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Role of reduction process in the transport properties of electron-doped oxide superconductors
iqlY" A ELSEVIER
Physica C 243 (1995) 319-326
Role of reduction process in the transport properties of electron-doped oxide superconductors J.E. Hirsch Department of Physics, University of California, San Diego, La Jolla, CA 92093-0319, USA Received 15 November 1994; revised manuscript received 5 December 1994
Abstract Electron-doped oxides such as Nd2_xCexCuO4 become metallic and superconducting only after annealing in a reducing atmosphere. Here we propose an explanation for this fact and discuss its implications for the understanding of the nature of the charge carders in these materials as well as in hole-doped oxide superconductors.
eCe doping
1. Introduction Electron-doped oxides such as Nd2_xCexCuO4 [ 1 ] become metallic and superconducting only after a reduction process that introduces oxygen vacancies. The reason for this is not understood. Here we propose an explanation for this fact, which has implications for the understanding of the nature of the charge carriers in these materials. In short, we propose that oxygen vacancies do not occur at random but preferentially in the neighborhood of Ce dopant atoms. We show that this implies in particular that hole carriers must exist in these electron-doped materials [ 2]. The way holes can be induced in these materials by electron doping is illustrated in Fig. 1 and will be discussed in more detail in the following sections.
2. Comparison of T' and T structures The T' structure in which these materials crystallize is characterized by having the oxygens near a given CuO2 plane located directly above and below the oxygens in the plane rather than the copper [ 1 ]. This 0921-4534/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSD10921-45 34 ( 94 ) 0 2 4 4 0 - 5
cu++
~
I result
cJ
o-
Fig. 1. Schematic depiction of how holes are created by electron doping. The electron added to Cu 2+ repels an electron from O 2- to the neighboring Cu 2 ÷, leaving behind a hole in oxygen ( O - ) .
absence of Cu apex oxygen is thought to be responsible for the fact that these materials are easily doped with electrons (which can go into planar Cu 2+ ions without experiencing the repulsion of nearby 0 2 - apex oxygen) but not with holes, unlike the 'hole-doped' oxide superconductors that always have apex oxygens in their structures [3,4]. Consider for comparison the hole-doped oxide Laz_xSrxCuO4 with the T structure, and the electrondoped oxide Nd2_xCexCuO4 with the T' structure. We use the structural parameters of Refs. [5,6] respectively: for the T structure, a = b = 3.779 ,~, c = 13.226
320
,I.E. Hirsch / Physica C 243 (1995) 319-326
•~,, Cu at (0, 0, 0), La at (0, 0, 0.3046c), 0 ( 2 ) (apex oxygen) at (0,o 0, 0.18240c);o for the T' structure, a = b = 3.9468 A, c = 12.0692 A, Cu at (0, 0, 0), Nd at (0, 0, 0.352360c) = (0, 0, z). The Madelung potentials [7] for planar Cu and O sites (denoted as O ( 1 ) ) , obtained by assuming the formal valences for all the ions involved, are: La2 _xSrxCuO4:
structure) are of order 2 and 1.4 eV respectively [ 10]. Note that transferring a hole from a Cu to an O site in the plane is equivalent to creating an electron-hole pair from the vacuum defined by Cu 2+ - O 2- ionic configurations. The absence of apex oxygens in the T' structure determines both the fact that these structures can be doped with electrons and that it should be relatively easy to create electron-hole pairs in them [2].
Uc, = - 28.63 eV,
(la)
Uo(l) =20.98 eV.
(lb)
3. Electron doping
Uc, = - 24.30 eV,
(2a)
Uo(1 ) =22.13 eV.
(2b)
In a tight binding description, the diagonal part of the Hamiltonian describing the holes in Cu d~2_y2 and O p(, orbitals is [ 11 ]
Nd2 - xCexCuO4:
The Madelung potentials are higher in the electrondoped oxide both at the Cu and O planar sites. This indicates that it will be more difficult to add holes to these planes but easier to add electrons, compared to the hole-doped materials. Furthermore, the difference in Madelung potentials between Cu and planar O sites [ 8] is larger in the holedoped than in the electron-doped materials. This measures the cost in energy in transferring a hole from Cu 2÷ to 0 2 - sites in the plane. In a simple ionic model this difference determines the 'charge transfer gap' A [9]:
Hdiag = E
( ~ d n d -]- ~dnp +[- Und't rid J,
+ Uvnp, npj, + Vndnp)
(5)
and the energy cost in transfering a hole from Cu to O, assuming all Cu sites are occupied by one hole, is A=Ep--~d+V.
(6)
Various estimates [ 11 ] have yielded ep - Ed ~ 2 - 4 eV for hole-doped oxides, and nearest-neighbor repulsion V of 1-2 eV. From the difference in Madelung potentials, Eq. (4) we conclude that it is reasonable to assume
e2
A = Uo(l) - Ucu - I c u ( 2 ) + A o ( 2 )
dcu-o(1) ,
(3)
with Ic. (2) the second ionization energy of Cu, Ao (2) the second electron affinity of O and dc.-o the Cu-O distance. The difference in charge transfer gaps in the two structures (ignoring the small variation in Cu-O distance between the two structures) is simply ALaSr -- ANdCe = ( U o ( l )
-- Ucu)LaS r
- (Uo(~) - UCu)NdC~,
(4)
which from Eqs. (1) and (2) is 3.18 eV. This is only a rough estimate, as screening and covalency effects also come into play. Nevertheless, Eq. (4) indicates that the cost in transferring a hole from Cu to O should be appreciably smaller in the T ' than in the T structure. This implies increased covalency in the T' structure which is also associated with the observed larger CuO bond distance [ 3 ]. Reported charge transfer gaps in La2_~SrxCu04 (T structure) and Nd2_xCe~CuO4 (T'
O<~A
(7)
in electron-doped oxides. This then implies that in the undoped material, the holes reside predominantly in the Cu sites, but upon electron doping when a hole is removed from a Cu-O plaquette, it becomes energetically favorable for a nearby Cu hole to move from Cu to O. The energy level structure is schematically shown in Fig. 2, and contrasted with the one in hole-doped oxides. The result of adding an electron to a Cu-O plaquette would then be removal of two holes from Cu E+ and creation of one hole in O 2- : le-
+ 2 C u 2+ + 0 2 -
~2Cu + +O- .
