### Abstract or Additional Information

We report a novel two-dimensional order reconstruction solution for nematic liquid crystals, in the Landau-de Gennes theoretical framework, found in square wells. This order reconstruction (OR) solution exists for all well sizes. We provide an analytic description of the OR solution at a special temperature below the nematic supercooling temperature and demonstrate that the OR solution exhibits an uniaxial cross (with negative scalar order parameter) connecting the four square vertices for small wells, complemented by an asymptotic description for large wells in terms of a well-known Gamma-Convergence result for the Modica-Mortola functional on bounded domains. We derive analytic stability criteria for the OR solution in terms of the well size and prove instability with respect to symmetry-breaking perturbations for large wells. Our analytic work is complemented by parallel numerical simulations. This is joint work with Samo Kralj, Giacomo Canevari, Amy Spicer, Martin Robinson, Chong Luo and Radek Erban.