- Email: [email protected]
Electronic structure of superconducting Cu oxides
~So
lid State Communications, Vol.63,No.9, pp.857-860, 1987. Printed in Great Britain.
0038-I098/87 $3.00 + .00 Pergamon Journals Ltd.
ELECTRONIC STRUCTURE OF SUPERCONDUCTING Cu OXIDES A. F u j i m o r i , E. T a k a y a m a - M u r o m a c h i and Y. U c h i d a N a t i o n a l I n s t i t u t e for R e s e a r c h in I n o r g a n i c M a t e r i a l s S a k u r a - m u r a , N i i h a r i - g u n , Ibaraki 305, J a p a n (Received
21 M a y
1987 by W.
Sasaki)
On the b a s i s of p h o t o e m i s s i o n r e s u l t s on La2 x S r x C U O 4 v and Y B a 2 C u 3 0 . it is s u g g e s t e d that c a r r i e r s d o p e d Yn theo t h e r w i s e i n s u l a t i n g s a m p l e s are o x y g e n p h o l e s r a t h e r than Cud holes. T h e p h o l e s i n t e r a c t w i t h the l o c a l i z e d C u d s t a t e s t h r o u g h h y b r i d i z a t i o n and m a y g i v e r i s e to an a n o m a l y n e a r the Fermi s u r f a c e as d e s c r i b e d by a p e r i o d i c A n d e r s o n m o d e l w i t h low c a r r i e r d e n s i t y .
M e c h a n i s m s so far p r o p o s e d for the recently discovered high-T c superconduct i v i t y h a v e b e e n b a s e d e i t h e r on a onee l e c t r o n b a n d model 1-s or on a localized-electron model s u c h as the H u b b a r d m o d e l w i t h large U 6-z and bipolaron tunneling, s A l t h o u g h the p h o t o e m i s s i o n s p e c t r a of La2 - -_X S r x C u O 4 s-~ h a v e b e e n r e p o r t e d to be in o v e r a l ~ Y a g r e e m e n t w i t h the d e n s i t y of s t a t e (DOS) g i v e n by d e n s i t y f u n c t i o n a l b a n d - s t r u c t u r e c a l c u l a t i o n s 4, the f o l l o w i n g d i s c r e p a n c i e s are n o t e d b e t w e e n t h e o r y and e x p e r i m e n t : (1) T h e e x p e r i m e n t a l v a l e n c e b a n d is s h i f t e d to h i g h e r b i n d i n g e n e r g y by 1-2 eV s ' 1 1 , ~ z and the D O S a r o u n d the Fermi level (E F) is v e r y low 9-13 as c o m p a r e d to the theory; (2) T h e b a n d g a p in L a z C u O 4 and its c h a n g e w i t h Sr s u b s t i t u t i o n is not c o n s i s t e n t w i t h a P e i e r l s g a p as p r e d i c t e d by the b a n d theory, la (3) A s a t e l l i t e d u e to l o c a l i z e d d s final s t a t e s is o b s e r v e d > 1 0 eV b e l o w E ~ z T h e s e o b s e r v a t i o n s ~ n d i c a t e the l ~ m i t e d a p p l i c a b i l i t y of the o n e - e l e c t r o n p i c t u r e and the i m p o r t a n c e of e l e c t r o n 12 correlation. In the p r e v i o u s p a p e r , we h a v e g i v e n e v i d e n c e for a l a r g e U c o m p a r a b l e to the total b a n d w i d t h , and presented a localized d-electron picture as a s t a r t i n g p o i n t to u n d e r s t a n d the e l e c t r o n i c s t r u c t u r e of the C u - o x i d e systems.
m a g n e t i c and t r a n s p o r t p r o p e r t i e s n o r m a l s t a t e and p o s s i b l y for the high-T c superconductivity.
