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Coupling of the ionic motions with the electronic structure in the YBa2Cu3O7 high Tc superconductor
Physiea C 235-240 (1994) 2375-2376 North-Holland
PHYSICA
Coupling of the ionic motions with the electronic structure in the YBa2CuaO z high T~ superconductor Pablo de la Mora ~ and Jaime Keller ~ ~Departarnento de Fisiea, Faeultad de Cieneias, Apartado Postal 70-542, UNAM, 04510 M6xico, DF, M6xico. bDepartamento de Fisiea y Quimiea Te6rica, Faeultad de Quimiea, Apartado Postal 70-528, UNAM, 04510 M~xico, DF, M6xico. A theoretical ~nalysis of the consequences of the experimentally measured double-well oscillation of the apical oxygen in YBa2Cu30 z is made. The electronic structure was calculated in the frozen phonon approximation with different apical oxygen positions of a cell consisting 4-unit cells. Chemical bond changes are related to chain-planes electronic interactions and with valence fluctuations of the Cu(1) atoms of the chains. A vibronic mechanism is substantiated as a candidate for strong phonon-electron interaction. The coupling of the ionic motions with electronic structure, in turn, explains valence fluctuation, bipolaron and magnetic-like phenomena in these type of compounds. 1. I N T R O D U C T I O N
Experimental evidence supports the idea that electron double-well axial displacements of the apical oxygen [0(4)] is intrinsically related to the superconductivity of YBa2CujOz and related materials ~. In fact, following the measurement of the movement of the 0(4) in YBa2Cu307 by Mustre de Le6n et a13, in which they found that the oxygen has a movement that can be modelled as moving in a double well 0.13,~ apart in the e direction, we calculated the electronic structure of this superconductor in the frozen phonon approximation. These oxygen movements should produce chargetransfer instabilities and band rearrangements that may couple directly with phonon modes in the plane, but they are certainly expected to couple with 0(4) vibrations involved in charge ~.msfer between chains and planes 3. Previous model calculations ,af ours had [ --r), r?v,.,'~ we,," for thc ~., "~'*~ . . . ~. ., ~ x , e , i *, S , shown that the double "'" coupled to the surrounding ions, should exist, see Keller 4 and references (3 & 4) therein and led us then to propose a vibronic mechanism for high temperature superconductivity. More recently x-ray diffraction measurements have questioned the interpretation of Mustre et al. 5, but Raman and photoluminescence measurements support them 6. In the present paper the electronic structure of YBaeCu30 z is calculated using a tight-binding type
method with a cell consisting of four unit-cells repeated in the b (chain) direction. Following Mustre et al. different O(4) positions were u~ed m different unit-cells. It was found that with some 0(4) arrangements there is a 5'e charge transfer between Cu(1) of different unit-cells. 2ELECTRONIC STRUCTURE CALCULATIONS When a calculation was made for a single unitcell with the two 0(4) in the 'far' position (1.955A from Cu(1)) compared to the 'close' position (1.82A) the band from the chains lowers and crosses the bands from the planes and there is a large charge transfer. It was therefore thought that a more realistic calculation should be made with a four unit cell where collective mode of 0(4) movements can be modelled, with a k = 2zt/4b (L=4b). Three eases were ea!cu!ated, the first one, the 3:1 case had three unit cells in the c l o s e position and the forth one in the far position, the other cases tw9 had the ratio 2:2 (two c l o s e and two far) and 1:3. The charges of the Cu(1) for the different unit-cells in the three cases are shown in the table below. The charge transfer are mainly due to the d:2 of Cu(1), the other atoms have little charge transfer. Due to the breaking of the translational symmetry in the b direction, the chain's band is split into tbur bands.
