Heavy fermions: superconductivity and its relationship to quantum criticality

Abstract

Anti-ferromagnetic (AF) heavy-fermion (HF) metals frequently exhibit a quantum critical point (QCP), i.e. a continuous disappearance of AF order at zero temperature as a function of a non-thermal control parameter, like pressure. Commonly, unconventional (d-wave) superconductivity (SC) is observed in the vicinity of such a QCP. In this article, the interplay between quantum criticality and SC in HF metals is discussed. The latter can be well described in the framework of the Kondo lattice (KL) model. After introducing HFs and giving an overview on HF superconductivity, the characteristic energy scales in KL systems are addressed. Subsequently, we concentrate on the isostructural compounds CeCu₂Si₂ and YbRh₂Si₂. CeCu₂Si₂ is a prototypical HF superconductor which shows a QCP of itinerant, i.e. three-dimensional (3D) spin-density-wave (SDW) type. Overdamped, nearly quantum-critical SDW fluctuations are concluded from inelastic-neutron-scattering results to be the driving force for SC (T _c≈ 0.6 K) in this compound. While the QCP in several other Ce-based HF superconductors is presumably of the SDW variety too, it is likely to be of the local, i.e. Kondo destroying type in the pressure-induced superconductor CeRhIn₅. YbRh₂Si₂ has been identified as a prototype HF metal exhibiting such a Kondo breakdown QCP, often named a (T = 0) 4f-orbital selective Mott transition. This compound is not a superconductor at T ˃ 10 mK. Systematically searching for and studying SC near Kondo destroying QCPs may offer a link to unconventional SC in other families of correlated materials, such as the doped Mott insulators in the high-T _c cuprates and some of the organic charge-transfer salts.

Keywords:

• heavy fermions
• quantum criticality
• superconductivity

Acknowledgements

I am very grateful to Y. Chen, chairman of the 2012 Fudan Summer School for Condensed Matter Physics, for stimulating discussions and his encouragement to draft this manuscript as well as Q. Si, P. Coleman, M. Brando, S. Friedemann, C. Geibel, S. Kirchner, H. Pfau, A. Pikul, O. Stockert, U. Stockert, P. Sun, S. Wirth and H.Q. Yuan for numerous valuable conversations. Part of this work was supported by the Deutsche Forschungsgemeinschaft through FOR 960 “Quantum Phase Transitions”.