in the
S i n t e r e d p e l l e t s of Y B a z C u a O . (y = 6.3 ± 0.i and 6.8 ± 0.I) h a v e b e e n Y p r e p a r e d as d e s c r i b e d in Ref. 14. T h e y = 6.8 sample shows superconductivity below T C ~ 90 K and is m e t a l l i c a b o v e T c, w h i l e V y = 6.3 is an i n s u l a t o r (p ~ 103 ~cm) s h o w i n g no s u p e r c o n d u c t i v i t y . ~4 E x p e r i m e n t a l p r o c e d u r e was the same as d e s c r i b e d in Ref. 12. In Fig. I, we c o m p a r e the v a l e n c e - b a n d p h o t o e m i s s i o n s p e c t r a w i t h the D O S g i v e n by the b a n d - s t r u c t u r e c a l c u l a t i o n , 5 by t a k i n g into a c c o u n t p h o t o i o n i z a t i o n c r o s s s e c t i o n s Is and the i n s t r u m e n t a l (~0.1 eV for hv = 21.2 eV and ~ 0 . 8 eV for h~ = 1 2 5 3 . 6 eV) and l i f e t i m e broadening effects. O n e can c l e a r l y see d i s c r e p a n c i e s b e t w e e n t h e o r y and e x p e r i m e n t of the s a m e k i n d s as n o t e d a b o v e for the L a - S r - C u - O s y s t e m even in a m o r e d r a m a t i c way. Then, a c o n f i g u r a t i o n - i n t e r a c t i o n c a l c u l a t i o n 16 has b e e n c a r r i e d out on a CuO6 c l u s t e r m o d e l as in Ref. 12. We c o n s i d e r Y B a 2 C u a O e . s in w h i c h the o x i d a t i o n s t a t e of C u is +2. Thus the g r o u n d s t a t e is a s s u m e d to be a l d g > + b l d l ° ~ > ( L = a l i g a n d hole), w h e r e the s e c o n d term a r i s e s f r o m the C u d - O p c o v a l e n c y , and the final s t a t e s as l i n e a r c o m b i n a t i o n s of d s, dgL, and d1°LZ configurations. T h e b e s t fit to the e x p e r i m e n t i n c l u d i n g the s a t e l l i t e r e g i o n has b e e n o b t a i n e d as s h o w n in Fig. 2 u s i n g p a r a m e t e r s (pd#) = - 2 ( p d x ) = -1.1 eV, A ~ < d 1 ° L I H [ d 1 ° L > - < d ~ I H l d S > = 0 eV, and U = 6 eV. As t h e s e p a r a m e t e r v a l u e s are q u i t e s i m i l a r to t h o s e of Lal _ S r _ C u O 4 . ~2 we m a y c o n s i d e r that both systems ~ave basically common e l e c t r o n i c s t r u c t u r e , a l t h o u g h in the
In this C o m m u n i c a t i o n , we p r e s e n t the r e s u l t s of a p h o t o e m i s s i o n s t u d y on Y B a z C u a O y to f u r t h e r d e m o n s t r a t e s t r o n g e l e c t r o n c o r r e l a t i o n , and a l s o d i s c u s s the n a t u r e of e l e c t r o n i c s t a t e s a r o u n d E F in d o p e d s a m p l e s . We will s h o w that the d o p e d c a r r i e s a r e not C u d holes (i.e., C u +3 s i t e s i n t r o d u c e d in the C u z+ l a t t i c e ) but are o x y g e n p h o l e s w h i c h are h y b r i d i z e d w i t h the l o c a l i z e d C u d s states. Such hybridization is s u g g e s t e d to be r e s p o n s i b l e for the u n u s u a l 857
858
ELECTRONIC STRUCTURE OF SUPERCONDUCTING Cu OXIDES I
[
I
r
l
1
I
I
#
htJ= 21.2 eV
_
EXPT. .-:~'"".
Vol. 63, No. 9 l
I
I
hi,, = 1253.6 eV SAT.
, ' A
:..:.:" :~...~ ~',~..._
u3 l-
"
EXPT.
z)
.:
y= 6.8
a~ n. <
~F
- .~ :-.~'-:..... "~",
,~x6
CI THEORY
v >l.--
./
".:
hi,'= 1253.6 eV
/
uoo
\
~/.~
dlOL2
o_ tn (/) :E ILl 0 I*0 -i0.
I
/1
BAND THEORY (Matthelss-Hamonn)
z
I
YBQ2Cu306. 8
YBa2Cu30y
z LU l-Z
I
5p
Bo
;'Y"
../""
-"~.
BAND THEO
--~
dgL
:%
.'t"
:::
d 8
'" I
:. .-. -'~'::
y "- 6.3
. .:." ,-'-'::"
"
".