(8)
This description is only qualitative, as in the presence of Cu-O hybridization one can no longer talk about integer values of the occupations at the sites, but it illustrates the basic point: that in the region where an electron is added to a Cu-O plane there should be an appreciable contribution to the ground state wave func-
J.E. Hirsch / Physica C 243 (1995) 319-326
hole-doped
*
Cu ++ 0 =
electron-dooed
than the Ce concentration, by a factor of about 1.5. Let us consider in more detail what happens when a Nd 3+ ion is replaced by a Ce 3 ÷ ion. Relevant ionization energies are [ 13 ] :
cu++, * - + Cu++ 0 =
adda hole
Cu ++ O - C u
++
1
Cu ++
addanelectron
Cu +
O-
321
Cu +
Fig. 2. Schematic hole energy level structure of hole-doped (T structure) and electron-doped (T' structure ) materials. In the hole-doped material the oxygen level is a few eV above the Cu level. When a hole is added, it goes onto the O level to avoid the large on-site Coulomb repulsion on the Cu atom. In the electron-doped material the oxygen level is close to the Cu level, but near-neighbor Coulomb repulsion prevents a hole from moving into the O level; as an electron is added (hole is removed), the remaining hole can move onto the O level.
Ice(4) = 36.72 e V ,
(9a)
INn(3) = 22.06 e V ,
(9b)
Icu(2) = 20.29 eV.
(9c)
We will also need the Cu and O Madelung potentials given in Eq. (2), as well as the Nd Madelung potential UNd = --29.95 eV.
(10)
Will the Ce 3+ ion donate an extra electron, and if so where will it go? If it went to a nearby Nd 3÷ ion the energy cost would be e2
AE= Ice(4) --INd(3)
= 10.62 e V .
(11)
c e - N d
~
e Ce~+
Here we have used for the shortest Nd-Ce distance dc~_Nd=3.564 ,~=C(1--2Z), and the fact that the Madelung energy is the same at both sites. The cost Eq. ( 11 ) is large, so this process is not likely to occur. If the extra electron goes to a Cu site in a nearby plane, the energy cost is
doping
e2 Fig. 3. A configuration of donated electron and induced electronhole pair in CuO2 plane. All the bonds in the plaquette are equidistant to the Ce so that delocalization in the plaquette will occur.
AE= Ic~(4) - I c u ( 2 ) + UNd -- Ucu
tion of configurations where electron-hole pairs at neighboring Cu and O sites exist. In support of this picture it is found in x-ray absorption experiments in Nd:_xCexCuO4 [ 12] that the 'amount of electron doping' (as measured by the charge on Cu ions) is larger
with dce-cu = 3.31 t A. This is substantially smaller than Eq. ( 11 ). There is additional Coulomb energy gain if a neighboring electron-hole pair is induced as shown in Fig. 3 (the interatomic distances needed in what follows are summarized in Table 1):
dce-Cu
= 6.43 e V ,
( l 2) o
Table 1 lnteratomic distances (in ,~) between the various atoms with extra charges indicated in Fig. 5. At the top we give the atomic position in units of the lattice constants: a =3.9468 .~, c = 12.0692/~, z = 0.352360 Atom
Ce Cul O( 1) 0(2) Nd Cu2
Ce
Cul
O( 1)
0(2)
Nd
Cu2
(o,o,~-z)
(~,½,o)
(o,~,o)
(o, ½,-¼)
(.~, ' ' -~,z )
(o,o, _1)
0
3.311 0
2.659 1.973 0
5.189 3.605 3.017 0
6.649 4.253 4.688 2.328 0
7.816 6.649 6.349 3.605 3.311 0
,I.E. Hirsch/ Physica C 243 (1995) 319-326
322
AE(1)=e2 ( 1 +
~ + ~ dcu-o(,) dcu-cu
1 dc,,-Cu
) = -2.58 eV.
Eb(ehe)
(13)
do(~)_Ce
If this energy is smaller than the charge-transfer gap, the process will take place and result in a lowering of energy. Finally, further gain in energy will arise from delocalization of the charges in the plaquette, as all the Cu and O atoms are equidistant to the Ce atom. The simplest estimate for this effect yields AE (1) = - 4 t ,
e2
Eb(e) = ~ =4.35 eV, dcu-ce
(15)
which is appreciable, so it is likely to remain localized. If the charge-transfer gap is small enough that important ground state configurations have an induced electron-hole pair as shown in Fig. 3, the binding energy of an electron in this unit is =e
2 ( 1 -dcu-o(l)
+
- -1 dcu-ce
dc--~)
= 8.00 eV
(16a)
and the binding energy of the hole is: Eb(h) = e2 (~/ci
2(2
dcu-ce
do(j-)-ce
=3.28 eV. (16c)
Even though the entire unit has smaller binding energy than the individual charges, its effective mass should be substantially larger than that of the individual charges. These numbers indicate that the doped electron, as well as any induced electron-hole pairs, are likely to remain localized in the Cu-O plaquette adjacent to the Ce dopant. Experimentally it is found that Ce-doped samples remain non-metallic [1,3,4], confirming that these binding energies are sufficient to localize the charges.
(14)
with t the Cu--O hopping amplitude, estimated to be around 1 eV [ 11 ]. The combination of these effects makes it plausible to assume that it is favorable for Ce 3+ to donate one extra electron to a nearby Cu-O plane and turn into C e 4 +. The lattice constant a is found experimentally to expand slightly upon Ce doping [ 1], which is consistent with the assumption that electrons are being added to the already negatively charged CuO planes, as well as with band structure calculations that predict that electrons are added to the Cu-O antibonding part of the band [ 14]. We next consider the question whether the charges will delocalize, within the simple ionic model. Assume first one extra electron at the Cu atom, with no electronhole pair induced. Its binding energy is
Eb(e)
=e
(I)
1 ) =9.18 eV. (16b) do(t-)~ze
Finally, the binding energy of the entire unit is
4. O x y g e n r e m o v a l and hole delocalization
Next the samples are annealed in a reducing atmosphere, and oxygen is removed. From the difference in Madelung potentials between O(1) (Cu-O planes) and 0 ( 2 ) (out of plane oxygen) sites Uo(l) =22.13 eV,
(17a)
Uo(z) = 20.43 eV
(17b)
we conclude that the electrons in the 0 2- at the 0 ( 2 ) sites lose less energy by moving to other regions than those of the O( 1) sites; furthermore covalency is higher for the O(1) electrons. These facts imply that the oxygen atoms at the 0 ( 2 ) sites are less strongly bound than those at the O(1) sites, hence they are the ones that are likely to be removed in the reduction process. This is what is observed experimentally [ 15]. In addition, since Ce doping has broken translational invariance, we can be more specific as to which 0 ( 2 ) atoms are likely to be removed: the 0 ( 2 ) atoms on the other side of the Cu-O plaquette where the Ce electron was donated will have their energy raised by Coulomb repulsion of the extra negative charge nearby. The extra energy of such an O z- ion relative to one far away, if we assume an extra electron on Cu and no electronhole pair, is AE(O) =2e 2
u--oc2)
1
l
do(~)_c~
= 2.44 eV.
