Nematic and spin-charge orders driven by hole-doping a charge-transfer insulator

Recent experimental discoveries have brought a diverse set of broken symmetry states and in particular, nematicity in the form of orbital ordering to the center stage of research on cuprate superconductors. Here, we present a thematic understanding of the diverse phenomenology by exploring a strong-coupling mechanism of symmetry breaking driven by frustration of antiferromagnetic order. We achieve this through a combination of numerically exact methods and variational analysis of a three-band model of the CuO₂ plane with Kondo type exchange couplings between doped oxygen holes and classical copper spins. In the resulting spin-fermion model, we find (1) that the symmetry hierarchy of spin stripe, charge stripe, intra-unit-cell nematic order, and isotropic phases are all accessible microscopically within the model, and (2) many symmetry-breaking patterns compete with energy differences within a few meV per Cu atom to produce a rich phase diagram. Finally, we study the tendency to orbital ordering in the various phases and signatures of the resulting nematicity.