":.,
':" """."•~'.'C".'.....':Y""
I 12
I
I 8
16
I J
I 4
I
,
:/"~':'~" EF-=O
BINDING ENERY (eV) Fig. 1 Valence-band photoemission spectra of YBa=Cu30 v compared with band-theoretical dehsity of states YBazCu3Ov (Ref. 5).
the of
Y-Ba-Cu-O system complication arises f r o m the p r e s e n c e of two i n e q u i v a l e n t Cu sites with different O coordinations and u n k n o w n v a l e n c e d i s t r i b u t i o n . 14
In order to discuss the electronic states in the vicinity o f E F , we f i r s t note that the undoped samplbs, La2CuO4 and YBazCu306, are insulators or semiconductors and that they can be doped with holes by substitution of alkaline-earth elements for La or by oxidation. The semiconducting properties of LazCuO4 are understood as a r e s u l ~ of the l o c a l i z e d d e l e c t r o n s of the Cu 2" ions and the c o m p l e t e l y filled O 2p band, and La2 x S r x C U O 4 . w i t h y/2 < x is d o p e d w i t h h o ~ e s . For-~Ba=CU3Oy also, y = 6.5 is i n s u l a t i n g p r o b a b l y e v e r y C u s i t e is d i v a l e n t . ~4 Thus s a m p l e s w i t h y > 6.5 a r e d o p e d w i t h holes, a l t h o u g h the d i s t r i b u t i o n of the h o l e s a m o n g the two k i n d s of C u s i t e s is not k n o w n at p r e s e n t . It has
been
usually
iJ
i
i
I
l
.I
considered
i
12
i
8
&
4
l
0
BINDING ENERGY (eV)
" 1'
I
Ih
c~:":'~',:.
•" ~ .
I
J ,,
;,
\~:t:~ :.~: , i
I 16
J
";" ~:---2",~..-
EXPT. y = 6.8
.,...-..."."'.-... .~..r ....
•
that
Fig. 2 Valence-band photoemission s p e c t r u m of Y B a z C u 3 O e a. T h e Ba 5p core-level e m i s s i o n has b e e n s u b t r a c t e d f r o m the r a w d a t a (dots). The spectrum is c o m p a r e d w i t h the c o n f i g u r a t i o n interaction (CI) c l u s t e r c a l c u l a t i o n . T h e final s t a t e s are d e c o m p o s e d into configuration components.
the doped holes are Cu d-like, i.e., s o m ~ o f t h e C u 2+ i o n s a r e c o n v e r t e d to Cu a T . Thus, for the photoemission spectra of metallic samples, one would expect that the lowest binding ene(gy multiplet originating from the Cu z" ion is pinned at EF since the ground-state energies o f t h e C u 2+ a n d Cu a+ i o n s should be degenerate. This was indeed the case for the photoemission spectra of FeaO4 which is mixed-valent between F e 2+ a n d F e 3+ a n d s h o w s m e t a l l i c conductivity a b o v e ~ 1 2 0 K. 1~ I n t h e present case, however, the valence-band spectra of the metallic Lal.sSro.zCuO4 . and YBa2CuaO6os have shown only very lo~ intensities around EF and therefore no evidence for the pinning of a mulitplet state (Figs. 1 and 2). Th~s the simple picture of the d-hole (Cu a ) conduction does not seem appropriate. Here, the "d holes" do not necessarily mean bare d holes (d n-l) but may also represent d holes which are screened by O-to-Cu charge-transfer (dnL). In the present case, conduction by bare d holes (d e ) is absolutely impossible since they lie as high a s - 1 0 eV a b o v e the ground state as can be seen from Fig. 2.
