Superconductivity was recently observed in iron-arsenic-based compounds with a superconducting transition temperature (T(c)) as high as 56 K, naturally raising comparisons with the high-T(c) copper oxides. The copper oxides have layered crystal structures with quasi-two-dimensional electronic properties, which led to speculation that reduced dimensionality (that is, extreme anisotropy) is a necessary prerequisite for superconductivity at temperatures above 40 K (refs 8, 9). Early work on the iron-arsenic compounds seemed to support this view. Here we report measurements of the electrical resistivity in single crystals of (Ba,K)Fe(2)As(2) in a magnetic field up to 60 T. We find that the superconducting properties are in fact quite isotropic, being rather independent of the direction of the applied magnetic fields at low temperature. Such behaviour is strikingly different from all previously known layered superconductors, and indicates that reduced dimensionality in these compounds is not a prerequisite for 'high-temperature' superconductivity. We suggest that this situation arises because of the underlying electronic structure of the iron-arsenic compounds, which appears to be much more three dimensional than that of the copper oxides. Extrapolations of low-field single-crystal data incorrectly suggest a high anisotropy and a greatly exaggerated zero-temperature upper critical field.

With only a few exceptions that are well understood, conventional superconductivity does not coexist with long-range magnetic order (for example, ref. 1). Unconventional superconductivity, on the other hand, develops near a phase boundary separating magnetically ordered and magnetically disordered phases. A maximum in the superconducting transition temperature T(c) develops where this boundary extrapolates to zero Kelvin, suggesting that fluctuations associated with this magnetic quantum-critical point are essential for unconventional superconductivity. Invariably, though, unconventional superconductivity masks the magnetic phase boundary when T < T(c), preventing proof of a magnetic quantum-critical point. Here we report specific-heat measurements of the pressure-tuned unconventional superconductor CeRhIn5 in which we find a line of quantum-phase transitions induced inside the superconducting state by an applied magnetic field. This quantum-critical line separates a phase of coexisting antiferromagnetism and superconductivity from a purely unconventional superconducting phase, and terminates at a quantum tetracritical point where the magnetic field completely suppresses superconductivity. The T --> 0 K magnetic field-pressure phase diagram of CeRhIn5 is well described with a theoretical model developed to explain field-induced magnetism in the high-T(c) copper oxides, but in which a clear delineation of quantum-phase boundaries has not been possible. These experiments establish a common relationship among hidden magnetism, quantum criticality and unconventional superconductivity in copper oxides and heavy-electron systems such as CeRhIn5.

In non-centrosymmetric superconductors, where the crystal structure lacks a centre of inversion, parity is no longer a good quantum number and an electronic antisymmetric spin-orbit coupling (ASOC) is allowed to exist by symmetry. If this ASOC is sufficiently large, it has profound consequences on the superconducting state. For example, it generally leads to a superconducting pairing state which is a mixture of spin-singlet and spin-triplet components. The possibility of such novel pairing states, as well as the potential for observing a variety of unusual behaviors, led to intensive theoretical and experimental investigations. Here we review the experimental and theoretical results for superconducting systems lacking inversion symmetry. Firstly we give a conceptual overview of the key theoretical results. We then review the experimental properties of both strongly and weakly correlated bulk materials, as well as two dimensional systems. Here the focus is on evaluating the effects of ASOC on the superconducting properties and the extent to which there is evidence for singlet-triplet mixing. This is followed by a more detailed overview of theoretical aspects of non-centrosymmetric superconductivity. This includes the effects of the ASOC on the pairing symmetry and the superconducting magnetic response, magneto-electric effects, superconducting finite momentum pairing states, and the potential for non-centrosymmetric superconductors to display topological superconductivity.

We investigate the order parameter of noncentrosymmetric superconductors Li2Pd3B and Li2Pt3B via the behavior of the penetration depth lambda(T). The low-temperature penetration depth shows BCS-like behavior in Li2Pd3B, while in Li2Pt3B it follows a linear temperature dependence. We propose that broken inversion symmetry and the accompanying antisymmetric spin-orbit coupling, which admix spin-singlet and spin-triplet pairing, are responsible for this behavior. The triplet contribution is weak in Li2Pd3B, leading to a wholly open but anisotropic gap. The significantly larger spin-orbit coupling in Li2Pt3B allows the spin-triplet component to be larger in Li2Pt3B, producing line nodes in the energy gap as evidenced by the linear temperature dependence of lambda(T). The experimental data are in quantitative agreement with theory.