Cluster dynamical mean field study of intra-unit-cell charge nematicity in hole-doped cuprates

Recent scanning-tunneling microscopy on hole-doped Bi$_2$Sr$_2$CaCu$_2$O$_8$, one of the materials of the cuprate family, finds a long-range ordered spontaneous splitting of the energy levels of oxygen orbitals inside the CuO$_2$ unit cells [S. Wang et al., Nat. Mat. 23, 492-498 (2024)]. This spontaneous intra-unit-cell orbital ordering, also known as electronic nematicity, breaks $C_4$ symmetry and is thought to arise from the Coulomb interaction (denoted by $V_{pp}$) between oxygen $p_x$ and $p_y$ electrons. In this work, we study the spontaneous emergence of electronic nematicity within the three-band Hubbard (aka the Emery-VSA model), using cluster dynamical mean field theory. This method incorporates short-range electronic correlations and gives us access to the density of states, a quantity that is directly probed in experiments. We argue that there is a delicate competition between $V_{pp}$ and $V_{pd}$ (the latter being the Coulomb interaction between copper $d_{x^2-y^2}$ and oxygen $p_{x,y}$ electrons) that must be taken into account in order to find a Zhang-Rice singlet band well-resolved from the upper Hubbard band, and a splitting of the charge-transfer band (one of the signatures of charge nematicity) by roughly 50 meV, as observed recently.