Interplay of heavy fermion quantum criticality and unconventional superconductivity

According to the ‘Quantum Critical Paradigm’, antiferromagnetic (AF) quantum critical points (QCPs) in pristine heavy fermion metals cause emergent unconventional superconductivity (SC). This will be demonstrated for both CeCu₂Si₂ (CCS) and YbRh₂Si₂ (YRS) [M. Smidman et al., Phil. Mag. 98, 2930 (2018)]. CCS exhibits a 3D spin-density-wave QCP and was considered a d-wave superconductor until recently, when its specific heat was found to follow an exponential temperature dependence at low temperatures [S. Kittaka et al., Phys. Rev. Lett. 112, 067002 (2014)]. Based on atomic - substitution, neutron - scattering and penetration - depth results we show that CCS cannot be an (isotropic/anisotropic) s-wave superconductor but is best described by a model for a fully gapped two-band d-wave superconductor [G. M. Pang et al., Proc. Natl. Acad. Sci. USA 115, 5343 (2018); E. N. Nica et al., npj Quantum Materials 2, 24 (2017)]. YRS exhibits a magnetic-field induced partial-Mott AF QCP. For this material, no SC had been detected above 10 mK. However, magnetic and specific-heat measurements performed to about 1 mK revealed HF, i.e., unconventional, SC to develop at T_c = 2 mK. This is ascribed to a competition between nuclear-dominated AF hybrid order and the primary AF order of the 4f-electron spins by which the system is pushed towards its QCP [E. Schuberth et al., Science 351, 485 (2016)]. Our observations support the relevance of the Quantum Critical Paradigm, regardless of the microscopic origin of the AF instability.