Renormalization and the Kosterlitz-Thouless transition in a two-dimensional superconductor

The nonlinear $I-V$ characteristics of thin high-sheet-resistance Hg-Xe alloy films are examined within the context of the Kosterlitz-Thouless theory of the superconducting transition. In the regime below the vortex-unbinding temperature $T_c$, where logarithmically bound vortices can be broken apart by a transport current, we find that $V\sim I^{a\left(T\right)\mathrm{}}$. Comparison with theory allows us to infer the value of $T_c$ and the mean-field temperature $T_{c0\mathrm{}}$ from $a\left(T\right)\mathrm{}$, and the dependence of these temperatures on $R_N^{\square }$ appears in approximate agreement with the microscopic theory of dirty superconductors. A systematic deviation appears to be consistent with renormalization of the vortex interaction close to $T_c$ due to the presence of small polarizable vortex pairs, and can be described by an effective vortex dielectric constant ${\epsilon }_c=1.2\mathrm{}$. Further evidence for this renormalization, which is a key feature of the Kosterlitz-Thouless transition, is obtained by examining the curvature of the $logV$ vs $logI$ plot very close to $T_c$. The current dependence of $a(I,T)=\frac{d\left(logV\right)}{d\left(logI\right)}$ is a direct measure of the spatial dependence of the vortex interaction, allowing a direct comparison with the analytic predictions of the renormalization equations. Satisfactory agreement is obtained using physically reasonable parameters.