0921-4534D4/$07.00 © 1994 - ElsevierScience B.V. All rights reserved. SS£'I 0921-4534(94)01753-0
2376
R de la Mora, J. Keller/Physica C 235-240 (1994) 2375-2376
3:1 Ca(l)
close 9.41
close 9.40
close 9.41
far 9.49
2:2 Cu(l)
close 9.46
close 9.46
far 10.04
far 10.04
1:3
close 9.46
far 9.76
far 10.00
far 9.76
Cu(l)
Valence orbital charges of the four unit-cell oxygen movements. Close and far refers to the Cu(I)-0(4) distance. In the 3:1 case one chain band shifts down to the Fermi energy and little charge is transferred between Cu(1) of different cells. For the 2:2 case two bands are lowered and E r, between them, is also lowered, in this case 0.58e is transferred between Cu(1) of different cells. In the last (1:3) case three chain bands are lowered, E r between the two lower ones. In this case there is again 0.55e charge transfer between the Cu(1) of the close unit-cell and the cell that is 2b apart, but in the cells in between these two the charge have an intermediate value. A new type of valence fluctuation, charge transfer, should be con::idered where a unit, a couple of Cu(1) atoms for example, looses or gains one electron charge in a cyclic form. Unfortunately it is difficult to parametrize the effect or either intraatomic or intraunit correlations to know if in tl, s case it is better to describe the fluctuation as that of an atom or as that of a unit (molecular or crystal-cell-like). We should also stress that some phonons are the ones that become strongly anharmonic due to the vibronic coupling of those particles vibration states, then a model where also one phonon type is used could provide a sound starting theoretical description. This should largely simplify the otherwise very complicated analysis of the vibronic coupling for superconductivity. In our previous work ~ we showed that the ground state configuration was described from the chemical point of view as if the chains acted only as an insulator layer between the planes, but with the 0(4) movements a different picture emerges, '~,¢ith a large correlation between the 0(4) movements and electronic structure. Two 0(4) that simultaneously move away from Cu(1) will put two localized
electron states below the Fermi level. Nevertheless it should be stressed that localized states do not necessarily give the lowest total energy and are therefore not thought to be the ones corresponding to the ground state; in general periodic boundary conditions create delocalized bands corresponding to the lower total energy. We have seen that the ionic motion of the apical 0(4) oxygen generates large electronic changes,, eases 2:2 (and 1:3), where a group of 2 (or 3) Cu atoms have a total fluctuation of one electron in the d,: copper atomic shell. As a consequence we can say that 1) Valence fluctuations occur, both of a group and if intraatomie correlations dominate (they are not included in our analysis), also of a single atom, then an analysis of high Tc phenomenon suitable to be expressed in terms of valence fluctuations should be possible, as found in the literature, 2) But the presence of traveling ionic charges will also induce a bipolaron-like analysis as a possible scheme, moreover as the valence fluctuation can be enhanced by exchange correlation, the ion may become spin polarized and the bipolarons could also be magnetically coupled or antiferromagnetic coupling become also a possible scheme for an analysis. Nevertheless all of those schemes are not ~eparated from the basic phenomenon, that of strong vibronic coupling. This is the main conclusion of the simple but straight forward model calculation reported in this paper. REFERENCES
S.D. Conradson and I.D. Raistrick, Science 243 (1989) 1340. J. Mustre de Le6n, S.D. Conradson, I. Batisti6, and A.R. Bishop, Phys Rev. Let:. 65 (1990) 1675. P.B. Littlewood et al., Phys. Rev. Lett. 63 (1989) 2602. J. Keller, Physica C, 153-155 (1988) 1321. .,.t). ~UlllX'an el al. ~'nys. Rev. /J, 4~ (i993) 10638. V.N. I)enisov et al., Phys. Rev. B, 48 (1993) 16714. P. de !a Mora and C. de Teresa, Solid State Commtm. 70 (1989) 745-749.
PHYSICA
Coupling of the ionic motions with the electronic structure in the YBa2CuaO z high T~ superconductor Pablo de la Mora ~ and Jaime Keller ~ ~Departarnento de Fisiea, Faeultad de Cieneias, Apartado Postal 70-542, UNAM, 04510 M6xico, DF, M6xico. bDepartamento de Fisiea y Quimiea Te6rica, Faeultad de Quimiea, Apartado Postal 70-528, UNAM, 04510 M~xico, DF, M6xico. A theoretical ~nalysis of the consequences of the experimentally measured double-well oscillation of the apical oxygen in YBa2Cu30 z is made. The electronic structure was calculated in the frozen phonon approximation with different apical oxygen positions of a cell consisting 4-unit cells. Chemical bond changes are related to chain-planes electronic interactions and with valence fluctuations of the Cu(1) atoms of the chains. A vibronic mechanism is substantiated as a candidate for strong phonon-electron interaction. The coupling of the ionic motions with electronic structure, in turn, explains valence fluctuation, bipolaron and magnetic-like phenomena in these type of compounds. 1. I N T R O D U C T I O N
Experimental evidence supports the idea that electron double-well axial displacements of the apical oxygen [0(4)] is intrinsically related to the superconductivity of YBa2CujOz and related materials ~. In fact, following the measurement of the movement of the 0(4) in YBa2Cu307 by Mustre de Le6n et a13, in which they found that the oxygen has a movement that can be modelled as moving in a double well 0.13,~ apart in the e direction, we calculated the electronic structure of this superconductor in the frozen phonon approximation. These oxygen movements should produce chargetransfer instabilities and band rearrangements that may couple directly with phonon modes in the plane, but they are certainly expected to couple with 0(4) vibrations involved in charge ~.msfer between chains and planes 3. Previous model calculations ,af ours had [ --r), r?v,.,'~ we,," for thc ~., "~'*~ . . . ~. ., ~ x , e , i *, S , shown that the double "'" coupled to the surrounding ions, should exist, see Keller 4 and references (3 & 4) therein and led us then to propose a vibronic mechanism for high temperature superconductivity. More recently x-ray diffraction measurements have questioned the interpretation of Mustre et al. 5, but Raman and photoluminescence measurements support them 6. In the present paper the electronic structure of YBaeCu30 z is calculated using a tight-binding type
method with a cell consisting of four unit-cells repeated in the b (chain) direction. Following Mustre et al. different O(4) positions were u~ed m different unit-cells. It was found that with some 0(4) arrangements there is a 5'e charge transfer between Cu(1) of different unit-cells. 2ELECTRONIC STRUCTURE CALCULATIONS When a calculation was made for a single unitcell with the two 0(4) in the 'far' position (1.955A from Cu(1)) compared to the 'close' position (1.82A) the band from the chains lowers and crosses the bands from the planes and there is a large charge transfer. It was therefore thought that a more realistic calculation should be made with a four unit cell where collective mode of 0(4) movements can be modelled, with a k = 2zt/4b (L=4b). Three eases were ea!cu!ated, the first one, the 3:1 case had three unit cells in the c l o s e position and the forth one in the far position, the other cases tw9 had the ratio 2:2 (two c l o s e and two far) and 1:3. The charges of the Cu(1) for the different unit-cells in the three cases are shown in the table below. The charge transfer are mainly due to the d:2 of Cu(1), the other atoms have little charge transfer. Due to the breaking of the translational symmetry in the b direction, the chain's band is split into tbur bands.