(18) If an electron-hole pair was induced, as in Fig. 3, the energy of that 0 2- is somewhat lower:
J.E. Hirsch / Physica C 243 (1995) 319-326
~
l
e
from a Ce is removed is e-t3ae(°); even for low concentration of Ce atoms this implies that essentially all the 0 ( 2 ) removed should be from the vicinity of Ce atoms. When such an 0 ( 2 ) atom leaves the sample, it will leave behind a doubly positively charged 0 ( 2 ) site relative to other 0 ( 2 ) sites, as indicated in Fig. 4. Assuming an induced electron-hole pair pre-exists in the Cu-O plaquette, the 0 ( 2 ) vacancy will exert a strong repulsion on this induced hole. The binding energy of the hole is now, instead of Eq. (16b):
localization
- ~ + Nd ~ ~
reducti°n
© Fig. 4. Upon reduction, the 0(2) atoms on the other side of the negatively charged CuO_, plaquette than the Ce ion are the most likely ones to be removed. The remaining doubly positive charge will repel the pre-existing or induced hole in the CuOz plaquette, causing it to delocalize.
AE(O) =2e 2
dc2 u2(2)
1
do(l)-O(2)
1 ) do(2~cc
=0.88 eV.
323
(19)
In either case it is positive, indicating that those 0 ( 2 ) atoms are the most likely to leave the sample upon reduction. More specifically, at temperature Tthe probability that one of these 0 ( 2 ) atoms will be removed relative to the probability that an 0 ( 2 ) atom far away
Eb(h)=e2(
2 dcu--7,( l )
1 do(, ,~c~
2
)
do(l) 0(2)
= - 0.36 eV
(20)
so that the hole is no longer bound, and will delocalize. Even if there was only a small amplitude in the ground state wave function for induced electron-hole pairs, the gain in energy by hole delocalization upon reduction would stabilize this configuration. Once the hole has delocalized, the binding energy of the remaining electrons is: Eb(e) = e
dcu~ce-
do(2)~u
=8.70 eV,
dc~-~cu (21)
which is even higher than the electron energy before the reduction process Eq. (16a) so that these electrons should remain localized.
~
Cu~ 'T)!+o(2)vacancy
Fig. 5. Charge distribution resulting from Ce doping and oxygen removal. One hole and one electron are likely to delocalize, as indicated in the figure by the dashed arrows. Distances between the labeled atoms are given in Table 1.
5. Electron delocalization
The above analysis indicates that hole carriers will be generated in a Ce-doped Nd2CuO 4 sample when oxygen is removed. Will electron carriers also exist? As discussed, the electrons in the Cu-O2 plaquette between the Ce dopant and the 0 ( 2 ) vacancy are likely to remain localized. However, we need to consider also the two electrons donated by the 02- ion when the 0 ( 2 ) is removed. The following is somewhat more speculative, as there are several possibilities. Due to repulsion from the negative charges in the Cu-O2 plaquette under consideration above, these electrons will tend to go away from that region. Let us consider the possibility that an electron goes to one of the Nd 3+ ions
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J.E. Hirsch / Physica C 243 (1995) 319-326
immediately below the 0 ( 2 ) vacancy in Fig. 5. Its energy from Madelung potential (Eq. (10) ) and ionization energy (Eq. (9b)) is E(Nd) = --INd(3) -- UNd =7.89 eV.
(22)
Its gain in Coulomb energy from interaction with the 0 ( 2 ) vacancy as well as the other extra charges in the system (Fig. 5) is found to be Ecou~(Nd) = - 8.67 eV.
(23)
On the other hand, if an electron goes to the Cu-O plane below, the Madelung potential Eq. (2a) and ionization energy Eq. (9c) yield an energy E(Cu) = - I c . ( 2 ) - Uc. =4.01 eV.
(24)
between the Ce and 0 ( 2 ) vacancy contribute to weaken the binding. In the presence of a substantial Cu-O hybridization ( ,-, 1 eV) this electron is likely to delocalize. The other electron, once the first delocalizes, has its binding energy substantially raised, to E~,(e) = 5.50 eV,
(28)
hence is likely to remain localized. In summary, the above analysis suggests that the outcome of doping with a Ce atom and of removing an 0 ( 2 ) oxygen is a single delocalized hole and a single delocalized electron, as well as three localized electrons. Electrons donated by C e 4+ that are not in the neighborhood of missing O(2)s are not expected to delocalize.
However, it is farther away from the O (2) vacancy and its Coulomb energy is only Ecoul(Cu) = - 5.50 eV.
(25)
When considering the two electrons we need to include also the Coulomb repulsion between them. One obtains for the total energies in the various cases: (i) Both electrons go to Nd ions (immediately below the 0 ( 2 ) vacancy in Fig. 5): E(Nd-Nd) = 2.09 eV.
(26a)
(ii) One electron goes to Nd, one to Cu: E(Nd-Cu) = 2.08 eV.
(26b)
(iii) Both electrons go to Cu: E(Cu-Cu) = 0.866 eV
(26c)
so that the last possibility is favored, particularly since these electrons have their energy further lowered by covalency. The resulting charge configuration is shown in Fig. 5. Will these electrons delocalize? The sum of Coulomb interactions with all the other extra charges yields for the binding energy of the less tightly bound of these electrons Eb(e) = 1.65 eV,
(27)
which is substantially less than the binding energy in the previous case where the electron was donated from Ce (Eq. 15 or 16a). This is because the donor here (the 0 ( 2 ) site) is further away from the Cu-O plane, and because two rather than one electron are involved. Furthermore, the localized electrons in the Cu-O plaquette
6. Implications If the phenomenology described above is correct, both hole and electron carriers should be generated in approximately equal numbers in reduced electrondoped samples. Will these carriers annihilate each other leading again to a non-metallic system? This will not occur if the carriers propagate in different bands, an electron and a hole band. The electron band is likely to be the usual Cu d~2_yr-O p,~ band [16], while the whole band should only involve oxygen orbitals. The possibility of hole conduction in a purely oxygen band arising from overlap of oxygen p~ orbitals in holedoped oxides was considered long ago [17-19] .The model of hole superconductivity [ 20] postulates that superconductivity in high-To oxides is driven by oxygen hole carriers in such a band, orthogonal to the conventional Cu-Op,~ band. When electron-doped oxide superconductors were discovered we proposed that a two-band model (a hole band and an electron band) should describe the transport properties of these materials [2]. At the time there was not much experimental support for this proposal, as experiments appeared to indicate that electrons were the only charge carriers [21]. However subsequent detailed experimental studies [22-25] independently found strong evidence for the existence of two-band conduction in these materials. In addition it was found in the experimental studies [22,24] that a positive contribution to the Hall coefficient at low temperatures, indicative of hole carriers, always exists in the samples that go super-
325
J.E. Hirsch/ Physica C 243 (1995) 319-326
conducting. These findings are consistent with the interpretation of the doping and reduction processes discussed here, as well as with the prediction of the model of hole superconductivity. It should also be noted that this model predicts [20] maximum Tc for hole concentration of 0.04-0.05 per planar oxygen, consistent with the reported value of y ~ 0.04 for optimal oxygen deficiency in Nd2_xCexCuO4_y and the analysis here suggesting that one hole carrier per O (2) vacancy is generated. However, it should also be pointed out that another model for electron-doped materials has been discussed in the literature [ 26], that predicted the existence of an electron and a hole band before the experiments suggested this. In this model the two bands arise from a superlattice structure that gives rise to two inequivalent Cu sites [26]. As the number of dopants and oxygen vacancies increases the situation becomes more complicated, as the possibility of more than one O vacancy or dopant atom in a given region increases. Furthermore, increased disorder results from doping, vacancies and the localized charges discussed above. Experiments [24] suggest that as increasing oxygen is removed for fixed Ce concentration the electron carriers localize, leaving only hole carriers. This could be interpreted within the model discussed here as due to the fact that the localized electrons resulting from the doping and reduction processes will interfere more with conduction in the Cu-O band than in the orthogonal oxygen p~ band. As reduction is further increased it is found that hole carriers eventually also disappear, presumably by being 'plugged' by the added electrons. This suggests that the properties of the system under increasing oxygen removal should parallel the behavior of holedoped oxides as the number of holes decreases in the underdoped regime. Concerning the disappearance of superconductivity with increasing Ce doping [ l] it is unclear whether it is due to an excess number of holes (overdoped regime as in the hole-doped oxides) or also to plugging of holes by excess electrons.
