Absence of a finite-temperature vortex-glass phase transition in two-dimensional ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ films

Nonlinear current-voltage characteristics are investigated for the high-magnetic-field state of ultrathin (down to ∼1 unit cell thick) ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ films. The current density where nonlinearity sets in, ${\mathit{J}}_{\mathrm{nl}}$, exhibits a nontrivial power-law temperature dependence, ${\mathit{J}}_{\mathrm{nl}}$∝${\mathit{T}}^{3.0\pm 0.3}$, which quantitatively verifies a prediction from the vortex-glass theory for two dimensions (2D). Additionally, a critical scaling analysis of the I-V data clearly manifests the differences between a 2D and 3D vortex glass. The results suggest that a 2D vortex glass does not order at finite temperatures.