Vol. 63, No. 9
ELECTRONIC STRUCTURE OF SUPERCONDUCTING Cu OXIDES
On t h e o t h e r h a n d , we n o t e t h a t , in spite of the low carrier density ~s'~g of t h e o r d e r o f 102~ cm - 3 o r t h e l o w photoemission intensity a r o u n d EF , t h e electronic specific-heat coefficient r and the Pauli-paramagnetic susceptibility Zo a r e n o t s m a l l , ~ s - 2 1 a n o r d e r o f magnitude greater than those in another h i g h - T _ o x i d e s y s t e m BaPb~ . B i O3 z2 TherefOre, i t i s t e m p t i n g -t ~ o i nxv o k"e a n analogy with f-electron systems, in which hybridization between the localized f and the extended valence orbitals l e a d s t o a n e n h a n c e d DOS n e a r EW. 23 W i t h i n t h e s i n g l e impurity model, t h e h i g h DOS i s a s s o c i a t e d with a Kondo peak appearing n e a r E F . z¢ S i n c e we h a v e shown that the doped barriers are not d holes, we may instead c o n s i d e r o x y g e n p holes. (We cannot rule out the p o s s i b i l i t y that some of the dnL states are c o n s i e r a b l y b r o a d e n e d due to, e.g., i n t e r s i t e d i s p e r s i o n and intersect E FHowever, since these states have also O p - h o l e c h a r a c t e r , no clear d i s t i n c t i o n can be made from the p holes c o n s i d e r e d here.) Then, h y b r i d i z a t i o n b e t w e e n the localized Cud and the e x t e n d e d O p states may lead to a K o n d o - l i k e a n o m a l y near Em. This a n a l o g y is i l l u s t r a t e d in Fig. 3"for Cu (d*) and Ce (f~) systems. W h i l e U ~ 5 eV for both systems, e l e c t r o n s and holes are i n t e r c h a n g e d b e t w e e n the two cases. Further, the
Cu oxide undoped
d9*d8
d9 Matt-Hubbard or Charge-transfer gap //,////,///~ I_ _l
bare non-f or non-d DOS a t E= is p r o b a b l y at least an order o~ m a g n i t u d e s m a l l e r for the Cu oxides than for Ce. The "Kondo peak" in the Cu oxides would be located b e l o w E~, 24 which seems c o n s i s t e n t w-ilt-h th~ p - t y p e c o n d u c t i o n , Is a l t h o u g h we cannot make a d e f i n i t e s t a t e m e n t w i t h o u t k n o w l e d g e of the effect of the lattice p e r i o d i c i t y on the DOS. T a k a h a s h i et al. g have indeed o b s e r v e d by p h o t o e m i s s i o n s p e c t r o s c o p y a w e a k peak at E F for L a l . s s S r o . l s C u O > 3 . s 6 , a l t h o u g h it is not so high as Would be e x p e c t e d from the r and Zo v a l u e s tg-zl p r o b a b l y due to the limited instrumental resolution. This peak cannot be due to a dSL m u l t i p l e t c o m p o n e n t b e c a u s e u n l i k e other dSL features it was o b s e r v e d only when the sample was cooled and d i s a p p e a r e d w i t h i n a few hours. 9 The p e a k can be a s s o c i a t e d with the p r e s e n c e of holes, if samples doped with holes or o x i d a t i o n states h i g h e r than 2+ are u n s t a b l e against oxygen d e s o r p t i o n in an u l t r a - h i g h v a c u u m at least w i t h i n the p h o t o e l e c t r o n escape depth (~5 A) for hv = 21.2 eV. We s u p p o s e that Cu 3+ is indeed u n s t a b l e in v a c u u m from the fact that LaCuO3 in which the o x i d i a t i o n state of Cu is 3+ can be s y n t h e s i z e d only under high oxygen pressure. A n o t h e r p o s s i b l e e x p l a n a t i o n for the e l e c t r o n i c states around E F would be defect levels, but such an e x p l a n a t i o n has been found quite difficult. 13 In a d d i t i o n to the s i n g l e - i m p u r i t y p r o p e r t i e s d i s c u s s e d above, we have to c o n s i d e r i n t e r s i t e i n t e r a c t i o n s for the C u - i o n lattice. Such a s y s t e m can be d e s c r i b e d by the p e r i o d i c A n d e r s o n H a m i l t o n i a n , zs
H = ~ ~k~Okv t O k~ kv + ~
d9
doped
Ce metal
+ ~ • d~ d . jn n jn jn
d~nd~n,djmdjm,
+ (1//N) kvjn Z V k r n ( d ~ nOk~
d9~d8
fl_~f2
Kondo
Energy
/
EF
Fig. 3 S c h e m a t i c spectral d e n s i t y of states for doped and u n d o p e d Cu oxides and m e t a l l i c Ce (Ref. 24). The h a t c h e d area c o r r e p o n d s to o c c u p i e d states.
859.
+ O~ vdjn),
(I)
where < j n , j n ' l e Z / r l j n , j n ' > ~ U. For large U, this model can be reduced to the local c l u s t e r model d e s c r i b e d above as far as gross features in the p h o t o e m i s s i o n s p e c t r a are concerend, while it can also d e s c r i b e in p r i n c i p l e e l e c t r o n i c states around EF on a low e n e r g y scale and Fermi surlaces in the spirit of r e n o r m a l i z e d band theory. 2s We note that Eq. (1) also r e p r e s e n t s a n t i f e r r o m e g n e t i c c o u p l i n g b e t w e e n local spins which is an essential feature for the H u b b a r d - m o d e l studies. 6-s U n f o r t u n a t e l y , the p e r i o d i c A n d e r s o n model is too c o m p l i c a t e d even in its s i m p l e s t v e r s i o n s and its p r o p e r t i e s have not been well studied. The H u b b a r d model, on the other hand, would be useful as an e f f e c t i v e H a m i l t o n i a n for
860
ELECTRONIC STRUCTURE OF SUPERCONDUCTING Cu OXIDES
low-energy (magnetic, thermal, and transport) properties, although it should be noted that the Hubbard U is not the same as the bare U obtained here [Eq. (1)] but should be regarded as a renormalized one.
