Study of Fluctuation Induced Conductivity and Pseudogap State in Single Grain GdBa₂Cu₃O_7−δ Superconductor in Presence of External Magnetic Field

In high-temperature superconductors (HTSCs), the appearance of superconducting fluctuations beyond the critical temperature (T_c) gives rise to the precursor effect of the occurrence of phase coherence even in the normal state, sometimes far from T_c. It is believed that the presence of Cooper pairs above T_c and their interactions with the normal state electrons are the primary cause of appearance of fluctuations in the sample. In earlier studies, it has been found that due to fluctuations present in HTSCs, heat capacity, conductivity, and diamagnetic susceptibility eventually enhance in the vicinity of T_c because of their high temperature, short coherence length, low density of carriers and anisotropic structures. Among various HTSCs, YBa₂Cu₃O_7−δ (YBCO) is the most studied and promising system both in scientific and technological aspects because of its high superconducting transition (T_c=92 K) with a high upper critical field (H_c2≈150 T at 0 K) as well as high critical current density (J_c≈0.33×10⁶ A-cm^-2 at 77 K ). In our study, we have chosen magnetically ordered rare earth element Gd³⁺ having moment, μ_eff=7.97 μ_B in place of Y³⁺. Though Gd has antiferromagnetic ordering at low temperature (T_N=2.24 K), still superconductivity arises in GdBa₂Cu₃O_7−δ(GdBCO) sample above the boiling point of liquid nitrogen. But, it is believed that magnetic ions have a negative impact on superconductivity. The contribution of localized magnetic moments of Gd³⁺ ion also produces tilted magnetic hysteresis loop which eventually affects the critical current density. Despite of its exceptional nature, no analysis of fluctuation conductivity and pseudogap behavior of GdBCO have been studied in the framework of existing theories. Based on the theory proposed by Aslamazov and Larkin, we have studied the fluctuation phenomenon in single grain GdBCO superconductor close to the superconducting mean field transition temperature (T^mf_c ) in the presence of external magnetic field. It is observed that the fluctuations in GdBCO, near T^mf_c (in the critical field region), are beyond 3D-XY-E scaling for both zero and finite fields, indicating weakly first-order transition from normal to superconducting state. Local pairs model suggests that at T=T′>T^mf_c (T′ is the temperature below which the metallic slope in the resistivity deviates), strongly coupled bosons (SCBs) obeying Bose-Einstein Condensation (BEC) theory, are first formed in the sample. However, as the temperature approaches towards T^mf_c, they will evolve into the fluctuating Cooper pairs (FCPs) obeying BCS theory. So, in the temperature limit T^mf_c<T< T′ there is a transformation from BEC to BCS phase. In GdBCO superconductor, we have investigated the complete evolution process of BEC to BCS phase meticulously in the presence of external magnetic field. From the temperature dependent study of the pseudogap parameter, it is found that the transformation from BEC to BCS phase is not abrupt in the sample. Initially at T=T′, the SCBs are formed and remain in the sample upto T=T_pair. Here, T_pair is the temperature where pseudogap parameter is maximized. Thereafter, in the range T_2D−SW<T<T_pair (T_2D−SW is the intersecting temperature between 2D fluctuation and Short-Wave region), the SCBs still exist but the number decreases rapidly because some of them initiate to pair up. Further decreasing the temperature at T<T_2D−SW, all the SCBs completely transform into weakly bounded and tightly overlapped FCPs and start to follow the classical fluctuation theories. The values of T_pair obtained from temperature dependent study of pseudogap parameter decrease when the 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.