Effects of vortex and antivortex excitations in underdoped Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$ bulk single crystals
The observance of vortex and anti-vortex effects in bulk crystals can prove the existence of phase-disordered superconductivity in the bulk. To gain insights into the mechanisms that govern superconducting transition in copper oxide high-transition temperature ($T_c$) superconductors, this study investigated the transport properties of underdoped Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$ (Bi-2223) bulk single crystals.The $I$-$V$ characteristics results and the typical tailing behavior owing to the temperature dependence of in-plane resistivity ($\rho_{ab}$) were consistent with the Kosterlitz-Thouless (KT) transition characteristics. Thus, with increasing temperature, copper oxide high-$T_c$ superconductors transitioned to their normal state owing to destruction of their phase correlations, although a finite Cooper pair density was prevalent at $T_c$. Further, magnetization measurements were performed to determine the temperature dependence of the irreversible magnetic field $B_{irr}$. Consequently, the mechanism governing the KT transition-like superconducting transition in this bulk system was elucidated. These results support the extreme strong-coupling models for high-$T_c$ superconductivity in cuprates.