Unraveling the Nature of Charge Excitations in La$_2$CuO$_4$ with Momentum-Resolved Cu $K$-edge Resonant Inelastic X-ray Scattering

Results of model calculations using exact diagonalization reveal the orbital character of states associated with different Raman loss peaks in Cu $K$-edge resonant inelastic X-ray scattering (RIXS) from La$_{2}$CuO$_{4}$. The model includes electronic orbitals necessary to highlight non-local Zhang-Rice singlet, charge transfer and $d$-$d$ excitations, as well as states with apical oxygen 2$p_z$ character. The dispersion of these excitations is discussed with prospects for resonant final state wave-function mapping. A good agreement with experiments emphasizes the substantial multi-orbital character of RIXS profiles in the energy transfer range 1-6 eV.