  We study the zero set of "generic" Laplace eigenfunctions on the standard two
dimensional flat torus $\mathbb{T}^2=\mathbb{R}^2/\mathbb{Z}^2$. We find the
asymptotic nodal length in any ball of radius larger than the Planck-scale. In
particular, we prove that the nodal set equidistributes on $\mathbb{T}^2$.
Moreover, we show that the nodal set equidistributes at Planck-scale around
almost every point for some eigenfunctions and give examples of eigenfunctions
whose nodal set fails to equidistribute at Planck-scale.
  The proof is based on Bourgain's de-randomisation and the main new ingredient
is the integrability of arbitrarily large powers of the logarithm of "generic"
eigenfunctions, based on the work of Nazarov, and some arithmetic ingredients
called semi-correlations.
