Disappearance of Hall resistance in one-unit-cell-thick ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$: Evidence of free vortex-antivortex excitation

Diagonal and Hall resistivities (${\mathrm{\rho }}_{\mathrm{\infty }}$ and ${\mathrm{\rho }}_{\mathit{x}\mathit{y}}$) in the normal and superconducting states are studied in one-unit-cell-thick ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ artificial materials. A number of transport properties in bulk ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ are shown to be inherent properties of the individual conducting ${\mathrm{CuO}}_2$ bilayer. Evidence of Kosterlitz-Thouless resistive transition as well as the excitation of free vortex and antivortex are presented.