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

Recent scanning-tunneling microscopy on hole-doped Bi[Formula: see text]Sr[Formula: see text]CaCu[Formula: see text]O[Formula: see text], 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[Formula: see text] 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 [Formula: see text] symmetry and is thought to arise from the Coulomb interaction (denoted by [Formula: see text]) between oxygen [Formula: see text] and [Formula: see text] 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 [Formula: see text] and [Formula: see text] (the latter being the Coulomb interaction between copper [Formula: see text] and oxygen [Formula: see text] 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.