Thickness dependence of the Kosterlitz-Thouless transition in ultrathinYBa2Cu3O7−δfilms

Abstract

The resistive transition is studied systematically on ultrathin ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ (YBCO) films with the number of layers n ranging from 1 to 10. The zero-resistance transition temperature, which is ${\mathit{T}}_{\mathit{c}}$=30 K for n=1, increases rapidly with increasing n. To interpret the results, topological excitation of vortices in thin films of a layered structure is discussed. A ``vortex-string pair,'' in which vortices and antivortices piercing all n layers are pairwise bounded, is shown to be an important topological excitation in thin films. Dissociation of the vortex-string pair gives rise to the Kosterlitz-Thouless (KT) resistive transition in thin films of layered structure. The observed dependence of ${\mathit{T}}_{\mathit{c}}$ on n is explained quantitatively by the increase of the projected two-dimensional carrier density with n in the framework of the KT theory. The result suggests that the KT transition at ${\mathit{T}}_{\mathit{c}}$=30 K is intrinsic to the ${\mathrm{CuO}}_{2}$ conducting planes in one YBCO layer, and questions the earlier interpretation ascribing ${\mathit{T}}_{\mathit{c}}$\ensuremath{\simeq}90 K in bulk YBCO to the KT transition.