Emergent states in heavy-electron materials

Abstract

We obtain the conditions necessary for the emergence of various low-temperature ordered states (local-moment antiferromagnetism, unconventional superconductivity, quantum criticality, and Landau Fermi liquid behavior) in Kondo lattice materials by extending the two-fluid phenomenological theory of heavy-electron behavior to incorporate the concept of hybridization effectiveness. We use this expanded framework to present a new phase diagram and consistent physical explanation and quantitative description of measured emergent behaviors such as the pressure variation of the onset of local-moment antiferromagnetic ordering at T N , the magnitude of the ordered moment, the growth of superconductivity within that ordered state, the location of a quantum critical point, and of a delocalization line in the pressure/temperature phase diagram at which local moments have disappeared and the heavy-electron Fermi surface has grown to its maximum size. We apply our model to CeRhIn 5 and a number of other heavy-electron materials and find good agreement with experiment.heavy fermion | kondo liquid | spin liquid H eavy-electron materials provide a unique f -electron laboratory for the study of the interplay between localized and itinerant behavior. At comparatively high temperatures, itinerancy emerges as the localized f -electrons collectively reduce their entropy by hybridizing with the conduction electrons to form a new state of matter, an itinerant heavy-electron Kondo liquid that displays scaling (non-Landau Fermi liquid) behavior (1-8). The emergent Kondo liquid coexists with the hybridized spin liquid that describes the lattice of local moments whose magnitude has been reduced by hybridization until one reaches the comparatively low temperatures at which unconventional superconductivity and hybridized local-moment antiferromagnetism compete to determine the ground state of the system over a wide regime of pressures. In practice, the phases often coexist, as experiments on the 115 [CeRhIn 5 (9-11) and CeCoIn 5 (12)] and 127 [CePt 2 In 7 (13)] Kondo lattice materials demonstrate. A major challenge for the heavy-electron community has been finding a consistent framework and simple phenomenological description of their measured emergent behaviors that include the pressure variation of the onset of antiferromagnetic ordering at T N , the growth of superconductivity within that ordered state, the onset of quantum critical behavior, and the growth of the heavy-electron Fermi surface.Although progress has been made on developing a phenomenological theory of Kondo lattice materials (6), we do not yet possess a microscopic theory of the emergence of the Kondo liquid as a new quantum state of matter that displays universal behavior below a characteristic temperature (1-3, 5), T Ã , or a satisfactory general framework for characterizing the conditions necessary for the emergence of the competing low-temperature ordered states, because experiments (4) have shown that the seminal phase diagram proposed by Doniach (14) does not apply t...

Universal Knight shift anomaly in the periodic Anderson model

“…Although this latter behavior is not fully understood, it has been proposed that it is associated with the "relocalization" of f -electrons observed in materials like CePt 2 In 7 whose ground states are antiferromagnetic [36]. In these materials, the finite value of K HF at T N suggests that the ordered local moments remain partially screened, emphasizing a continued competition between the heavy-fermion Kondo liquid and a hybridized "spin liquid" with a lattice of local moments associated with f-electrons [18]. Because T * is an approximate measure of the onset of coherence between the itinerant and localized electrons, the twofluid theory argues that the entropy at the crossover temperature T ⋆ approaches ln 2 at this temperature [14].…”

“…T S is lower than T ⋆ in our calculations, because S includes a background contribution from free conduction electrons. In future work we intend to develop ways to isolate the entropy associated with magnetic correlations, and better test predictions [18] that T S ≈ T ⋆ .…”

“…Recent progress has emerged in the context of a twofluid model, in which localized f -electron spins and itinerant conduction electron spins interact with the nuclear spins via two different hyperfine couplings [18,[20][21][22][23].…”

Emergence of superconductivity in heavy-electron materials

“…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)(8)(9)(10)(11)(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)(14)(15)(16)(17).…”

“…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.…”