7. Conclusions and s u m m a r y
The analysis in this paper predicts that in reduced electron-doped superconducting samples such as Nd2_xCexCuO4_y there should be a correlation
between the location of the dopant atoms and the location of the missing oxygens, as depicted in Fig. 5. Furthermore, localized negative charges should exist as shown in Fig. 5. This prediction may be experimentally testable by probes that are sensitive to the local environment of the atoms in the crystal such as NQR. For example, for some of those signals where a shift is seen under Ce doping a further shift should be seen under reduction indicating that the local environment is again changing. In the absence of correlation such additional shift should not occur for low amounts of doping and reduction. It has been reported that superconductivity in Nd2CuO4 can also be induced without oxygen deficiency by substitution of oxygen by fluorine, i.e. in Nd2CuO4_xFx [27]. This is not necessarily inconsistent with the analysis presented here. Substitution of 0 2 - by F - will also donate one electron, similarly to Ce doping; however the F - ion ( presumably at a O (2) site) is located further away from the Cu-O planes, and hence the F - impurity should be less effective in localizing the charges than the Ce 4+ impurity. It should also be mentioned that another explanation for the role of the reduction process in electron-doped oxides has been proposed before: [28] that in fact the as-prepared samples contain excess interstitial oxygen that localizes the doped electrons, and these oxygens are the ones being removed upon reduction. The model discussed here instead assumes no excess oxygen before reduction. In summary, the main consequence of our analysis is that delocalized oxygen holes are induced by the doping and reduction processes. The key condition for this to occur is the relation between interatomic distances 1
dc~-o~t)
+
2
2
do
dcu-o(l)
(29)
which causes the binding energy of an induced oxygen hole in the configuration of Fig. 4 to essentially vanish, thus allowing it to delocalize. In that case delocalization will occur even if the band where the hole propagates, the oxygen p~ band, is very narrow as expected in the model of hole superconductivity [20]. This scenario has consequences that go beyond the class of electron-doped materials. Let us assume that indeed as the recent experiments suggest conduction in electron-doped materials occurs through both an elec-
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J.E. Hirsch/ Physica C 243 (1995) 319-326
tron and a hole band [22-25 ], and it is the existence of hole carriers that is directly associated with the occurrence of superconductivity. It is reasonable to conclude as discussed above that electrons conduct in a Cu dx2_y2--O p,~ band and holes in an O p,, band arising from the planar oxygen p,~ orbitals perpendicular to the C u - O bonds. If as suggested by the experiments [22,24] the hole-like carriers in electron-doped materials are of similar nature as in the hole-doped materials, it would imply that in hole-doped materials also doped holes become carriers in the O p,~ band rather than in the C u - O po band as generally assumed. In support of this interpretation it should be noted that recent NMR experiments in La2_xSr~CuO4 [ 29] appear to be inconsistent with a one-band description of this material and also suggest the existence of a purely 'oxygen band' in that system. If superconductivity is indeed caused by holes conducting in an oxygen p , band in both hole- and electron-doped oxides, what are the implications with respect to mechanisms? In the early theories that assumed conduction of hole carriers in such a band [ 17-19] it was proposed that superconductivity would be driven by either spin or charge excitations of the holes in the Cu 2 ÷ background. However, in the electron-doped materials this background is rapidly being destroyed by the added and induced electrons that turn Cu 2+ into Cu +. This would argue against such mechanisms to explain the superconductivity, and instead support mechanisms that depend solely on the dynamics of the carriers in the oxygen p~ band, as proposed in the model of hole superconductivity.
Acknowledgements The author is grateful to L. Garwin for stimulating correspondence.
