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

Recent scanning-tunneling microscopy on hole-doped Bi2Sr2CaCu2O8, one of the materials of the cuprate family, finds a long-range ordered spontaneous splitting of the energy levels of oxygen orbitals inside the CuO2 unit cells [S. Wang etal., Nat. Mat. 23, 492-498 (2024)]. This spontaneous intra-unit-cell orbital ordering, also known as electronic nematicity, breaks C4 symmetry and is thought to arise from the Coulomb interaction (denoted by Vpp) between oxygen px and py electrons. In this work, we study the spontaneous emergence of electronic nematicity within the three-band Hubbard [aka the Emery-VSA (Varma-Schmitt-Rink-Abrahams) 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 Vpp and Vpd (the latter being the Coulomb interaction between copper dx2-y2 and oxygen px,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.