Now you are in the subtree of High-Temperatures Superconductivity project.

# Parent insulating state

The parent compounds of cuprate superconductors contain CuO2 planes, in which Cu$^{2+}$ ions have one hole in $d_{x^2 - y^2}$ orbitals. This implies a half-filled band, and for non-interacting electrons would correspond to a metallic state. However, due to electron-electron interactions, below the Neel temperature, the parent compounds become antiferromagnetic, with a gap in the electronic excitation spectrum and a characteristic magnetic excitations spectrum.

A system that is insulating due to Coulomb repulsion among electrons within a single
band is commonly labeled a Mott insulator. This categorization is often applied to
the cuprate parent compounds; however, they are more accurately described as charge-transfer insulators. The distinction between Mott insulators and charge transfer insulators is based upon comparison of Mott gap $U$ and charge transfer gap $\Delta$ [1]. In the context of cuprates, $U$ corresponds to the energy cost associated with moving an electron from one Cu ion to another (cost of double occupancy), while $\Delta$ is the cost of moving an electron from O ion to Cu. Since for cuprates $\Delta < U$, they belong to the charge transfer insulator class.

A cubic crystal field causes a splitting of the Cu 3d
orbitals into two groups: $e_g$ symmetry ($x^2-y^2$, $3z^2 - r^2$ and $t_{2g}$ ($xy$, $xz$, $yz$), with $e_g$ being at higher energy. With a tetragonal elongation of the CuO6 octahedra, the $3z^2-r^2$ orbital is lowered in energy relative to the $x^2-y^2$, so that the one hole sits in the latter orbital. It has recently become possible to determine the energy splittings between Cu 3d orbitals with resonant inelastic x-ray scattering at the Cu L3 edge [2]. Recent ab
initio calculations are in good agreement with the measurements [3]. For La2CuO4,
measurements show that the d-d excitation energies from the $x^2-y^2$ state are 1.7 eV to $3z^2-r^2$, 1.8 eV to $xy$, and 2.1 eV to $xz$, $yz$.

Early ab initio calculations yielded good results for the electronic spectra at high energies (> 5 eV) but were predicting metallic conductivity at low frequencies [4], [5].