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[2] J.E. Hirsch, Electron Superconductivityin Oxides?, UCSD Report, March 2, 1989 (unpublished);MRS Symp. Proc. 156 (1989) 349; J.E. Hirsch and F. Marsiglio, Phys. Lett. A 140 (1989) 122; Physica C 162-164 (1989) 591. [3] Y. Tokura,JJAP Ser. 7 (1992) 14, and referencestherein. [4l C.C. Almasan and M.B. Maple, Chemistry of High Temperature Superconductors, ed. C.N.R. Rao (World Scientific,Singapore, 1991), and referencestherein. [5] R.A. Cavaet al., Phys. Rev. B 35 (1987) 6716. [6] T. Kamimayaet al., PhysicaC 229 (1994) 377. [7] J. Kondo,Y. Asai and S. Nagi, J. Phys. Soc. Jpn. 57 (1988) 4334. [8] J.B. Torrance and R.M. Metzger, Phys. Rev. Lett. 63 (1989) 1515. [9] Y. Ohta and S. Maekawa, Phys. Rev. B 41 (1990) 6524. [ 10] Y. Ohta, T. Tohyama and S. Maekawa, Phys. Rev. Lett. 66 (1991) 1228. [ 11] F. Mila, Phys. Rev. B 38 (1988) 11358; E.B. Stecheland D.R. Jennison,Phys. Rev. B 38 (1988) 4632; A.K. McMahan,J.F. Annettand R.M. Martin,Phys. Rev. B 42 (1990) 6268. [ 12] E.E. Alp et al., Phys. Rev. B 40 (1989) 2617. [ ! 3] L.H. Ahrens,IonizationPotentials(Pergamon,Oxford, 1983). [ 14] S. Massidaet al., PhysicaC 157 (1989) 571. [ 15] F. Izumiet al., PhysicaC 158 (1989) 433. [ 16] It may appear that electronsadded to the half-filledCu-O band should give rise to hole rather than electron carders [14]; however, in a lightlydoped Mottinsulatorthe' 'band structure" interpretation of the nature of the charge carders (whether electronor hole) is expectedto be inveerted:H.E. Castilloand C.A. Balseiro, Phys. Rev. Lett. 68 (1992) 121; A.G. Rojo, G. Kotliar and G.S. Canright, Phys, Rev. B 47 (1993) 9240. [ 17] Y. Guo,J.M. LangloisandW.A.Goddard,Science239 ( 1988) 896. [181 A. Aharony, R.J. Birgeneau, A. Coniglio,M.A. Kastner and H.E. Stanley,Phys. Rev. Lett. 60 (1988) 1330. [ 19] M. Ogata and H. Shiba, J. Phys. Soc. Jpn. 57 (1988) 3074. [20] J.E. Hirsch and F. Marsiglio,Phys. Rev. B 39 (1989) 11515; 43 (1991) 424; F. Marsiglioand J.E. Hirsch, Phys. Rev. B 41 (1990) 6435; J.E. Hirsch and S. Tang,SolidState Commun.69 (1989) 987. J.E. Hirsch, Phys. Rev. B 48 (1993) 9815. [21] See e.g.R. Pohl, Science243 (1989) 1436. [22] Z.Z. Wanget al., Phys. Rev. B 43 ( 1991) 3020. [23] M.A. Crusellaset al., PhysicaC 210 (1993) 221. [24] Wu Jiang et al., Phys. Rev. Lett. 73 (1994) 1291. [25] M. Suzukiet al., Phys. Rev. B 50 (1994) 9434. [26] N.C. Baird and J.K. Burdett, PhysicaC 168 (1990) 637. [27] A.C.W.P.James, S.M. Zahurakand D.W. Murphy,Nature338 (1989) 240. 1281 Wu Jiang et al., Phys. Rev. B 47 (1993) 8151. [29] R.E. Walstedt,B.S. Shastryand S.W. Cbeong,Phys. Rev.Lett. 72 (1994) 3610; R.E. Walstedtand S.W.Cheong,Phys.Rev. B, to be published.
Physica C 243 (1995) 319-326
Role of reduction process in the transport properties of electron-doped oxide superconductors J.E. Hirsch Department of Physics, University of California, San Diego, La Jolla, CA 92093-0319, USA Received 15 November 1994; revised manuscript received 5 December 1994
Abstract Electron-doped oxides such as Nd2_xCexCuO4 become metallic and superconducting only after annealing in a reducing atmosphere. Here we propose an explanation for this fact and discuss its implications for the understanding of the nature of the charge carders in these materials as well as in hole-doped oxide superconductors.
eCe doping
1. Introduction Electron-doped oxides such as Nd2_xCexCuO4 [ 1 ] become metallic and superconducting only after a reduction process that introduces oxygen vacancies. The reason for this is not understood. Here we propose an explanation for this fact, which has implications for the understanding of the nature of the charge carriers in these materials. In short, we propose that oxygen vacancies do not occur at random but preferentially in the neighborhood of Ce dopant atoms. We show that this implies in particular that hole carriers must exist in these electron-doped materials [ 2]. The way holes can be induced in these materials by electron doping is illustrated in Fig. 1 and will be discussed in more detail in the following sections.
2. Comparison of T' and T structures The T' structure in which these materials crystallize is characterized by having the oxygens near a given CuO2 plane located directly above and below the oxygens in the plane rather than the copper [ 1 ]. This 0921-4534/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSD10921-45 34 ( 94 ) 0 2 4 4 0 - 5
cu++
~
I result
cJ
o-
Fig. 1. Schematic depiction of how holes are created by electron doping. The electron added to Cu 2+ repels an electron from O 2- to the neighboring Cu 2 ÷, leaving behind a hole in oxygen ( O - ) .
absence of Cu apex oxygen is thought to be responsible for the fact that these materials are easily doped with electrons (which can go into planar Cu 2+ ions without experiencing the repulsion of nearby 0 2 - apex oxygen) but not with holes, unlike the 'hole-doped' oxide superconductors that always have apex oxygens in their structures [3,4]. Consider for comparison the hole-doped oxide Laz_xSrxCuO4 with the T structure, and the electrondoped oxide Nd2_xCexCuO4 with the T' structure. We use the structural parameters of Refs. [5,6] respectively: for the T structure, a = b = 3.779 ,~, c = 13.226
320
,I.E. Hirsch / Physica C 243 (1995) 319-326
•~,, Cu at (0, 0, 0), La at (0, 0, 0.3046c), 0 ( 2 ) (apex oxygen) at (0,o 0, 0.18240c);o for the T' structure, a = b = 3.9468 A, c = 12.0692 A, Cu at (0, 0, 0), Nd at (0, 0, 0.352360c) = (0, 0, z). The Madelung potentials [7] for planar Cu and O sites (denoted as O ( 1 ) ) , obtained by assuming the formal valences for all the ions involved, are: La2 _xSrxCuO4:
structure) are of order 2 and 1.4 eV respectively [ 10]. Note that transferring a hole from a Cu to an O site in the plane is equivalent to creating an electron-hole pair from the vacuum defined by Cu 2+ - O 2- ionic configurations. The absence of apex oxygens in the T' structure determines both the fact that these structures can be doped with electrons and that it should be relatively easy to create electron-hole pairs in them [2].
Uc, = - 28.63 eV,
(la)
Uo(l) =20.98 eV.
(lb)
3. Electron doping
Uc, = - 24.30 eV,
(2a)
Uo(1 ) =22.13 eV.
(2b)
In a tight binding description, the diagonal part of the Hamiltonian describing the holes in Cu d~2_y2 and O p(, orbitals is [ 11 ]
Nd2 - xCexCuO4:
The Madelung potentials are higher in the electrondoped oxide both at the Cu and O planar sites. This indicates that it will be more difficult to add holes to these planes but easier to add electrons, compared to the hole-doped materials. Furthermore, the difference in Madelung potentials between Cu and planar O sites [ 8] is larger in the holedoped than in the electron-doped materials. This measures the cost in energy in transferring a hole from Cu 2÷ to 0 2 - sites in the plane. In a simple ionic model this difference determines the 'charge transfer gap' A [9]:
Hdiag = E
( ~ d n d -]- ~dnp +[- Und't rid J,
+ Uvnp, npj, + Vndnp)
(5)
and the energy cost in transfering a hole from Cu to O, assuming all Cu sites are occupied by one hole, is A=Ep--~d+V.
