The study of quantum critical phenomena has attracted considerable attention because of the fascinating physical properties caused by quantum fluctuations. In Ce-based HF compounds, superconductivity, likely paired via magnetic interaction, is generally observed in the vicinity of an antiferromagnetic (AFM) quantum critical point (QCP). However, in the prototype HF superconductor CeCu2Si2 and its isoelectronic compound CeCu2Ge2, superconductivity survives over a very broad pressure regime (about 10 GPa away from the AFM QCP) with an unusual pressure dependence of Tc , which has largely puzzled the community for many years. In this talk, I will review the recent progress on the study of CeCu2Si2. By deliberately reducing the quasiparticle mean free path via partially substituting Si with Ge, two distinct superconducting phases were observed under pressure [3, 4]. Superconductivity in the low-p regime is centered around an AFM QCP, suggesting a uniform picture of magnetically mediated superconductivity in the Ce-based HF systems. The occurrence of superconductivity in the high-p regime is closely associated with a weak first-order valence quantum phase transition [4, 5]. These observations highlight the existence of two different types of pairing mechanisms mediated by spin fluctuations (at low p) and charge/valence fluctuations (at high p) in CeCu2Si2 [4, 5].
The recent discovery of non-centrosymmetric superconductiviy in the HF system CePt3Si  has stimulated a tremendous effort devoted to revealing how the absence of parity symmetry changes the superconducting state. However, superconductivity in CePt3Si is complicated by its HF nature and its coexistence with magnetism. In this talk, I will present our recent results on two closely related cubic compounds Li2Pd3B and Li2Pt3B . These materials lack inversion symmetry and show no evidence of magnetism or heavy fermion behavior, providing us a "model" system to study parity broken superconductivity. Superconductivity in the Pd material is very conventional while it is surprisingly unconventional in the isoelectronic Pt material. These results are best understood as arising from the admixing of spin-singlet and spin-triplet order parameters, which is only allowed when inversion symmetry is broken. The triplet contribution is weak in Li2Pd3B, a BCS-like superconductor with an anisotropic gap. With increased spin-orbit coupling, the spin-triplet component dominates in Li2Pt3B, producing line nodes in the energy gap. Results are supported by the quantitative agreement between experimental penetration depth data and theory.
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