Magnetic field-dependent study of excess conductivity and pseudogap state of single grain GdBa${}_2$Cu${}_3$O${}_{7-\delta }$ superconductor

Finite probability of creation of Cooper pairs in the normal state near the superconducting transition and their interaction with the remnant electrons cause superconducting fluctuation which eventually increase the conductivity in high-temperature superconductor. Based on the theory proposed by Aslamazov and Larkin, fluctuation phenomenon in GdBa${}_2$Cu${}_3$O${}_{7-\delta }$ superconductor has been studied close to the superconducting mean field transition temperature (T${}_c^{mf}$) in presence of external magnetic field. Weakly first-order transition from normal to superconducting state has been observed as fluctuations near to T${}_c^{mf}$ (in the critical field region) is beyond 3D-XY-E scaling for both zero and finite fields. Following the novel approach of local pairs model, evolution process of fluctuating Cooper pairs (FCPs) obeying BCS theory from strongly coupled bosons (SCBs) which obey Bose-Einstein Condensation (BEC) theory in the temperature limit T${}_c^{mf}$< T < T* (T* is the temperature below which SCBs start to form) has been studied meticulously. The results indicate that pseudogap parameters Δ*(T) shifted towards BCS phase from BEC state with decreasing temperature after exceeding the maximum critical size of the local pairs (28 Å) in the CuO${}_2$ plane. The values of T${}_{pair}$ (at which SCBs initiate to transform into FCPs) obtained from temperature-dependent study of Δ*(T) decreases when magnetic field increases from zero to 4 T. Superconducting gap (Δ(0)) for all magnetic fields calculated from the local pairs model are within the BCS limit but the magnitudes reduce as the field escalates.