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Fluctuations around an antiferromagnetic quantum critical point (QCP) are believed to lead to unconventional superconductivity and in some cases to high-temperature superconductivity. However, the exact mechanism by which this occurs remains poorly understood. The iron-pnictide superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$ is perhaps the clearest example to date of a high temperature quantum critical superconductor, and so it is a particularly suitable system in which to study how the quantum critical fluctuations affect the superconducting state. Here we show that the proximity of the QCP yields unexpected anomalies in the superconducting critical fields. We find that both the lower and upper critical fields strongly violate the expectations from the conventional theory taking into account the observed mass enhancement near the QCP. These anomalous behaviours of the critical fields imply that the energy of superconducting vortices is enhanced, possibly due to a microscopic mixing of antiferromagnetism and superconductivity, suggesting that a highly unusual vortex state is realised in quantum critical superconductors.
When a second-order magnetic phase transition is tuned to zero temperature by a non-thermal parameter, quantum fluctuations are critically enhanced, often leading to the emergence of unconventional superconductivity. In these `quantum critical superc
Recent high-precision measurements employing different experimental techniques have unveiled an anomalous peak in the doping dependence of the London penetration depth which is accompanied by anomalies in the heat capacity in iron-pnictide supercondu
Upper critical field, H_c2, in quasi-1D superconductors is investigated by the weak coupling renormalization group technique. It is shown that H_c2 greatly exceeds not only the Pauli limit, but also the conventional paramagnetic limit of the Flude-Fe
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The transition temperature Tc of cuprate superconductors falls when the doping p is reduced below a certain optimal value. It is unclear whether this fall is due to strong phase fluctuations or to a decrease in the pairing gap. Different interpretati