III. THE CHARGE CARRIERS ARE MADE OF TWO COMPONENTS (two different kinds of charge carriers)
Experimental evidence for a second component for doped holes: 3d⁹L carriers with a mixed orbital angular momentum of b₁ (ml=2) [or 3d_3z2_-r 2 ] and a₁ (ml=0.1) [or 3d(z²)] symmetry

 "Bianconi, De Santis et al. (1988) have made a high resolution, polarized study of the structure and symmetry of the unoccupied hole states in YBa₂Cu₃O_7-y.By varying y they identify an extra spectral density from 932 to 935.5 eV for y=0.0-0.15 which is absent for y>0.3. They assign the new peak to transitions from 3d⁹L^* to 2p3d¹⁰L^* final state, where L^* denotes the hole in the ligand orbital (present in the ground state).... The hole-induced peak is more intense for x rays polarized along the c axis than for x rays polarized in the Cu-O plane.... Bianconi, De Santis et al. (1988) suggest that holes must therefore have strong O4 character, since the O4 atom is the only O atom with p(z) orbitals that couple to d(z²) Cu orbitals, and it does so for both Cu1 and Cu2 sites.
The corresponding data for Bi₂Sr₂CaCuO₂O_y (T_c=85 K samples, presumably with y near 8) have been reported by Bianconi, Castrucci et al. (1988).... Since the hole band appears in both polarizations, Bianconi, Castrucci et al. (1988) suggest that the unoccupied states involve both Cu d(z²) and Cu d(x²-y²) character in this material."

Excerpt from the review paper by Warren E. Pickett "Electronic structure of the high temperature oxide superconductors" published in Review Modern Physics Vol. 61, No 2, April 1989, 433-510; (from pag. 473)

see more by this:(5) "Determination of the symmetry of the 3d⁹L states" by A. Bianconi, M. De Santis, A. Di Cicco, A. M. Flank, A. Fontaine, P. Lagarde, H. Katayama-Yoshida, A. Kotani and A. Marcelli published in Physical Review B (Rapid Communications) Vol. 38, pag. 7196-7199 (1988)
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see more by this:(6) "Symmetry of the hole states in single crystals of high T_c superconductors" (invited talk at the Adriatico meeting held in Trieste 20 June-29 July 1988 published in the book "Towards the theoretical understanding of high T_c superconductors", edited by S. Lundquist, E. Tosatti, M. P. Tosi and Yu Lu, World Scientific Singapore pag. 615); by A. Bianconi, P. Castrucci, M. De Santis, A. Di Cicco, A. M. Flank, P. Lagarde, H. Katayama -Yoshida, A. Marcelli, and Z. X. Zhao, International Journal of Modern Physics B Vol. 1 No. 5, pag. 1151-1152(1988)

IV. COEXISTENCE OF POLARONS AND FREE CARRIERS

 "Using X-ray absorption spectroscopy Bianconi et al.³⁶ find that... a Zhang Rice singlet pair is unstable against the creation of a similar pair, but with Cu d_3z2_-r 2 instead of Cu(d_x2_-y2) hole. They further suggest that the lattice responds to the creation of this pair by local displacements. They call the singlet pair, with the surrounding lattice deformation a d_z2 polaron. There is strong experimental support for the existence of these d_z2 polarons. Pulsed neutron scattering ²⁶ and EXAFS ²⁹ measurements show dynamic structural irregularities consistent with the assumption the neighboring apical and planar oxygen atoms vary their positions between two short time scale equilibria, which should occur when such d_z2 polaron is part of the time in that vicinity."

Excerpt from the review paper by J. Ashkenazi, D. Vacaru, and C. G. Kuper "Search of the correct microscopic theory for high temperature cuprate superconductors" in High Temperature Superconductivity edited by J. Ashkenazi et al. Plenum Press New York 1991, p. 569-582 (from pag. 574)

see more by this:(7) "On the Cu 3d holes in high T_c superconductors" (Invited talk at the Miami Workshop, Miami 3-9 January 1991) by A. Bianconi, A. -M. Flank, P. Lagarde, C. Li, I. Pettiti, M. Pompa, and D. Udron, published in the book " Electronic Structure and Mechanisms of High Temperature Superconductivity" edited by J. Ashkenazi, and G. Vezzoli (Plenum, New York, 1992) pag.363-378

"In particular, calculations aiming at the realistic description of the electronic structure have indicated that, in addition to the Copper 3d_x2_-y2 and Oxygen 2p_x and 2p_y s orbitals included in the three-band model, the copper 3d_3z2_-r2 orbital may also be involved in accommodating doped holes. This has been confirmed by electron energy loss spectroscopy and polarized x-ray absorption spectroscopy".