Vol. 63, No. 9
Useful d i s c u s s i o n s with Drs. B. Okai and T. Takahashi are g r a t e f u l l y acknowledged.
REFERENCES [1] H. F u k u y a m a and Y. Hasegawa, J. Phys. Soc. Jpn. (to be published); Y. H a s e g a w a and H. Fukuyama, Jpn. J. Appl. Phys. 26, L322 (1987). [2] K. Machida and M. Kato, Jpn. J. Appl. Phys. (to be published). [3] W. Weber, Phys. Rev. Lett. 5__88, 1371 (1987). [4] L. F. Mattheiss, Phys. Rev. Left. 5-6, 1024 (1987); J. Yu, A. J. Freeman, and J.-H. Xu, ibid, 1035. [5] L. F. Mattheiss and D. R. Hamann, Solid State Commun. (to be published). [6] P. W. Anderson, Science 235, 1196 (1987); G. Baskaran, Z. Zou, and P. W. Anderson, Solid Sate Commun. (to be published). [7] H. Fukuyama and K. Yoshida, Jpn. J. Appl. Phys. 26, L371 (1987). [8] H. Kamimura, Jpn. J. Appl. Phys. (to be published). [9] T. Takahashi, F. Maeda, S. Hosoya, and M. Sato, Jpn. J. Appl. Phys. 2__66, L349 (1987). [10] H. lhara, M. Hirabayashi, N. Terada, Y. Kimura, K. Senzaki, and M. Tokumoto, Jpn. J. Appl. Phys. 26, L450, L463 (1987). [11] B. Reihl, T. Rissterer, J. G. Bednorz, and K. A. Muller, Phys. Rev. B (to be published). [12] A. Fujimori, E. T a k a y a m a - M u r o m a c h i , Y. Uchida, and B. Okai, Phys. Rev. B, (to be published). [13] N. Nucker, J. Pink, B. Renker, D. Ewert, C. Politis, J. W. P. Weijs, and J. C. Fuggle, Z. Phys. B (to be published). [14] E. T a k a y a m a - M u r o m a c h i , Y. Uchida, Y. Matsui, and K. Kato, Jpn. J. Appl. Phys. 2-6, L476 (1987); E. TakayamaMuromachi, Y. Uchida, K. Yukino, T.
Tanaka, and K. Kato, ibid 26, No. 5; E. T a k a y a m a - M u r o m a c h i , Y. Uchida, M. Ishii, T. Tanaka, and K. Kato, Jpn. J. Appl. Phys. (submitted). [15] J. J. Yeh and I. Lindau, At. Data and Nucl. Data Tables 32, 1 (1985). [16] A. Fujimori, F. Minami, and S. Sugano, Phys. Rev. B29, 5225 (1984); 30, 957 (1984). [17] K. Siratori, S. Suga, M. Taniguchi, K. Soda, S. Kimura, and A. Yanase, J. Phys. Soc. Jpn. 55, 690 (1986). [18] S. Uchida, H. Takagi, K. Kishio, K. Kitazawa, K. Fueki, and S. Tanaka, Jpn. J. Appl. Phys. 26, L443 (1987). [19] W. K. Kwok, G. W. Crabtree, D. H. Hinks, D. W. Capone, J. D. Jorgensen, and K. Zhang, Phys. Rev. B35, 5343 (1987). [20] K. Kitazawa, M. Sakai, S. Uchida, H. Takagi, K. Kishio, S. Kambe, S. Tanaka, and K. Fueki, Jpn. J. Appl. Phys. 26, L342 (1987). [21] H. Takagi, S. Uchida, H. Obara, K. Kishio, K. Kitazawa, K. Fueki, and S. Tanaka, Jpn. J. Appl. Phys. 2-6, L434 (1987). [22] B. Batlogg, Physica B126, 275 (1984); K. Kitazawa, A. Katsumi, A. Toriumi, and S. Tanaka, Solid State Commun. 5-2, 459 (1984). [23] P. A. Lee, T. M. Rice, J. W. Serene, L. J. Sham, and J. W. Wilkins, Comments Cond. Mat. Phys. 12, 99 (1986). [24] N. E. Bickers, D. L. Cox, and J. W. Wilkins, Phys. Rev. Left. 54, 230 (1985). [25] J. W. Allen, J. Magn. Magn. Mater. 47~48, 168 (1985). [26] B. H. Brandow, Phys. Rev. B3__3_3, 215 (1986).
lid State Communications, Vol.63,No.9, pp.857-860, 1987. Printed in Great Britain.
