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Materials-realistic microscopic theoretical descriptions of copper-basedsuperconductors are challenging due to their complex crystal structurescombined with strong electron interactions. Here, we demonstrate how ab initiocalculations can accurately describe key structural, electronic, and magneticproperties of the normal state of the prototypical cuprateBi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi-2212). We emphasize the importance ofaccounting for energy-lowering structural distortions, which then allows us to:(a) accurately describe the insulating antiferromagnetic (AFM) ground state ofthe undoped parent compound (in contrast to the metallic state predicted byprevious {\it ab initio} studies); (b) identify numerous low-energy competingspin and charge stripe orders in the hole-overdoped material that are nearlydegenerate in energy with the G-AFM ordered state, indicating strong spinfluctuations; (c) predict the lowest-energy hole-doped crystal structure whichexhibits long-range structural distortions and oxygen dopant positions matchinghigh-resolution scanning transmission electron microscopy (STEM) measurements;and (d) describe electronic bands near the Fermi energy with flat antinodaldispersions and Fermi surfaces that in agreement with angle-resolvedphotoemission spectroscopy (ARPES) measurements and provide a clear explanationfor the structural origin of the so-called "shadow bands".

AFM insulating state and normal state of cuprates from first principle