Excerpt from the article " Effective single band models for the hih Tc cuprates. II. Role of apical oxygen" by R. Raimondi J. H. Jefferson, L. H. Feiner Phys. Rev. B vol. 53, p.p. 8774-8788 (1996) pag. 8774

see more by this: in (10) On the Orbital Angular Momentum of Cu 3d Hole States in Superconducting La_2-xSr_xCuO₄ by M. Pompa, P. Castrucci, C. Li, D. Udron, A. M. Flank, P. Lagarde, H. Katayama-Yoshida, S. Della Longa, and A. Bianconi published in Physica C Vol. 184, pag, 102-112 (1991) "Jahn Teller (JT) polarons were proposed by a theoretical group in Basel (H.-K. Höck, H. Nikisch, and H. Thomas Helv. Phys. Acta 56, 237 (1983)). In the JT effect the Born-Oppenheimer approximation, i.e., the decoupling of nuclear and electronic motion, breakes down. The concept of JT polarons -which do not need to be small ones - ed to the discovery of copper oxide superconductors (J.G. Bednorz and K. A. Müller Z. Physics B 64, 189 (1986)). In the cuprates the small polarons are indeed of the Q₂-variety as inferred from EXAFS, (Bianconi et al.) NMR, and optical pulse experiments as well as most recently by means of EPR (9). On the other hand in the manganites La _1-xCa_xMnO₃ they are of the Q₃ type (10).
Most recent research indicates that in several copper oxides large polarons, i.e., free-carrier-type ones, and small polarons coexists as was deduced much earlier to be the case for oxides WO_3-x (E. Salje and B. Guuttler Phil. Mag. B 50 607 (1984)) and NbO_2.5-x(8)
These measurements indicate the coexistence of small polarons and free carriers above the concentration x_t=0.09, the concentration of free carriers increases rapidly with x- x_t reaching a maximum for optimal doping x=0.15."

Excerpt from the paper "The ratio of small polarons to free carriers in La _2-x Sr_xCuO₄ derived from susceptibility measurements " by K. A. Müller, Guo-meng Zhao, K. Conder, and H. Keller
J. Phys. Condens. Matter 10 (1998) L291-L296 (see pag. L293)
(N.B. Compelling evidence for dominant role of polarons in underdoped phase come also from recent isotope effect experiments on the in plane penetration depth reported by the same authors in Guo-meng Zhao, M. B. Hunt, H. Keller, and K. A. Müller Nature 385, pag. 236 (1997).

see more by this: (8) A. Bianconi N. L Saini, A. Lanzara, M. Missori, T. Rossetti, H. Oyanagi, H. Yamaguchi, K. Oka, T. Ito Phys. Rev. Lett 76, 3412-3415 (1996).
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see more by this: (9) Coupling Between the Charge Carriers and Lattice Distortions via Modulations of the Orbital Angular Momentum ml=0 of the 3d Holes by Polarized XAS Spectroscopy (Proc. of the International M2S HTSC Conference, Kanazawa, Japan, July 22-26 1991) by M. Pompa, S. Turtù, A. Bianconi, F. Campanella, A. M. Flank, P. Lagarde, C. Li, I. Pettiti, and D. Udron published in Physica CVol. 185-189, pag. 1061-1062 (1991)
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see more by this: in (11) Y. Seino, A. Kotani and A. Bianconi published in Journal of Physical Society of Japan Vol, 59, pag. 815 (1990)
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see more by this: in (12) the invited talk at the 10^th VUV conference Paris July 27-31, 1992) Full multiple scattering interpretation of the Cu L₃ edge XANES in High T_c superconductors by M. Pompa, A. Bianconi, S. Della Longa, and P. Lagarde published in the book "Vacuum Ultraviolet Radiation Physics" edted by F.J. Wuilleumier Y. Petroff and I. Nenner
World Scientific Singapore1993 pag. 310-319
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see more by this: in (13) the Proc. of the EXAFS conference held in Kobe, Japan August 1992 by
A. Bianconi M. Pompa, S. Turtu, S. Pagliuca, P. Lagarde, A. M. Flank, and C. Li
Jpn. J. Appl. Phys.Vol, 32 (1993) Suppl. 32-2 pag. 581-583