Using first-principles calculations, we predict a strong coupling of lattice, charge, and spin degrees of freedom in Ruddlesden-Popper phase La3Ni2O7, which enables a phase control with epitaxial strain. While the bulk ground state is metallic, moderate compressive strain is found to trigger a Peierls transition to an insulating state in concurrence with a breathing distortion of NiO6 octahedra. The Peierls transition is microscopically interpreted as a band-gap opening arising from lifting and lowering of the Ni d-eg states due to the octahedral breathing.
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