0038-I098/87 $3.00 + .00 Pergamon Journals Ltd.
ELECTRONIC STRUCTURE OF SUPERCONDUCTING Cu OXIDES A. F u j i m o r i , E. T a k a y a m a - M u r o m a c h i and Y. U c h i d a N a t i o n a l I n s t i t u t e for R e s e a r c h in I n o r g a n i c M a t e r i a l s S a k u r a - m u r a , N i i h a r i - g u n , Ibaraki 305, J a p a n (Received
21 M a y
1987 by W.
Sasaki)
On the b a s i s of p h o t o e m i s s i o n r e s u l t s on La2 x S r x C U O 4 v and Y B a 2 C u 3 0 . it is s u g g e s t e d that c a r r i e r s d o p e d Yn theo t h e r w i s e i n s u l a t i n g s a m p l e s are o x y g e n p h o l e s r a t h e r than Cud holes. T h e p h o l e s i n t e r a c t w i t h the l o c a l i z e d C u d s t a t e s t h r o u g h h y b r i d i z a t i o n and m a y g i v e r i s e to an a n o m a l y n e a r the Fermi s u r f a c e as d e s c r i b e d by a p e r i o d i c A n d e r s o n m o d e l w i t h low c a r r i e r d e n s i t y .
M e c h a n i s m s so far p r o p o s e d for the recently discovered high-T c superconduct i v i t y h a v e b e e n b a s e d e i t h e r on a onee l e c t r o n b a n d model 1-s or on a localized-electron model s u c h as the H u b b a r d m o d e l w i t h large U 6-z and bipolaron tunneling, s A l t h o u g h the p h o t o e m i s s i o n s p e c t r a of La2 - -_X S r x C u O 4 s-~ h a v e b e e n r e p o r t e d to be in o v e r a l ~ Y a g r e e m e n t w i t h the d e n s i t y of s t a t e (DOS) g i v e n by d e n s i t y f u n c t i o n a l b a n d - s t r u c t u r e c a l c u l a t i o n s 4, the f o l l o w i n g d i s c r e p a n c i e s are n o t e d b e t w e e n t h e o r y and e x p e r i m e n t : (1) T h e e x p e r i m e n t a l v a l e n c e b a n d is s h i f t e d to h i g h e r b i n d i n g e n e r g y by 1-2 eV s ' 1 1 , ~ z and the D O S a r o u n d the Fermi level (E F) is v e r y low 9-13 as c o m p a r e d to the theory; (2) T h e b a n d g a p in L a z C u O 4 and its c h a n g e w i t h Sr s u b s t i t u t i o n is not c o n s i s t e n t w i t h a P e i e r l s g a p as p r e d i c t e d by the b a n d theory, la (3) A s a t e l l i t e d u e to l o c a l i z e d d s final s t a t e s is o b s e r v e d > 1 0 eV b e l o w E ~ z T h e s e o b s e r v a t i o n s ~ n d i c a t e the l ~ m i t e d a p p l i c a b i l i t y of the o n e - e l e c t r o n p i c t u r e and the i m p o r t a n c e of e l e c t r o n 12 correlation. In the p r e v i o u s p a p e r , we h a v e g i v e n e v i d e n c e for a l a r g e U c o m p a r a b l e to the total b a n d w i d t h , and presented a localized d-electron picture as a s t a r t i n g p o i n t to u n d e r s t a n d the e l e c t r o n i c s t r u c t u r e of the C u - o x i d e systems.
m a g n e t i c and t r a n s p o r t p r o p e r t i e s n o r m a l s t a t e and p o s s i b l y for the high-T c superconductivity.
