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.