Superconductivity and quantum criticality in the heavy-fermion system β-YbAlB4

A long-standing question in the field of superconductivity is whether pairing of electrons can arise in some cases as a result of magnetic interactions instead of electron-phonon-induced interactions as in the conventional Bardeen-Cooper-Schrie V er theory(1). A major challenge to the idea of magnetically mediated superconductivity has been the dramatically different behaviour of the cerium and ytterbium heavy-fermion compounds. The cerium-based systems are often found to be superconducting(1-6), in keeping with a magnetic pairing scenario, but corresponding ytterbium systems, or hole analogues of the cerium systems, are not. Despite searches over two decades there has been no evidence of heavy-fermion superconductivity in an ytterbium system, casting doubt on our understanding of the electron-hole parallelism between the cerium and the ytterbium compounds. Here we present the first empirical evidence that superconductivity is indeed possible in an ytterbium-based heavy-fermion system. In particular, we observe a superconducting transition at T-c = 80mK in high-purity single crystals of YbAlB4 in the new structural beta phase(7). We also observe a novel type of non-Fermi-liquid state above T c that arises without chemical doping, in zero applied magnetic field and at ambient pressure, establishing beta-YbAlB4 as a unique system showing quantum criticality without external tuning.