Interplay between unconventional superconductivity and heavy-fermion quantum criticality: CeCu₂Si₂ versus YbRh₂Si₂

ABSTRACT

In this paper the low-temperature properties of two isostructural canonical heavy-fermion compounds are contrasted with regards to the interplay between antiferromagnetic (AF) quantum criticality and superconductivity. For CeCu₂Si₂, fully-gapped d-wave superconductivity forms in the vicinity of an itinerant three-dimensional heavy-fermion spin-density-wave (SDW) quantum critical point (QCP). Inelastic neutron scattering results highlight that both quantum critical SDW fluctuations as well as Mott-type fluctuations of local magnetic moments contribute to the formation of Cooper pairs in CeCu₂Si₂. In YbRh₂Si₂, superconductivity appears to be suppressed at T ⪆ 10 mK by AF order (T_N = 70 mK). Ultra-low temperature measurements reveal a hybrid order between nuclear and 4f-electronic spins, which is dominated by the Yb-derived nuclear spins, to develop at T_A slightly above 2 mK. The hybrid order turns out to strongly compete with the primary 4f-electronic order and to push the material towards its QCP. Apparently, this paves the way for heavy-fermion superconductivity to form at T_c = 2 mK. Like the pressure – induced QCP in CeRhIn₅, the magnetic field – induced one in YbRh₂Si₂ is of the local Kondo-destroying variety which corresponds to a Mott-type transition at zero temperature. Therefore, these materials form the link between the large family of about fifty low-T unconventional heavy – fermion superconductors and other families of unconventional superconductors with higher T_cs, notably the doped Mott insulators of the cuprates, organic charge-transfer salts and some of the Fe-based superconductors. Our study suggests that heavy-fermion superconductivity near an AF QCP is a robust phenomenon.

KEYWORDS:

• Heavy-fermion metals
• superconductivity
• quantum critical phenomena

Acknowledgments

The authors acknowledge stimulating discussions with Piers Coleman, Philipp Gegenwart, Silke Paschen and Doug Scalapino. M. Smidman, H.Q. Yuan, S. Kirchner, and F. Steglich acknowledge support from the National Key R&D Program of China (Nos. 2016YFA0300202 and 2017YFA0303100). M. Smidman, H.Q. Yuan and F. Steglich acknowledge support from the National Natural Science Foundation of China (Nos. U1632275 and 11474251), and the Science Challenge Project of China (No. TZ2016004). S. Kirchner acknowledges support by the National Natural Science Foundation of China (Nos. 11474250 and 11774307). Work done at the MPI CPfS was partially supported by the German Research Foundation through the DFG Research Unit 960 ‘Quantum Phase Transitions’. Work at Rice University was in part supported by the NSF Grant No. DMR-1611392 and the Robert A. Welch Foundation Grant No. C-1411.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

M. Smidman, H.Q. Yuan, S. Kirchner, and F. Steglich acknowledge support from the National Key R&D Program of China [grant numbers 2016YFA0300202 and 2017YFA0303100]. M. Smidman, H.Q. Yuan and F. Steglich acknowledge support from the National Natural Science Foundation of China [grant numbers U1632275 and 11474251], and the Science Challenge Project of China [grant number TZ2016004]. S. Kirchner acknowledges support by the National Natural Science Foundation of China [grant numbers 11474250 and 11774307]. Work done at the MPI CPfS was partially supported by the German Research Foundation through the DFG Research Unit 960 ‘Quantum Phase Transitions’. Work at Rice University was in part supported by the National Science Foundation (NSF) [grant number DMR-1611392] and the Robert A. Welch Foundation [grant number C-1411].