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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.


  1. J. M. Tranquada, S. M. Heald, A. Moodenbaugh, and M. Suenaga, Phys. Rev. B 35, 7187–7190 (1987).
  2. A. Bianconi, J. Budnick, A. Flank, A. Fontaine, P. Lagarde, A. Marcelli, H. Tolentino, B. Chamberland, C. Michel, B. Raveau, and G. Demazeau, Phys. Lett. A 127, 285–291 (1988).
  3. C. T. Chen, F. Sette, Y. Ma, M. S. Hybertsen, E. B. Stechel, W. M. C. Foulkes, M. Schulter, S.-W. Cheong, A. S. Cooper, L. W. Rupp, B. Batlogg, Y. L. Soo, Z. H. Ming, A. Krol, and Y. H. Kao, Phys. Rev. Lett. 66, 104–107 (1991).
  4. E. Pellegrin, N. Nücker, J. Fink, S. L. Molodtsov, A. Gutiérrez, E. Navas, O. Strebel, Z. Hu, M. Domke, G. Kaindl, S. Uchida, Y. Nakamura, J. Markl, M. Klauda, G. Saemann-Ischenko, A. Krol, J. L. Peng, Z. Y. Li, and R. L. Greene, Phys. Rev. B 47, 3354–3367 (1993).