Cellular Dynamical Mean Field Study of Intra-Unit-Cell Charged Nematicity in Cuprates

A recent experiment on hole-doped Bi₂Sr₂CaCu₂O₈, one of the materials of the cuprate family, finds a splitting in the energy levels of the oxygen orbitals of the CuO₂ unit cell. This observation has been predicted to occur due to spontaneous intra-unit-cell orbital ordering, caused by the Coulomb interaction (denoted by Vpp) between electrons of 2p⁶ orbitals of neighboring planar oxygen atom. In our work, we verify this prediction by analyzing the three-band Hubbard (or Emery) model using cluster dynamical mean field theory (CDMFT). We find that indeed the system develops intra-unit-cell charged-nematic order (the name by which this orbital ordering is known) when the Vpp interaction is finite. However, the crucial interplay of this interaction with other ones in the unit cell, such as the oxygen on-site interaction (Up) and the Coulomb interaction between electrons of Copper and oxygen orbitals (Vpd), results in robust nematicity only at large hole doping. We also compare our findings with those from Hartree-Fock mean field theory (MFT). The predicted nematicity is also much larger than the observed signature, casting doubts on the actual cause of the splitting.