Charge transfer energy and band filling effects on two-hole Auger resonances in strongly correlated systems

We investigate the impact of charge transfer energy and band filling on the stability of the two-hole resonance relevant for Auger electron spectroscopy (AES) in transition-metal oxides. As a minimal model to study charge transfer effects in a transition metal (TM) and oxygen (OX) chain, we consider a one-dimensional chain with spinless fermions with an alternating motif of site-pairs with nearest-neighbor (NN) repulsion U and uncorrelated site-pairs, separated by a charge transfer gap Delta. We first show that while two holes added in a filled band of NN interacting fermions in one dimension can stabilize to a two-hole bound pair, the bound pair delocalizes with a U-dependent bandwidth. In contrast, we establish that the bandwidth of two holes added on a TM site pair in a filled band is dramatically suppressed, realizing a "local" two-hole resonance (L2HR) at the same TM site pair mimicking the AES phenomenology. Employing a memory-efficient exact numerical scheme and standard Lanczos-based diagonalization, we then study two-hole spectra for holes added at TM site pairs in partially filled bands. We analyze the multiple features that arise in the two-hole spectra at partial filling of the ground state. We uncover that in the strong-U limit, there is a filling-dependent Acrit above which the L2HR remains stable for any band filling greater than 75%. In this regime, the energy location of the L2HR provides a direct estimate of the correlation strength at TM site pairs for partial filling and is reminiscent of the Cini-Sawatzky theory for the filled band case. At 75% band filling, an abrupt redistribution of two-hole spectral weight destroys the L2HR regardless of the U or A values. We discuss the relevance of these nonperturbative results, obtained with full lattice symmetry, for understanding the AES of partially filled bands in terms of the local two-hole spectrum.