Renormalization effects near the vortex-unbinding transition of two-dimensional superconductors

Abstract

The theory of topological phase transitions predicts a universal relation between the vortex-unbinding temperature ${T}_{c}$ and the areal superelectron density ${n}_{s}({T}_{c})$ in two-dimensional superconductors. Evaluating ${n}_{s}({T}_{c})$ with the theory of dirty superconductors leads to a relation between ${T}_{c}$ and the normal-state sheet resistance ${R}_{N}^{\ensuremath{\square}}$. This latter relation, however, must be modified to account for the distinction between the unrenormalized ${{n}_{s}}^{0}$ and the renormalized value ${{n}_{s}}^{R}$, in the critical region near ${T}_{c}$. This can be expressed via a nonuniversal parameter ${\ensuremath{\epsilon}}_{c}=\frac{{{n}_{s}}^{0}({T}_{c})}{{{n}_{s}}^{R}({T}_{c})}$, which depends in turn for homogeneous films on ${N}_{0}$, the density of statistically independent vortices within an area ${\ensuremath{\xi}}^{2}$. For the Hg-Xe thin films studied earlier, we find that ${\ensuremath{\epsilon}}_{c}=1.2\ifmmode\pm\else\textpm\fi{}0.1$ and ${N}_{0}=0.05\ifmmode\pm\else\textpm\fi{}0.03$.