(6)
Various estimates [ 11 ] have yielded ep - Ed ~ 2 - 4 eV for hole-doped oxides, and nearest-neighbor repulsion V of 1-2 eV. From the difference in Madelung potentials, Eq. (4) we conclude that it is reasonable to assume
e2
A = Uo(l) - Ucu - I c u ( 2 ) + A o ( 2 )
dcu-o(1) ,
(3)
with Ic. (2) the second ionization energy of Cu, Ao (2) the second electron affinity of O and dc.-o the Cu-O distance. The difference in charge transfer gaps in the two structures (ignoring the small variation in Cu-O distance between the two structures) is simply ALaSr -- ANdCe = ( U o ( l )
-- Ucu)LaS r
- (Uo(~) - UCu)NdC~,
(4)
which from Eqs. (1) and (2) is 3.18 eV. This is only a rough estimate, as screening and covalency effects also come into play. Nevertheless, Eq. (4) indicates that the cost in transferring a hole from Cu to O should be appreciably smaller in the T ' than in the T structure. This implies increased covalency in the T' structure which is also associated with the observed larger CuO bond distance [ 3 ]. Reported charge transfer gaps in La2_~SrxCu04 (T structure) and Nd2_xCe~CuO4 (T'
O<~A
(7)
in electron-doped oxides. This then implies that in the undoped material, the holes reside predominantly in the Cu sites, but upon electron doping when a hole is removed from a Cu-O plaquette, it becomes energetically favorable for a nearby Cu hole to move from Cu to O. The energy level structure is schematically shown in Fig. 2, and contrasted with the one in hole-doped oxides. The result of adding an electron to a Cu-O plaquette would then be removal of two holes from Cu E+ and creation of one hole in O 2- : le-
+ 2 C u 2+ + 0 2 -
~2Cu + +O- .
(8)
This description is only qualitative, as in the presence of Cu-O hybridization one can no longer talk about integer values of the occupations at the sites, but it illustrates the basic point: that in the region where an electron is added to a Cu-O plane there should be an appreciable contribution to the ground state wave func-
J.E. Hirsch / Physica C 243 (1995) 319-326
hole-doped
*
Cu ++ 0 =
electron-dooed
than the Ce concentration, by a factor of about 1.5. Let us consider in more detail what happens when a Nd 3+ ion is replaced by a Ce 3 ÷ ion. Relevant ionization energies are [ 13 ] :
cu++, * - + Cu++ 0 =
adda hole
Cu ++ O - C u
++
1
Cu ++
addanelectron
Cu +
O-
321
Cu +
Fig. 2. Schematic hole energy level structure of hole-doped (T structure) and electron-doped (T' structure ) materials. In the hole-doped material the oxygen level is a few eV above the Cu level. When a hole is added, it goes onto the O level to avoid the large on-site Coulomb repulsion on the Cu atom. In the electron-doped material the oxygen level is close to the Cu level, but near-neighbor Coulomb repulsion prevents a hole from moving into the O level; as an electron is added (hole is removed), the remaining hole can move onto the O level.
Ice(4) = 36.72 e V ,
(9a)
INn(3) = 22.06 e V ,
(9b)
Icu(2) = 20.29 eV.
(9c)
We will also need the Cu and O Madelung potentials given in Eq. (2), as well as the Nd Madelung potential UNd = --29.95 eV.
(10)
Will the Ce 3+ ion donate an extra electron, and if so where will it go? If it went to a nearby Nd 3÷ ion the energy cost would be e2
AE= Ice(4) --INd(3)
= 10.62 e V .
(11)
c e - N d
~
e Ce~+
Here we have used for the shortest Nd-Ce distance dc~_Nd=3.564 ,~=C(1--2Z), and the fact that the Madelung energy is the same at both sites. The cost Eq. ( 11 ) is large, so this process is not likely to occur. If the extra electron goes to a Cu site in a nearby plane, the energy cost is
doping
e2 Fig. 3. A configuration of donated electron and induced electronhole pair in CuO2 plane. All the bonds in the plaquette are equidistant to the Ce so that delocalization in the plaquette will occur.
AE= Ic~(4) - I c u ( 2 ) + UNd -- Ucu
tion of configurations where electron-hole pairs at neighboring Cu and O sites exist. In support of this picture it is found in x-ray absorption experiments in Nd:_xCexCuO4 [ 12] that the 'amount of electron doping' (as measured by the charge on Cu ions) is larger
with dce-cu = 3.31 t A. This is substantially smaller than Eq. ( 11 ). There is additional Coulomb energy gain if a neighboring electron-hole pair is induced as shown in Fig. 3 (the interatomic distances needed in what follows are summarized in Table 1):
dce-Cu
= 6.43 e V ,
( l 2) o
Table 1 lnteratomic distances (in ,~) between the various atoms with extra charges indicated in Fig. 5. At the top we give the atomic position in units of the lattice constants: a =3.9468 .~, c = 12.0692/~, z = 0.352360 Atom
Ce Cul O( 1) 0(2) Nd Cu2
Ce
Cul
O( 1)
0(2)
Nd
Cu2
(o,o,~-z)
(~,½,o)
(o,~,o)
(o, ½,-¼)
(.~, ' ' -~,z )
(o,o, _1)
0
3.311 0
2.659 1.973 0
5.189 3.605 3.017 0
6.649 4.253 4.688 2.328 0
7.816 6.649 6.349 3.605 3.311 0
,I.E. Hirsch/ Physica C 243 (1995) 319-326
322
AE(1)=e2 ( 1 +
~ + ~ dcu-o(,) dcu-cu
1 dc,,-Cu
) = -2.58 eV.
Eb(ehe)
(13)
do(~)_Ce
If this energy is smaller than the charge-transfer gap, the process will take place and result in a lowering of energy. Finally, further gain in energy will arise from delocalization of the charges in the plaquette, as all the Cu and O atoms are equidistant to the Ce atom. The simplest estimate for this effect yields AE (1) = - 4 t ,
e2
Eb(e) = ~ =4.35 eV, dcu-ce
(15)
which is appreciable, so it is likely to remain localized. If the charge-transfer gap is small enough that important ground state configurations have an induced electron-hole pair as shown in Fig. 3, the binding energy of an electron in this unit is =e
2 ( 1 -dcu-o(l)
+
- -1 dcu-ce
dc--~)
= 8.00 eV
(16a)
and the binding energy of the hole is: Eb(h) = e2 (~/ci
2(2
dcu-ce
do(j-)-ce
=3.28 eV. (16c)
Even though the entire unit has smaller binding energy than the individual charges, its effective mass should be substantially larger than that of the individual charges. These numbers indicate that the doped electron, as well as any induced electron-hole pairs, are likely to remain localized in the Cu-O plaquette adjacent to the Ce dopant. Experimentally it is found that Ce-doped samples remain non-metallic [1,3,4], confirming that these binding energies are sufficient to localize the charges.
