Vortex state microwave resistivity in cuprates

The microwave response of high-Tc superconductors yielded information, among the others, on the symmetry of the order parameter and on the temperature dependence of the superfluid fraction (via the measurement of the temperature dependence of the London penetration depth [1]). In the mixed state, most of the attention focussed on the motion of flux lines, with estimates of vortex parameters such as the vortex viscosity and depinning frequency [2]. While the determination of the field dependences of the superfluid and normal fluid could give important information on the electronic structure of the superconducting state, a very few reports dealt with them [3] due to the unavoidable vortex motion contribution. Aim of this work is to determine the field dependent superfluid fraction ns(T,B) from the data of the microwave complex resistivity. With the preliminary identification of the vortex motion contribution, we find that in various cuprate superconductors ns(T,B)=ns(T,0)-AB1/2 up to temperatures T ¡Ö 0.98 Tc. This finding is common to YBa2Cu3O7-d, SmBa2Cu3O7-d and Bi2Sr2CaCu2O8+x, and it can be interpreted by a d-wave pairing (or, at least, a pairing with lines of nodes in the gap) persisting up to high temperatures. We have measured the complex resistivity at 48 GHz in several highly oriented cuprate superconducting thin films, grown by different sputtering techniques [4] on substrates suitable for microwave measurements. Qfactor and frequency shift measurements of a resonant cavity with the superconducting film placed in the end-wall configuration yielded the (a,b) plane complex resitivity r(T,B)=r1(T,B)+ir2(T,B)$, for temperatures from 65 K to Tc and magnetic fields up to 0.8 T (applied along the c axis). The field dependence of r is found to comprise a substantial {sublinear} contribution in almost the full temperature range explored (in the Figure we report a typical measurement taken in SmBa2Cu3O7-d at a single temperature). This is at odds with simple flux motion [5], where r1(T,B)-r1(T,B=0) is proportional to B with no flux creep, while flux creep would change the field dependence to a superlinear one[6]. We identify the vortex motion contribution with the linear term alone: this yields absolute values of vortex viscosities that compare well with published data. We then evaluate the superfluid field dependent conductivity ssf = ns(T,B)/ m0wl02 by subtracting the vortex motion contribution from the measured complex resistivity and inverting the data. The resulting field dependence of ssf is linear with B1/2 in all samples investigated, as reported in the Figure. This is in agreement with the predictions for a superconductor with lines of nodes in the gap[7]. Moreover, the extension of the B1/2 dependence in nearly the full temperature range explored (T> 65 K) and up to temperatures close to Tc indicates that such pairing is not smeared out by the high operating temperatures.