in the
S i n t e r e d p e l l e t s of Y B a z C u a O . (y = 6.3 ± 0.i and 6.8 ± 0.I) h a v e b e e n Y p r e p a r e d as d e s c r i b e d in Ref. 14. T h e y = 6.8 sample shows superconductivity below T C ~ 90 K and is m e t a l l i c a b o v e T c, w h i l e V y = 6.3 is an i n s u l a t o r (p ~ 103 ~cm) s h o w i n g no s u p e r c o n d u c t i v i t y . ~4 E x p e r i m e n t a l p r o c e d u r e was the same as d e s c r i b e d in Ref. 12. In Fig. I, we c o m p a r e the v a l e n c e - b a n d p h o t o e m i s s i o n s p e c t r a w i t h the D O S g i v e n by the b a n d - s t r u c t u r e c a l c u l a t i o n , 5 by t a k i n g into a c c o u n t p h o t o i o n i z a t i o n c r o s s s e c t i o n s Is and the i n s t r u m e n t a l (~0.1 eV for hv = 21.2 eV and ~ 0 . 8 eV for h~ = 1 2 5 3 . 6 eV) and l i f e t i m e broadening effects. O n e can c l e a r l y see d i s c r e p a n c i e s b e t w e e n t h e o r y and e x p e r i m e n t of the s a m e k i n d s as n o t e d a b o v e for the L a - S r - C u - O s y s t e m even in a m o r e d r a m a t i c way. Then, a c o n f i g u r a t i o n - i n t e r a c t i o n c a l c u l a t i o n 16 has b e e n c a r r i e d out on a CuO6 c l u s t e r m o d e l as in Ref. 12. We c o n s i d e r Y B a 2 C u a O e . s in w h i c h the o x i d a t i o n s t a t e of C u is +2. Thus the g r o u n d s t a t e is a s s u m e d to be a l d g > + b l d l ° ~ > ( L = a l i g a n d hole), w h e r e the s e c o n d term a r i s e s f r o m the C u d - O p c o v a l e n c y , and the final s t a t e s as l i n e a r c o m b i n a t i o n s of d s, dgL, and d1°LZ configurations. T h e b e s t fit to the e x p e r i m e n t i n c l u d i n g the s a t e l l i t e r e g i o n has b e e n o b t a i n e d as s h o w n in Fig. 2 u s i n g p a r a m e t e r s (pd#) = - 2 ( p d x ) = -1.1 eV, A ~ < d 1 ° L I H [ d 1 ° L > - < d ~ I H l d S > = 0 eV, and U = 6 eV. As t h e s e p a r a m e t e r v a l u e s are q u i t e s i m i l a r to t h o s e of Lal _ S r _ C u O 4 . ~2 we m a y c o n s i d e r that both systems ~ave basically common e l e c t r o n i c s t r u c t u r e , a l t h o u g h in the
In this C o m m u n i c a t i o n , we p r e s e n t the r e s u l t s of a p h o t o e m i s s i o n s t u d y on Y B a z C u a O y to f u r t h e r d e m o n s t r a t e s t r o n g e l e c t r o n c o r r e l a t i o n , and a l s o d i s c u s s the n a t u r e of e l e c t r o n i c s t a t e s a r o u n d E F in d o p e d s a m p l e s . We will s h o w that the d o p e d c a r r i e s a r e not C u d holes (i.e., C u +3 s i t e s i n t r o d u c e d in the C u z+ l a t t i c e ) but are o x y g e n p h o l e s w h i c h are h y b r i d i z e d w i t h the l o c a l i z e d C u d s states. Such hybridization is s u g g e s t e d to be r e s p o n s i b l e for the u n u s u a l 857
858
ELECTRONIC STRUCTURE OF SUPERCONDUCTING Cu OXIDES I
[
I
r
l
1
I
I
#
htJ= 21.2 eV
_
EXPT. .-:~'"".
Vol. 63, No. 9 l
I
I
hi,, = 1253.6 eV SAT.
, ' A
:..:.:" :~...~ ~',~..._
u3 l-
"
EXPT.
z)
.:
y= 6.8
a~ n. <
~F
- .~ :-.~'-:..... "~",
,~x6
CI THEORY
v >l.--
./
".:
hi,'= 1253.6 eV
/
uoo
\
~/.~
dlOL2
o_ tn (/) :E ILl 0 I*0 -i0.
I
/1
BAND THEORY (Matthelss-Hamonn)
z
I
YBQ2Cu306. 8
YBa2Cu30y
z LU l-Z
I
5p
Bo
;'Y"
../""
-"~.
BAND THEO
--~
dgL
:%
.'t"
:::
d 8
'" I
:. .-. -'~'::
y "- 6.3
. .:." ,-'-'::"
"
".
