Evidence for two-dimensional nucleation of superconductivity in MgB${}_2$

According to the crystal structure of MgB${}_2$ and band structure calculations quasi-two-dimensional (2D) boron planes are responsible for the superconductivity. We report on critical fields and resistance measurements of 30 nm thick MgB${}_2$ films grown on MgO single crystalline substrate. A linear temperature dependence of the parallel and perpendicular upper critical fields indicate a 3D-like penetration of magnetic field into the sample. Resistivity measurements, in contrast, yield a temperature dependence of fluctuation conductivity above T${}_c$ which agrees with the Aslamazov-Larkin theory of fluctuations in 2D superconductors. We consider this finding as an experimental evidence of two-dimensional nucleation of superconductivity in MgB${}_2$.