BKT transition observed in magnetic and electric properties of YBa${}_2$Cu${}_3$O${}_{7-\delta }$ single crystals

Superconductivity of YBa${}_2$Cu${}_3$O${}_{7-\delta }$ single crystals was investigated in small magnetic fields. In magnetic measurements the superconducting transition for $\mathbf{\text{H}}\mathrm{\parallel }c$ appears 0.4 K higher than for $\mathbf{\text{H}}\mathrm{\perp }c$. In this temperature range superconductivity is two-dimensional and the total thickness of superconducting layers is about 0.83 of the sample thickness, which is a consequence of the occurrence of the quasi-insulating plane in the unit cell of the crystal structure. Resistivity in the $\mathit{\text{ab}}$-plane and along the $\mathit{\text{c}}$-axis was measured simultaneously. In these measurements two-dimensional superconductivity was observed in a temperature range of 0.6-0.8 K with the clear signs of the Berezinskii-Kosterlitz-Touless (BKT) transition which occurs approximately 0.15 K below $T_c$, the mean-field transition temperature.