttinger theorem on the Fermi volume is violated, and this requires the presence of emergent gauge fields, and the associated loss of adiabatic continuity with the free electron state. Finally, I present a brief survey of some recent experiments in the hole-doped cuprate superconductors, and interpret the properties of the pseudogap regime in the framework of the FL* theory.This article is part of the themed issue 'Unifying physics and technology in light of Maxwell's equations'.

How many quantum phase transitions exist inside the superconducting dome of the iron pnictides?

Recent experiments on two iron-pnictide families suggest the existence of a single quantum phase transition inside the superconducting dome despite the fact that two separate transition lines--magnetic and nematic-cross the superconducting dome at T(c). Here we argue that these two observations are actually consistent. We show, using a microscopic model, that each order coexists with superconductivity for a wide range of parameters, and both transition lines continue into the superconducting dome below T(c). However, at some T(merge)<T(c), the two transitions merge and continue down to T=0 as a single simultaneous first-order nematic-magnetic transition. We show that superconductivity has a profound effect on the character of this first-order transition, rendering it weakly first order and allowing strong fluctuations to exist near the quantum phase transition.