0921-4534D4/$07.00 © 1994 - ElsevierScience B.V. All rights reserved. SS£'I 0921-4534(94)01753-0
2376
R de la Mora, J. Keller/Physica C 235-240 (1994) 2375-2376
3:1 Ca(l)
close 9.41
close 9.40
close 9.41
far 9.49
2:2 Cu(l)
close 9.46
close 9.46
far 10.04
far 10.04
1:3
close 9.46
far 9.76
far 10.00
far 9.76
Cu(l)
Valence orbital charges of the four unit-cell oxygen movements. Close and far refers to the Cu(I)-0(4) distance. In the 3:1 case one chain band shifts down to the Fermi energy and little charge is transferred between Cu(1) of different cells. For the 2:2 case two bands are lowered and E r, between them, is also lowered, in this case 0.58e is transferred between Cu(1) of different cells. In the last (1:3) case three chain bands are lowered, E r between the two lower ones. In this case there is again 0.55e charge transfer between the Cu(1) of the close unit-cell and the cell that is 2b apart, but in the cells in between these two the charge have an intermediate value. A new type of valence fluctuation, charge transfer, should be con::idered where a unit, a couple of Cu(1) atoms for example, looses or gains one electron charge in a cyclic form. Unfortunately it is difficult to parametrize the effect or either intraatomic or intraunit correlations to know if in tl, s case it is better to describe the fluctuation as that of an atom or as that of a unit (molecular or crystal-cell-like). We should also stress that some phonons are the ones that become strongly anharmonic due to the vibronic coupling of those particles vibration states, then a model where also one phonon type is used could provide a sound starting theoretical description. This should largely simplify the otherwise very complicated analysis of the vibronic coupling for superconductivity. In our previous work ~ we showed that the ground state configuration was described from the chemical point of view as if the chains acted only as an insulator layer between the planes, but with the 0(4) movements a different picture emerges, '~,¢ith a large correlation between the 0(4) movements and electronic structure. Two 0(4) that simultaneously move away from Cu(1) will put two localized
electron states below the Fermi level. Nevertheless it should be stressed that localized states do not necessarily give the lowest total energy and are therefore not thought to be the ones corresponding to the ground state; in general periodic boundary conditions create delocalized bands corresponding to the lower total energy. We have seen that the ionic motion of the apical 0(4) oxygen generates large electronic changes,, eases 2:2 (and 1:3), where a group of 2 (or 3) Cu atoms have a total fluctuation of one electron in the d,: copper atomic shell. As a consequence we can say that 1) Valence fluctuations occur, both of a group and if intraatomie correlations dominate (they are not included in our analysis), also of a single atom, then an analysis of high Tc phenomenon suitable to be expressed in terms of valence fluctuations should be possible, as found in the literature, 2) But the presence of traveling ionic charges will also induce a bipolaron-like analysis as a possible scheme, moreover as the valence fluctuation can be enhanced by exchange correlation, the ion may become spin polarized and the bipolarons could also be magnetically coupled or antiferromagnetic coupling become also a possible scheme for an analysis. Nevertheless all of those schemes are not ~eparated from the basic phenomenon, that of strong vibronic coupling. This is the main conclusion of the simple but straight forward model calculation reported in this paper. REFERENCES
S.D. Conradson and I.D. Raistrick, Science 243 (1989) 1340. J. Mustre de Le6n, S.D. Conradson, I. Batisti6, and A.R. Bishop, Phys Rev. Let:. 65 (1990) 1675. P.B. Littlewood et al., Phys. Rev. Lett. 63 (1989) 2602. J. Keller, Physica C, 153-155 (1988) 1321. .,.t). ~UlllX'an el al. ~'nys. Rev. /J, 4~ (i993) 10638. V.N. I)enisov et al., Phys. Rev. B, 48 (1993) 16714. P. de !a Mora and C. de Teresa, Solid State Commtm. 70 (1989) 745-749.