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# Orbital character of carriers (X-Ray)

To determine the orbital character of the holes, one can use x-ray absorption spectroscopy. For example, measurements at the Cu $K$ edge involve transitions from the $1s$ core level to states with $p$ symmetry with respect to the absorbing Cu site. Measurements on LSCO showed an absence of significant change with doping [1]. Measurements at the Cu $L_3$ edge detect transitions from a $2p$ core level to $d$ symmetry final states. It was found [2] that doping does not change the density of unfilled $3d$ states, which contribute to the strong low-energy peak, but that it does introduce holes at slightly higher energy, corresponding to hybridized O $2p$ states, as apparent in Fig. 1.
(The empty $3d$ states are pulled down in energy relative to these by the potential of the x-ray-induced core hole.)

The significance of the O $2p$ character was firmly established by measurements of O $K$-edge spectra in LSCO [3], as shown in Fig. 2. Here the excitation is from the O $1s$ level to states with $p$-symmetry with respective to the absorbing atom. Two peaks are observed in the pre-edge region, with A labeling the O $2p$ peak and B the upper Hubbard band. In the undoped state, peak A is absent while B is strong. With doping peak A grows while B decreases. The growth of A indicates the O $2p$ character of the doped holes. Later measurements on single crystals, taking advantage of the polarization sensitivity of the absorption process, have demonstrated that the holes are dominantly within the CuO$_2$ planes, with little weight on apical oxygens [4].

The lesson from x-ray absorption spectroscopy is that the dopant-induced holes have strong O $2p$ character. Combining this with the optical spectroscopy and Hall-effect results, we can conclude that the Cu $3d$ holes of the parent insulator remain localized at low temperature, even after substantial doping.