Inhomogeneous fluctuating superconductivity in YBa$_2$Cu$_3$O$_y$ and La$_{2-x}$Sr$_x$CuO$_4$ above $T_c$

Abstract. Over the past decade, a diverse set of experiments on high-transition temperature (Tc) cuprate superconductors have produced evidence for the existence of superconducting correlations at temperatures well above the bulk Tc. Included in this group of experimental findings is the discovery of an unusual magnetic-field induced effect in YBa2Cu3Oy and La2−xSrxCuO4 above Tc by transverse-field muon spin rotation (TF-µSR). The TF-µSR measurements show that an externally applied field induces a static internal magnetic field distribution, which persists to remarkably high temperatures above Tc. What is more, the inhomogeneous field distribution above Tc tracks both Tc and the superfluid density below Tc over an extensive hole-doping range. Given that other experiments signify the presence of fluctuating amplitude and/or phase fluctuations of the superconducting order parameter in this region of the phase diagram above Tc, the observed presence of spatially non-uniform static internal fields of this kind is at first glance somewhat surprising. Here the key observations of the TF-µSR experiments are reviewed, and it is explained how the inhomogeneous line broadening above Tc signifies the occurrence of non-uniform fluctuating superconductivity. PACS numbers: 74.25.Ha, 74.81.-g, 76.75.+i2 1.