Temperature dependences of the surface resistance and the diamagnetic shielding susceptibility at Tc-T≪Tc for high-Tc superconductors

At T_c-T≪≪T_c (i.e., near T_c), in order to demonstrate the conduction mechanism and temperature dependencies of the diamagnetic-shielding susceptibility and the penetration depth, we fabricated Ba_1-xK_xBiO ₃ (BKBO) thin films and measured the energy gap by tunnel effect and shielding susceptibilities which are compared with those measured for BKBO and YBCO single crystals. The shielding susceptibilities for BKBO and YBCO crystals well-fit χ(T)/χ(0)=1-exp(-2Δ(T)/k_BT), while that for the BKBO film follows χ(T)/χ(0)=(1-T/T_c) which may not be intrinsic. The exponential decrease of the susceptibilities near T_c indicates that the conduction mechanism is hopping. The energy gaps are observed as 2Δ(0)=(3.5±0.1)k_BT_c for the BKBO film by the tunnel effect, 2Δ(0)=(3.9±0.1)k_BT_c for the BKBO single crystal, and 2Δ(0)=(8±0.2)k_BT_c for the YBa₂Cu₃O₇ single crystal. Furthermore, for microwave device applications of superconductors, at T _c-T≪T_c, the surface resistance R_s(T)≈√(ωμ₀/(2))/(σ_n +(σ_s(0)-σ_n)f(T)) is derived from the surface impedance at ωτ_tr≪, where σ _s(0) and σ_n are the conductivities of the superconducting state and the normal state, respectively, and f(T)=χ(T)/χ(0)=(1-exp(-2Δ(T)/k_BT))