Quantum critical scaling and superconductivity in heavy electron materials

Abstract

We use the two fluid model to determine the conditions under which the nuclear spin-lattice lattice relaxation rate, T1, of candidate heavy quantum critical superconductors can exhibit scaling behavior and find that it can occur if and only if their "hidden" quantum critical spin fluctuations give rise to a temperature-independent intrinsic heavy electron spin-lattice relaxation rate. The resulting scaling of T1 with the strength of the heavy electron component and the coherence temperature, T * , provides a simple test for their presence at pressures at which the superconducting transition temperature, Tc, is maximum and is proportional to T * . These findings support the previously noted partial scaling of the spin-lattice relaxation rate with Tc in a number of important heavy electron materials and provide additional evidence that in these materials their optimal superconductivity originates in the quantum critical spin fluctuations associated with a nearby phase transition from partially localized to fully itinerant quasiparticles.PACS numbers: 71.27.+a, 74.70.Tx, 76.60.-k A tantalizing hint that the spin fluctuations seen in the nuclear spin relaxation rate for a number of unconventional superconductors might be the magnetic glue responsible for their superconductivity appears in a scaling relation between that rate and the optimal superconducting transition temperature, T c , that was first noted by Curro et al [1]. In the present communication we focus on understanding this scaling relation for one important member of this family, the heavy electron materials, for which some experimental results are given in Fig. 1 [1, 2]. As may be seen in Fig. 2, finding such a relation appears at first sight highly problematic because the scaling covers a range of temperatures (T c < T < T * ) in the normal state in which both hybridized localized spins and the itinerant heavy electron Kondo liquid contribute to the spin-lattice relaxation rate. However, we find that rigorous Curro T c scaling can become possible if three conditions are met: (1) the maximum in T c occurs at the pressure p L , at which the line marking the boundary between partially localized and fully itinerant behavior for heavy electron quasiparticles, T L , intersects with T c , so that T max c = T L (p L ); (2) at p L the total spin-lattice relaxation rate scales with the coherence temperature, T

Emergence of superconductivity in heavy-electron materials

“…The experiment-based expression proposed here parameterizes the effective frequency-dependent quasiparticle interactions in terms of their unusual normal-state properties; it provides a quantitative explanation of the measured pressure-induced variation in T c in the "hydrogen atoms" of unconventional superconductivity, CeCoIn 5 and CeRhIn 5 , predicts a similar pressure variation for other heavy-electron quantum critical superconductors, and quantifies their variations in T c with a single parameter. To whom correspondence may be addressed.…”

“…In this paper we use these important scaling results to develop a simple BCS-like phenomenological expression for the superconducting transition temperature, show that it explains the variation of T c with pressure for both CeCoIn 5 and CeRhIn 5 , and offer a detailed prediction for a similar dome-like structure in other quantum critical heavy-electron superconductors.…”

“…As discussed in Methods, in the absence of systematic specific heat measurements κ(p) may be determined from experiment by using a two-fluid analysis (7)(8)(9)(10)(11)(12) to obtain the heavy-electron density of states, N F ; the resulting values of κ(p) for CeCoIn 5 and CeRhIn 5 are given in Fig. 2A.…”

“…Here we propose such a model: a phenomenological BCS-like expression for T c in heavy-electron materials that is based on a simple model for the effective range and strength of the spin-fluctuation-induced quasiparticle interaction and reflects the unusual properties of the heavy-electron normal state from which superconductivity emerges. We show that it provides a quantitative understanding of the pressure-induced variation of T c in the "hydrogen atoms" of unconventional superconductivity, CeCoIn 5 and CeRhIn 5 , predicts scaling behavior and a dome-like structure for T c in all heavy-electron quantum critical superconductors, provides unexpected connections between members of this family, and quantifies their variations in T c with a single parameter. B ecause the unconventional superconductivity found in many heavy-electron materials arises at the border of antiferromagnetic long-range order, it is natural to consider the possibility that its physical origin is its proximity to a quantum critical point that marks a transition from localized to itinerant behavior, and that the associated magnetic quantum critical spin fluctuations provide the pairing glue (1)(2)(3)(4)(5), in contrast to conventional superconductors, where phonons provide the pairing glue (6).…”

“…In finding a way to characterize heavy-electron quantum critical superconductivity it is helpful to begin by recalling the principal features of its remarkably similar emergence in two of the best-studied materials, CeCoIn 5 and CeRhIn 5 (18)(19)(20)(21)(22)(23). As may be seen in Fig.…”