Emergence of superconductivity in heavy-electron materials

Abstract

Although the pairing glue for the attractive quasiparticle interaction responsible for unconventional superconductivity in heavy-electron materials has been identified as the spin fluctuations that arise from their proximity to a magnetic quantum critical point, there has been no model to describe their superconducting transition at temperature T c that is comparable to that found by Bardeen, Cooper, and Schrieffer (BCS) for conventional superconductors, where phonons provide the pairing glue. 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 (1-5), in contrast to conventional superconductors, where phonons provide the pairing glue (6). However, developing a simple physical picture for the behavior of such quantum critical superconductors, including a Bardeen, Cooper, and Schrieffer (BCS)-like expression for their superconducting transition temperature (T c ), has proven difficult. In part, this is because of the unusual normal state from which superconductivity emerges (7-12), and in part it stems from the difficulty in finding a simple model for an effective frequency-dependent attractive quasiparticle interaction that closely resembles that proposed earlier for the cuprates (13-17).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 (18-23). As may be seen in Fig. 1, there are three distinct regions of emergent heavyelectron superconductivity in their pressure-temperature phase diagrams that are defined by a line marking the delocalization cross-over temperature, T L , at which the collective hybridization of the local moments becomes complete and the Néel temperature, T N , that marks the onset of long-range antiferromagnetic order of the hybridized local moments.Region I: T c ≤ T L . Superconductivity emerges from a full...

Quantum critical scaling and superconductivity in heavy electron materials

“…For CeRhIn 5 at p = 2.7 GPa, a pressure that is larger than its experimental value of p L = 2.4 GPa, we see that scaling behavior is found down to a temperature T x ∼ T L , its delocalization temperature, that is calculated to be 5.7 K using T * = 42 K and f 0 (2.7 GPa)=1.24 estimated from other experiments [15]; the loss of scaling below T x must be attributed to the intrinsic Kondo liquid. As may be seen in Fig.…”

“…The phenomenological two-fluid model, which explains so many other aspects of heavy electron behavior [4][5][6][7][8][9][10][11][12], is also key to understanding the remarkable scaling of their dynamic behavior. In it, below T * , the collective hybridization of the Kondo lattice of f -electron local moments with the background conduction electrons gives rise to an itinerant heavy electron Kondo liquid (KL) of strength (or volume fraction), f , that coexists with the hybridized local moment spin liquid, of strength 1 − f , with [5] …”

“…For pressures less than p L , partial quasiparticle localization reduces the number of heavy electrons able to become superconducting and so suppresses T c , while for pressures greater than p L , it is physically appealing to assume that the attractive interaction between heavy electron quasiparticles becomes increasingly less effective [15].…”

Differential conductance and defect states in the heavy-fermion superconductorCeCoIn5

“…CeCoIn 5 1 has long been considered the "hydrogen atom" of heavy fermion superconductivity [2][3][4][5][6][7][8] , and much experimental [9][10][11][12][13][14][15][16][17][18][19] and theoretical effort [20][21][22][23][24][25][26][27] has focused on illuminating its unconventional properties [28][29][30][31][32] , and the microscopic mechanism underlying the emergence of superconductivity. While a variety of experimental probes have reported evidence for the existence of nodes [9][10][11][12] , a sign change of the superconducting (SC) order parameter along the Fermi surface 13,14 , and spinsinglet pairing 11,12 , theoretical efforts [20][21][22][23][24][25][26] to provide a quantitative or even qualitative exp...…”

“…While a variety of experimental probes have reported evidence for the existence of nodes [9][10][11][12] , a sign change of the superconducting (SC) order parameter along the Fermi surface 13,14 , and spinsinglet pairing 11,12 , theoretical efforts [20][21][22][23][24][25][26] to provide a quantitative or even qualitative explanation for the properties of the superconducting state in CeCoIn 5 have been hampered by insufficient insight into the material's complex electronic bandstructure 16 . This situation, however, has recently changed due to a series of groundbreaking scanning tunneling spectroscopy (STS) experiments [33][34][35] which have yielded unprecedented insight into the electronic structure of the superconducting state, providing strong evidence for its unconventional d x 2 −y 2 -wave symmetry.…”