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We propose utilizing the Cooper pair to induce magnetic frustration insystems of two-dimensional (2D) magnetic adatom lattices on s-wavesuperconducting surfaces. The competition between singlet electron correlationsand the RKKY coupling is shown to lead to a variety of hidden order states thatbreak the point-group symmetry of the 2D adatom lattice at finite temperature.The phase diagram is constructed using a newly developed effective bond theory[M. Schecter et al., Phys. Rev. Lett. 119, 157202 (2017)], and exhibits broadregions of long-range vestigial nematic order.

Cooper Pair Induced Frustration and Nematicity of Two-Dimensional Magnetic Adatom Lattices