Electronic inhomogeneity in a Kondo lattice

Abstract

Inhomogeneous electronic states resulting from entangled spin, charge, and lattice degrees of freedom are hallmarks of strongly correlated electron materials; such behavior has been observed in many classes of d-electron materials, including the high-T c copperoxide superconductors, manganites, and most recently the ironpnictide superconductors. The complexity generated by competing phases in these materials constitutes a considerable theoretical challenge-one that still defies a complete description. Here, we report a manifestation of electronic inhomogeneity in a strongly correlated f-electron system, using CeCoIn 5 as an example. A thermodynamic analysis of its superconductivity, combined with nuclear quadrupole resonance measurements, shows that nonmagnetic impurities (Y, La, Yb, Th, Hg, and Sn) locally suppress unconventional superconductivity, generating an inhomogeneous electronic "Swiss cheese" due to disrupted periodicity of the Kondo lattice. Our analysis may be generalized to include related systems, suggesting that electronic inhomogeneity should be considered broadly in Kondo lattice materials.Kondo effect | heavy fermion E lectronic inhomogeneity is commonplace in materials in which strong correlations among electrons produce electronic states that compete with one another on multiple length scales (1). One early indication of such heterogeneity came from studies of the high-T c cuprate superconductors in which nonmagnetic Zn impurities were introduced into the CuO 2 planes of YBa 2 Cu 3 O 6þx (YBCO) and La 2-x Sr x CuO 4 ðLSCOÞ 2 ; the anomalous suppression of the superfluid density of the superconducting condensate was explained within a Swiss cheese model comprised of normal regions around the impurity that healed over a (short) coherence length of order 20 Å within a superconducting matrix (2), later verified by scanning tunneling spectroscopy (3). Not only is superconductivity locally suppressed in the Swiss cheese regions, but new electronic states emerge, such as impurity resonances and other exotic forms of electronic inhomogeneity (e.g., "stripe" and "checkerboard" phases) observed in cuprates and also in other d-electron materials (e.g., manganites) (1, 4). In contrast, electronic inhomogeneity has rarely been considered in the prototypical correlated system: f -electron materials (5) in which itinerant heavy quasiparticles emerge at low temperature due to a periodic lattice of Kondo ions. In this work, we investigate the underlying electronic structure of the Kondo lattice compound CeCoIn 5 whose heavy quasiparticles pair to create a d-wave superconducting state below 2.3 K (6). As will be discussed, the superconductivity itself serves as a mirror that reflects the presence of electronic inhomogeneity. A thermodynamic analysis of high-purity single crystals of CeCoIn 5 , doped with different impurities (Y 3þ , La 3þ , Yb 2þ , Th 4þ , Hg, and Sn), reveals that lattice sites filled by these impurities create "Kondo holes" (7, 8) that produce a nonsuperconducting component within the superc...

Fermi-surface evolution in Yb-substituted CeCoIn5

“…Some ideas on possible cluster formations of strongly correlated Yb impurities have been suggested in order to explain the robust Kondo state and the different evolution of the physical properties of Yb doping versus La doping in CeCoIn 5 . 26,46 These seem to suggest that the Kondo holes around Yb dopants do not lead to strong additional scattering, which, for example, is the case for La doping. 47 Such an ansatz would allow us to reconcile with the low effective masses and well-resolved dHvA signals in the Yb-rich materials proving their well-ordered crystalline structure.…”

“…19 Besides pressure and magnetic field, substitutional changes on the different lattice sites in CeCoIn 5 have served as useful tuning parameters for the study of the quantum-critical behavior. 4,[20][21][22][23][24][25][26] For example, an analysis of the entropy change between the normal and superconducting state combined with nuclear quadrupolar resonance seems to indicate that superconductivity is destroyed locally around the dopant center for substitutions on both the rare-earth as well as the indium site. 26 Moreover, the substitution on the rare-earth site has been found to influence the Kondo-lattice coherence and Cooper pairing in a rapid and uniform way.…”

“…4,[20][21][22][23][24][25][26] For example, an analysis of the entropy change between the normal and superconducting state combined with nuclear quadrupolar resonance seems to indicate that superconductivity is destroyed locally around the dopant center for substitutions on both the rare-earth as well as the indium site. 26 Moreover, the substitution on the rare-earth site has been found to influence the Kondo-lattice coherence and Cooper pairing in a rapid and uniform way. 20 Yb substitution, however, shows a different behavior 4,24,25 in that T c and the Kondo-coherence temperature do not scale, in contrast to other heavy-fermion compounds.…”

Non-Fermi liquid regimes with and without quantum criticality in Ce 1− x Yb x CoIn 5

“…An intriguing candidate is the alloy Yb-doped CeCoIn 5 that exhibits an unconventional T − x phase diagram without an apparent QCP, whereas the onset of coherence in the Kondo lattice and the superconducting transition temperature T c are only weakly dependent on Yb concentration and prevail for doping up to x = 0:65 (15). However, the presence of a QCP in the parent CeCoIn 5 compound and the logarithmic temperature dependence of the normal state Sommerfeld coefficient in lightly doped Ce 1−x Yb x CoIn 5 crystals (16) show that this system is in the vicinity to a QCP. Therefore, we are presented with the remarkable opportunity to elucidate the nature of the NFL behavior and unconventional SC in such a system, to search for possible QCPs, and to determine the specific role the QCP plays in defining the low-temperature properties of this material and, in particular, to determine the degree to which quantum criticality and SC are coupled to each other.…”

Holes in a Kondo lattice

“…A lesson from the work of Hamidian et al (4) is that nanoscale electronic heterogeneity may be far more prevalent than often assumed and may have many unexpected consequences (10). Although the mechanism of heterogeneity induced by a Kondo-hole may be specific to nonmagnetic impurities in a Kondo lattice, scanning tunneling spectroscopy of the much-studied copper oxide high-temperature superconductors reveals real-space patches of electronic inhomogeneity (11), similar to what is seen in Th-doped URu 2 Si 2 .…”