Thermodynamics of phase formation in the quantum critical metal Sr ₃ Ru ₂ O ₇

Abstract

The behavior of matter near zero temperature continuous phase transitions, or "quantum critical points" is a central topic of study in condensed matter physics. In fermionic systems, fundamental questions remain unanswered: the nature of the quantum critical regime is unclear because of the apparent breakdown of the concept of the quasiparticle, a cornerstone of existing theories of strongly interacting metals. Even less is known experimentally about the formation of ordered phases from such a quantum critical "soup." Here, we report a study of the specific heat across the phase diagram of the model system Sr 3 Ru 2 O 7 , which features an anomalous phase whose transport properties are consistent with those of an electronic nematic. We show that this phase, which exists at low temperatures in a narrow range of magnetic fields, forms directly from a quantum critical state, and contains more entropy than mean-field calculations predict. Our results suggest that this extra entropy is due to remnant degrees of freedom from the highly entropic state above T c . The associated quantum critical point, which is "concealed" by the nematic phase, separates two Fermi liquids, neither of which has an identifiable spontaneously broken symmetry, but which likely differ in the topology of their Fermi surfaces.heavy Fermion behavior | nematic metal O ne of the most striking empirical facts about quantum criticality is that, in systems with low disorder, the approach to quantum critical points (QCPs) is often cut off by the formation of new broken symmetry phases. Although this phase formation is widely discussed (1-4), thermodynamic data probing how it occurs are surprisingly sparse. The properties of a low temperature ordered phase are usually linked to those of the metal from which it condenses. Many states form from the background of well understood Fermi liquids, so investigations of the metal are used to gain insight into the properties of the ordered phase. For example, the existence of sharply defined quasiparticles in a simple (Fermi liquid) metal implies the well known "Cooper instability" that leads to the formation of a low temperature superconducting state, and the spectrum of phonons and/or magnetic excitations determines the structure of the gap function in that state. The case of phase formation from a quantum critical background is more challenging and possibly richer, because the metal itself is so mysterious; understanding the thermodynamics of phase formation might yield insight into the quantum critical metal as well as the ordered phase.In-depth studies of the specific heat are difficult in prototypical quantum critical superconductors such as CeIn 3 and CePd 2 Si 2 because of the need to work in pressure cells. Both constructing measurement apparatus suited to the high pressure environment and subtracting the huge addenda background due to the pressure cell are challenging experimental problems that have not yet fully been solved. In this paper we give a concrete example in which the material can be tuned ...

Fermi surface instabilities at finite temperature

“…By combining a mean-field analysis with the Pomeranchuk stability analysis developed in the present paper we reproduced many features of the experimentally observed phase diagram 37 .…”

“…Finally, we have applied our method to a d-wave interaction function in the square lattice, which has been proposed to describe nematic Fermi liquids 31,36,37,41 . By combining a mean-field analysis with the Pomeranchuk stability analysis developed in the present paper we reproduced many features of the experimentally observed phase diagram 37 .…”

“…This kind of interaction has been proposed to describe nematic Fermi liquids 31 and shown to be relevant in the discussion of the reentrant behavior manifested in ultra-clean samples of Sr 3 Ru 2 O 7 at low temperatures 36,37 . There, as the external magnetic field is increased, the compound goes from an isotropic Fermi liquid phase to a nematic one, and then back to the isotropic phase.…”

Cascade of phase transitions in the vicinity of a quantum critical point

“…Approaching the complexity of the cuprates from the perspective of this universal singularity, we provide an extensive study of a single antiferromagnetic two-dimensional quantum critical point (QCP). Proximity to quantum phase transitions 19,20 is generally believed important to explain the intriguing behavior of high-T c cuprates 2,3,21 , heavy fermions 22 , or doped ferromagnets 23 . Our study unveils that this QCP triggers a cascade of phase transitions with symmetries different from those of the parent transition.…”

Equivalence of Single-Particle and Transport Lifetimes from Hybridization Fluctuations

“…The most well-known example is perhaps the linear-T resistivity observed in the cuprates in their normal phase [3,4]. Strikingly, the same behavior is found close to a metamagnetic phase transition in Sr 3 Ru 2 O 7 [5]. While in heavy fermion metals the behavior is sometimes sub-linear in T [6] and sometimes quasi-linear [7], there is now a large body of experimental data that establishes the universality of the observation of anomalous exponents [8].…”