(14)
with t the Cu--O hopping amplitude, estimated to be around 1 eV [ 11 ]. The combination of these effects makes it plausible to assume that it is favorable for Ce 3+ to donate one extra electron to a nearby Cu-O plane and turn into C e 4 +. The lattice constant a is found experimentally to expand slightly upon Ce doping [ 1], which is consistent with the assumption that electrons are being added to the already negatively charged CuO planes, as well as with band structure calculations that predict that electrons are added to the Cu-O antibonding part of the band [ 14]. We next consider the question whether the charges will delocalize, within the simple ionic model. Assume first one extra electron at the Cu atom, with no electronhole pair induced. Its binding energy is
Eb(e)
=e
(I)
1 ) =9.18 eV. (16b) do(t-)~ze
Finally, the binding energy of the entire unit is
4. O x y g e n r e m o v a l and hole delocalization
Next the samples are annealed in a reducing atmosphere, and oxygen is removed. From the difference in Madelung potentials between O(1) (Cu-O planes) and 0 ( 2 ) (out of plane oxygen) sites Uo(l) =22.13 eV,
(17a)
Uo(z) = 20.43 eV
(17b)
we conclude that the electrons in the 0 2- at the 0 ( 2 ) sites lose less energy by moving to other regions than those of the O( 1) sites; furthermore covalency is higher for the O(1) electrons. These facts imply that the oxygen atoms at the 0 ( 2 ) sites are less strongly bound than those at the O(1) sites, hence they are the ones that are likely to be removed in the reduction process. This is what is observed experimentally [ 15]. In addition, since Ce doping has broken translational invariance, we can be more specific as to which 0 ( 2 ) atoms are likely to be removed: the 0 ( 2 ) atoms on the other side of the Cu-O plaquette where the Ce electron was donated will have their energy raised by Coulomb repulsion of the extra negative charge nearby. The extra energy of such an O z- ion relative to one far away, if we assume an extra electron on Cu and no electronhole pair, is AE(O) =2e 2
u--oc2)
1
l
do(~)_c~
= 2.44 eV.
(18) If an electron-hole pair was induced, as in Fig. 3, the energy of that 0 2- is somewhat lower:
J.E. Hirsch / Physica C 243 (1995) 319-326
~
l
e
from a Ce is removed is e-t3ae(°); even for low concentration of Ce atoms this implies that essentially all the 0 ( 2 ) removed should be from the vicinity of Ce atoms. When such an 0 ( 2 ) atom leaves the sample, it will leave behind a doubly positively charged 0 ( 2 ) site relative to other 0 ( 2 ) sites, as indicated in Fig. 4. Assuming an induced electron-hole pair pre-exists in the Cu-O plaquette, the 0 ( 2 ) vacancy will exert a strong repulsion on this induced hole. The binding energy of the hole is now, instead of Eq. (16b):
localization
- ~ + Nd ~ ~
reducti°n
© Fig. 4. Upon reduction, the 0(2) atoms on the other side of the negatively charged CuO_, plaquette than the Ce ion are the most likely ones to be removed. The remaining doubly positive charge will repel the pre-existing or induced hole in the CuOz plaquette, causing it to delocalize.
AE(O) =2e 2
dc2 u2(2)
1
do(l)-O(2)
1 ) do(2~cc
=0.88 eV.
323
(19)
In either case it is positive, indicating that those 0 ( 2 ) atoms are the most likely to leave the sample upon reduction. More specifically, at temperature Tthe probability that one of these 0 ( 2 ) atoms will be removed relative to the probability that an 0 ( 2 ) atom far away
Eb(h)=e2(
2 dcu--7,( l )
1 do(, ,~c~
2
)
do(l) 0(2)
= - 0.36 eV
(20)
so that the hole is no longer bound, and will delocalize. Even if there was only a small amplitude in the ground state wave function for induced electron-hole pairs, the gain in energy by hole delocalization upon reduction would stabilize this configuration. Once the hole has delocalized, the binding energy of the remaining electrons is: Eb(e) = e
dcu~ce-
do(2)~u
=8.70 eV,
dc~-~cu (21)
which is even higher than the electron energy before the reduction process Eq. (16a) so that these electrons should remain localized.
~
Cu~ 'T)!+o(2)vacancy
Fig. 5. Charge distribution resulting from Ce doping and oxygen removal. One hole and one electron are likely to delocalize, as indicated in the figure by the dashed arrows. Distances between the labeled atoms are given in Table 1.
5. Electron delocalization
The above analysis indicates that hole carriers will be generated in a Ce-doped Nd2CuO 4 sample when oxygen is removed. Will electron carriers also exist? As discussed, the electrons in the Cu-O2 plaquette between the Ce dopant and the 0 ( 2 ) vacancy are likely to remain localized. However, we need to consider also the two electrons donated by the 02- ion when the 0 ( 2 ) is removed. The following is somewhat more speculative, as there are several possibilities. Due to repulsion from the negative charges in the Cu-O2 plaquette under consideration above, these electrons will tend to go away from that region. Let us consider the possibility that an electron goes to one of the Nd 3+ ions
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J.E. Hirsch / Physica C 243 (1995) 319-326
immediately below the 0 ( 2 ) vacancy in Fig. 5. Its energy from Madelung potential (Eq. (10) ) and ionization energy (Eq. (9b)) is E(Nd) = --INd(3) -- UNd =7.89 eV.
(22)
Its gain in Coulomb energy from interaction with the 0 ( 2 ) vacancy as well as the other extra charges in the system (Fig. 5) is found to be Ecou~(Nd) = - 8.67 eV.
(23)
On the other hand, if an electron goes to the Cu-O plane below, the Madelung potential Eq. (2a) and ionization energy Eq. (9c) yield an energy E(Cu) = - I c . ( 2 ) - Uc. =4.01 eV.
(24)
between the Ce and 0 ( 2 ) vacancy contribute to weaken the binding. In the presence of a substantial Cu-O hybridization ( ,-, 1 eV) this electron is likely to delocalize. The other electron, once the first delocalizes, has its binding energy substantially raised, to E~,(e) = 5.50 eV,
(28)
hence is likely to remain localized. In summary, the above analysis suggests that the outcome of doping with a Ce atom and of removing an 0 ( 2 ) oxygen is a single delocalized hole and a single delocalized electron, as well as three localized electrons. Electrons donated by C e 4+ that are not in the neighborhood of missing O(2)s are not expected to delocalize.
However, it is farther away from the O (2) vacancy and its Coulomb energy is only Ecoul(Cu) = - 5.50 eV.
(25)
When considering the two electrons we need to include also the Coulomb repulsion between them. One obtains for the total energies in the various cases: (i) Both electrons go to Nd ions (immediately below the 0 ( 2 ) vacancy in Fig. 5): E(Nd-Nd) = 2.09 eV.
(26a)
(ii) One electron goes to Nd, one to Cu: E(Nd-Cu) = 2.08 eV.
