The high-temperature superconducting cuprate La_2−xSr_xCuO₄ (LSCO) shows several phases ranging from antiferromagnetic insulator to metal with increasing hole doping. To understand how the nature of the hole state evolves with doping, we have carried out high-resolution Compton scattering measurements at room temperature together with first-principles electronic structure computations on a series of LSCO single crystals in which the hole doping level varies from the underdoped (UD) to the overdoped (OD) regime. Holes in the UD system are found to primarily populate the O 2p_x/p_y orbitals. In contrast, the character of holes in the OD system is very different in that these holes mostly enter Cu d orbitals. High-resolution Compton scattering provides a bulk-sensitive method for imaging the orbital character of dopants in complex materials.

The combination of new experimental and theoretical techniques provides evidence of instantaneous electron correlation effects in directional Compton profiles of crystalline silicon, which cannot be reproduced when reference is made to a density matrix obtained from a single-determinantal wavefunction. These effects are instead accounted for by a recently implemented post-Hartree–Fock periodic scheme, which gives results in quite good agreement with the high-quality experimental data.

Cobalt is used in Li-ion batteries, but it is expensive and could be replaced by nickel to deliver better performance at a lower cost. With this motivation, we discuss how the character of redox orbitals of ${\mathrm{LiNiO}}_2$ can be ascertained through x-ray Compton scattering measurements combined with parallel first-principles simulations. Our analysis reveals the nature of hole states in Li-doped NiO resulting from the hybridization of $\text{O}2p$ and $\text{Ni}3d$ orbitals. Our study also gives insight into the ferromagnetic ground state and provides a pathway toward the rational design of next-generation battery materials.