Broken time-reversal symmetry in cuprate superconductors: The nonreciprocal polar Kerr effect

We report measurements of the nonreciprocal polar Kerr ellipticity (NPKE) in cuprate superconductors which exclude the reciprocal portion of the effect. The new technique is discussed in detail, including the exclusion of the reciprocal effects, suppression of surface-roughness effects, and the effects of the laser spot profile on the domain averaging. The present results for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ films on ${\mathrm{SrTiO}}_3$ substrates show a standard deviation of ∼150 μrad for the NPKE signal, with a spot size of ∼20 μm, for T∼100 K. This value is comparable to that which we reported previously, using a technique that responded to the full PKE signal (nonreciprocal plus reciprocal). A film of superconducting ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_4$ shows no observable effect, consistent with a model due to Dzyaloshinskii, which also predicts the zero Faraday rotation observed by Spielman et al. Furthermore, as expected, a film with a high a-axis content (b-c twins) shows zero NPKE. Due to the excellent rejection of reciprocal effects in this technique, it is possible to use it to study ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ films on ${\mathrm{LaAlO}}_3$. These films, with excellent superconducting qualities, show no NPKE signal, possibly due to a smaller average domain size. We speculate that some microstructural property characteristic of films on ${\mathrm{LaAlO}}_3$ might be responsible for limiting the chiral domain size and thus reducing the NPKE signal.