Superconductivity in heavy fermion compounds

We review the current state of experimental and theoretical investigations of heavy fermion superconductors. We discuss most of the Ce-based compounds like Ce122, Ce115, Ce218 and Ce131 classes and U-based superconductors like UBe_13 and UPd_2Al_3. In the former the emphasis is on the connection to quantum critical phenomena and non-Fermi liquid behaviour. Recent neutron scattering and hydrostatic pressure results on SDW/SC competition in the Ce122 system are included. For the U-compounds we discuss the significance of dual models with both localised and itinerant 5f electrons for mass enhancement and superconducting pair formation. Itinerant spin fluctuation theories for unconventional superconductivity are also reviewed.Comment: 74 pages, 29 figures. For a version of the manuscript including higher-resolution figures, see http://www.cpfs.mpg.de/~thalm/SCMaterials.pd

Multidimensional entropy landscape of quantum criticality

The Third Law of Thermodynamics states that the entropy of any system in equilibrium has to vanish at absolute zero temperature. At nonzero temperatures, on the other hand, matter is expected to accumulate entropy near a quantum critical point (QCP), where it undergoes a continuous transition from one ground state to another. Here, we determine, based on general thermodynamic principles, the spatial-dimensional profile of the entropy S near a QCP and its steepest descent in the corresponding multidimensional stress space. We demonstrate this approach for the canonical quantum critical compound CeCu6-xAux near its onset of antiferromagnetic order. We are able to link the directional stress dependence of S to the previously determined geometry of quantum critical fluctuations. Our demonstration of the multidimensional entropy landscape provides the foundation to understand how quantum criticality nucleates novel phases such as high-temperature superconductivity.Comment: 14 pages, 4 figure

High-temperature signatures of quantum criticality in heavy fermion systems

We propose a new criterion for distinguishing the Hertz-Millis (HM) and the local quantum critical (LQC) mechanism in heavy fermion systems with a magnetic quantum phase transition (QPT). The criterion is based on our finding that the spin screening of Kondo ions can be completely suppressed by the RKKY coupling to the surrounding magnetic ions even without magnetic ordering and that, consequently, the signature of this suppression can be observed in spectroscopic measurements above the magnetic ordering temperature. We apply the criterion to high-resolution photoemission (UPS) measurements on CeCu$_{6-x}$Au$_{x}$ and conclude that the QPT in this system is dominated by the LQC scenario.Comment: Inveted paper, International Conference on Magnetism, ICM 2009, Karlsruhe. Published version, added discussions of the relevance of Fermi-surface fluctuations and of a structural transition near the QC

Echo of the Quantum Phase Transition of CeCu6−x_{6-x}Aux_x in XPS: Breakdown of Kondo Screening

We present an X-ray photoemission study of the heavy-fermion system CeCu$_{6-x}$Au$_x$ across the magnetic quantum phase transition of this compound at temperatures above the single-ion Kondo temperature $T_K$. In dependence of the Au concentration $x$ we observe a sudden change of the $f$-occupation number $n_f$ and the core-hole potential $U_{df}$ at the critical concentration $x_c=0.1$. We interpret these findings in the framework of the single-impurity Anderson model. Our results are in excellent agreement with findings from earlier UPS measurements %\cite{klein08qpt} and provide further information about the precursors of quantum criticality at elevated temperatures.Comment: 5 pages, 3 figures; published version, references updated, minor changes in wordin

Magnetic-field enhanced aniferromagnetism in non-centrosymmetric heavy-fermion superconductor CePt3_3Si

The effect of magnetic field on the static and dynamic spin correlations in the non-centrosymmetric heavy-fermion superconductor CePt$_3$Si was investigated by neutron scattering. The application of a magnetic field B increases the antiferromagnetic (AFM) peak intensity. This increase depends strongly on the field direction: for B${\parallel}$[0 0 1] the intensity increases by a factor of 4.6 at a field of 6.6 T, which corresponds to more than a doubling of the AFM moment, while the moment increases by only 10 % for B${\parallel}$[1 0 0] at 5 T. This is in strong contrast to the inelastic response near the antiferromagnetic ordering vector, where no marked field variations are observed for B${\parallel}$[0 0 1] up to 3.8 T. The results reveal that the AFM state in CePt$_3$Si, which coexists with superconductivity, is distinctly different from other unconventional superconductors.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev.

Time-resolved collapse and revival of the Kondo state near a quantum phase transition

One of the most successful paradigms of many-body physics is the concept of quasiparticles: excitations in strongly interacting matter behaving like weakly interacting particles in free space. Quasiparticles in metals are very robust objects. Yet, when a system's ground state undergoes a qualitative change at a quantum critical point (QCP), the quasiparticles may disintegrate and give way to an exotic quantum-fluid state of matter. The nature of this breakdown is intensely debated, because the emergent quantum fluid dominates the material properties up to high temperature and might even be related to the occurence of superconductivity in some compounds. Here we trace the dynamics of heavy-fermion quasiparticles in CeCu$_{6-x}$Au$_{x}$ and monitor their evolution towards the QCP in time-resolved experiments, supported by many-body calculations. A terahertz pulse disrupts the many-body heavy-fermion state. Under emission of a delayed, phase-coherent terahertz reflex the heavy-fermion state recovers, with a coherence time 100 times longer than typically associated with correlated metals. The quasiparticle weight collapses towards the QCP, yet its formation temperature remains constant -- phenomena believed to be mutually exclusive. Coexistence in the same experiment calls for revisions in our view on quantum criticality.Comment: Published version, including data on CeCu6, CeCu5.9Au0.1, and CeCu5Au1 and extended Supplementary Information. 7 pages, 4 figures, Supplementary Information: 5 pages, 3 figure

Quantum criticality in the cubic heavy-fermion system CeIn_{3-x}Sn_x

We report a comprehensive study of CeIn$_{3-x}$Sn$_x$ $(0.55 \leq x \leq 0.8)$ single crystals close to the antiferromagnetic (AF) quantum critical point (QCP) at $x_c\approx 0.67$ by means of the low-temperature thermal expansion and Gr\"uneisen parameter. This system represents the first example for a {\it cubic} heavy fermion (HF) in which $T_{\rm N}$ can be suppressed {\it continuously} down to T=0. A characteristic sign change of the Gr\"uneisen parameter between the AF and paramagnetic state indicates the accumulation of entropy close to the QCP. The observed quantum critical behavior is compatible with the predictions of the itinerant theory for three-dimensional critical spinfluctuations. This has important implications for the role of the dimensionality in HF QCPs.Comment: Physical Review Letters, to be publishe