(26b)
(iii) Both electrons go to Cu: E(Cu-Cu) = 0.866 eV
(26c)
so that the last possibility is favored, particularly since these electrons have their energy further lowered by covalency. The resulting charge configuration is shown in Fig. 5. Will these electrons delocalize? The sum of Coulomb interactions with all the other extra charges yields for the binding energy of the less tightly bound of these electrons Eb(e) = 1.65 eV,
(27)
which is substantially less than the binding energy in the previous case where the electron was donated from Ce (Eq. 15 or 16a). This is because the donor here (the 0 ( 2 ) site) is further away from the Cu-O plane, and because two rather than one electron are involved. Furthermore, the localized electrons in the Cu-O plaquette
6. Implications If the phenomenology described above is correct, both hole and electron carriers should be generated in approximately equal numbers in reduced electrondoped samples. Will these carriers annihilate each other leading again to a non-metallic system? This will not occur if the carriers propagate in different bands, an electron and a hole band. The electron band is likely to be the usual Cu d~2_yr-O p,~ band [16], while the whole band should only involve oxygen orbitals. The possibility of hole conduction in a purely oxygen band arising from overlap of oxygen p~ orbitals in holedoped oxides was considered long ago [17-19] .The model of hole superconductivity [ 20] postulates that superconductivity in high-To oxides is driven by oxygen hole carriers in such a band, orthogonal to the conventional Cu-Op,~ band. When electron-doped oxide superconductors were discovered we proposed that a two-band model (a hole band and an electron band) should describe the transport properties of these materials [2]. At the time there was not much experimental support for this proposal, as experiments appeared to indicate that electrons were the only charge carriers [21]. However subsequent detailed experimental studies [22-25] independently found strong evidence for the existence of two-band conduction in these materials. In addition it was found in the experimental studies [22,24] that a positive contribution to the Hall coefficient at low temperatures, indicative of hole carriers, always exists in the samples that go super-
325
J.E. Hirsch/ Physica C 243 (1995) 319-326
conducting. These findings are consistent with the interpretation of the doping and reduction processes discussed here, as well as with the prediction of the model of hole superconductivity. It should also be noted that this model predicts [20] maximum Tc for hole concentration of 0.04-0.05 per planar oxygen, consistent with the reported value of y ~ 0.04 for optimal oxygen deficiency in Nd2_xCexCuO4_y and the analysis here suggesting that one hole carrier per O (2) vacancy is generated. However, it should also be pointed out that another model for electron-doped materials has been discussed in the literature [ 26], that predicted the existence of an electron and a hole band before the experiments suggested this. In this model the two bands arise from a superlattice structure that gives rise to two inequivalent Cu sites [26]. As the number of dopants and oxygen vacancies increases the situation becomes more complicated, as the possibility of more than one O vacancy or dopant atom in a given region increases. Furthermore, increased disorder results from doping, vacancies and the localized charges discussed above. Experiments [24] suggest that as increasing oxygen is removed for fixed Ce concentration the electron carriers localize, leaving only hole carriers. This could be interpreted within the model discussed here as due to the fact that the localized electrons resulting from the doping and reduction processes will interfere more with conduction in the Cu-O band than in the orthogonal oxygen p~ band. As reduction is further increased it is found that hole carriers eventually also disappear, presumably by being 'plugged' by the added electrons. This suggests that the properties of the system under increasing oxygen removal should parallel the behavior of holedoped oxides as the number of holes decreases in the underdoped regime. Concerning the disappearance of superconductivity with increasing Ce doping [ l] it is unclear whether it is due to an excess number of holes (overdoped regime as in the hole-doped oxides) or also to plugging of holes by excess electrons.
7. Conclusions and s u m m a r y
The analysis in this paper predicts that in reduced electron-doped superconducting samples such as Nd2_xCexCuO4_y there should be a correlation
between the location of the dopant atoms and the location of the missing oxygens, as depicted in Fig. 5. Furthermore, localized negative charges should exist as shown in Fig. 5. This prediction may be experimentally testable by probes that are sensitive to the local environment of the atoms in the crystal such as NQR. For example, for some of those signals where a shift is seen under Ce doping a further shift should be seen under reduction indicating that the local environment is again changing. In the absence of correlation such additional shift should not occur for low amounts of doping and reduction. It has been reported that superconductivity in Nd2CuO4 can also be induced without oxygen deficiency by substitution of oxygen by fluorine, i.e. in Nd2CuO4_xFx [27]. This is not necessarily inconsistent with the analysis presented here. Substitution of 0 2 - by F - will also donate one electron, similarly to Ce doping; however the F - ion ( presumably at a O (2) site) is located further away from the Cu-O planes, and hence the F - impurity should be less effective in localizing the charges than the Ce 4+ impurity. It should also be mentioned that another explanation for the role of the reduction process in electron-doped oxides has been proposed before: [28] that in fact the as-prepared samples contain excess interstitial oxygen that localizes the doped electrons, and these oxygens are the ones being removed upon reduction. The model discussed here instead assumes no excess oxygen before reduction. In summary, the main consequence of our analysis is that delocalized oxygen holes are induced by the doping and reduction processes. The key condition for this to occur is the relation between interatomic distances 1
dc~-o~t)
+
2
2
do
dcu-o(l)
(29)
which causes the binding energy of an induced oxygen hole in the configuration of Fig. 4 to essentially vanish, thus allowing it to delocalize. In that case delocalization will occur even if the band where the hole propagates, the oxygen p~ band, is very narrow as expected in the model of hole superconductivity [20]. This scenario has consequences that go beyond the class of electron-doped materials. Let us assume that indeed as the recent experiments suggest conduction in electron-doped materials occurs through both an elec-
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J.E. Hirsch/ Physica C 243 (1995) 319-326
tron and a hole band [22-25 ], and it is the existence of hole carriers that is directly associated with the occurrence of superconductivity. It is reasonable to conclude as discussed above that electrons conduct in a Cu dx2_y2--O p,~ band and holes in an O p,, band arising from the planar oxygen p,~ orbitals perpendicular to the C u - O bonds. If as suggested by the experiments [22,24] the hole-like carriers in electron-doped materials are of similar nature as in the hole-doped materials, it would imply that in hole-doped materials also doped holes become carriers in the O p,~ band rather than in the C u - O po band as generally assumed. In support of this interpretation it should be noted that recent NMR experiments in La2_xSr~CuO4 [ 29] appear to be inconsistent with a one-band description of this material and also suggest the existence of a purely 'oxygen band' in that system. If superconductivity is indeed caused by holes conducting in an oxygen p , band in both hole- and electron-doped oxides, what are the implications with respect to mechanisms? In the early theories that assumed conduction of hole carriers in such a band [ 17-19] it was proposed that superconductivity would be driven by either spin or charge excitations of the holes in the Cu 2 ÷ background. However, in the electron-doped materials this background is rapidly being destroyed by the added and induced electrons that turn Cu 2+ into Cu +. This would argue against such mechanisms to explain the superconductivity, and instead support mechanisms that depend solely on the dynamics of the carriers in the oxygen p~ band, as proposed in the model of hole superconductivity.
Acknowledgements The author is grateful to L. Garwin for stimulating correspondence.
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