Kosterlitz-Thouless Transition in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8+δ$ Thin Films
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Current-voltage ($I-V$) characteristics and the increase of superconducting transition temperature $T_c$ as a function of the number of half-unit-cell layers $n$ are studied on Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+δ}$ thin films grown by molecular beam epitaxy. These observations are interpreted in terms of Kosterlitz-Thouless (KT) transition associated with vortex string threading the film. Considering the change in the types of the lowest free-energy excitations as a function of the size of vortex pair, we have formulated KT renormalization-group (RG) equations. Using experimental data obtained with Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+δ}$ thin films, we have solved the RG equations. It is shown that the KT transition occurs in the vortex-string region with interstring $\ln r$ interaction only. Our calculation successfully explains KT scaling in $I-V$ characteristics and the relation between $T_c$ and $n$. These results indicate that the interlayer interaction plays an important role in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+δ}$ thin films.
27 pages and 10 figures (uuencoded postscript files) appended, RevTeX 3.0 (Minor corrections are made concerning citations.)
27 pages and 10 figures (uuencoded postscript files) appended, RevTeX 3.0 (Minor corrections are made concerning citations.)