Absence of a Kosterlitz-Thouless transition in ultrathin films

We have performed nanovolt-level dc measurements on single-unit-cell films of (Formula presented). When only the low-sensitivity data are analyzed, they are roughly consistent with the occurrence of a Kosterlitz-Thouless transition. At the lowest currents and voltages, however, the samples are ohmic at temperatures quite far below the nominal Kosterlitz-Thouless transition temperature, contrary to the theory. The ohmic response at low currents implies that there are unbound vortices present well below the nominal Kosterlitz-Thouless transition temperature.