":.,
':" """."•~'.'C".'.....':Y""
I 12
I
I 8
16
I J
I 4
I
,
:/"~':'~" EF-=O
BINDING ENERY (eV) Fig. 1 Valence-band photoemission spectra of YBa=Cu30 v compared with band-theoretical dehsity of states YBazCu3Ov (Ref. 5).
the of
Y-Ba-Cu-O system complication arises f r o m the p r e s e n c e of two i n e q u i v a l e n t Cu sites with different O coordinations and u n k n o w n v a l e n c e d i s t r i b u t i o n . 14
In order to discuss the electronic states in the vicinity o f E F , we f i r s t note that the undoped samplbs, La2CuO4 and YBazCu306, are insulators or semiconductors and that they can be doped with holes by substitution of alkaline-earth elements for La or by oxidation. The semiconducting properties of LazCuO4 are understood as a r e s u l ~ of the l o c a l i z e d d e l e c t r o n s of the Cu 2" ions and the c o m p l e t e l y filled O 2p band, and La2 x S r x C U O 4 . w i t h y/2 < x is d o p e d w i t h h o ~ e s . For-~Ba=CU3Oy also, y = 6.5 is i n s u l a t i n g p r o b a b l y e v e r y C u s i t e is d i v a l e n t . ~4 Thus s a m p l e s w i t h y > 6.5 a r e d o p e d w i t h holes, a l t h o u g h the d i s t r i b u t i o n of the h o l e s a m o n g the two k i n d s of C u s i t e s is not k n o w n at p r e s e n t . It has
been
usually
iJ
i
i
I
l
.I
considered
i
12
i
8
&
4
l
0
BINDING ENERGY (eV)
" 1'
I
Ih
c~:":'~',:.
•" ~ .
I
J ,,
;,
\~:t:~ :.~: , i
I 16
J
";" ~:---2",~..-
EXPT. y = 6.8
.,...-..."."'.-... .~..r ....
•
that
Fig. 2 Valence-band photoemission s p e c t r u m of Y B a z C u 3 O e a. T h e Ba 5p core-level e m i s s i o n has b e e n s u b t r a c t e d f r o m the r a w d a t a (dots). The spectrum is c o m p a r e d w i t h the c o n f i g u r a t i o n interaction (CI) c l u s t e r c a l c u l a t i o n . T h e final s t a t e s are d e c o m p o s e d into configuration components.
the doped holes are Cu d-like, i.e., s o m ~ o f t h e C u 2+ i o n s a r e c o n v e r t e d to Cu a T . Thus, for the photoemission spectra of metallic samples, one would expect that the lowest binding ene(gy multiplet originating from the Cu z" ion is pinned at EF since the ground-state energies o f t h e C u 2+ a n d Cu a+ i o n s should be degenerate. This was indeed the case for the photoemission spectra of FeaO4 which is mixed-valent between F e 2+ a n d F e 3+ a n d s h o w s m e t a l l i c conductivity a b o v e ~ 1 2 0 K. 1~ I n t h e present case, however, the valence-band spectra of the metallic Lal.sSro.zCuO4 . and YBa2CuaO6os have shown only very lo~ intensities around EF and therefore no evidence for the pinning of a mulitplet state (Figs. 1 and 2). Th~s the simple picture of the d-hole (Cu a ) conduction does not seem appropriate. Here, the "d holes" do not necessarily mean bare d holes (d n-l) but may also represent d holes which are screened by O-to-Cu charge-transfer (dnL). In the present case, conduction by bare d holes (d e ) is absolutely impossible since they lie as high a s - 1 0 eV a b o v e the ground state as can be seen from Fig. 2.
Vol. 63, No. 9
ELECTRONIC STRUCTURE OF SUPERCONDUCTING Cu OXIDES
On t h e o t h e r h a n d , we n o t e t h a t , in spite of the low carrier density ~s'~g of t h e o r d e r o f 102~ cm - 3 o r t h e l o w photoemission intensity a r o u n d EF , t h e electronic specific-heat coefficient r and the Pauli-paramagnetic susceptibility Zo a r e n o t s m a l l , ~ s - 2 1 a n o r d e r o f magnitude greater than those in another h i g h - T _ o x i d e s y s t e m BaPb~ . B i O3 z2 TherefOre, i t i s t e m p t i n g -t ~ o i nxv o k"e a n analogy with f-electron systems, in which hybridization between the localized f and the extended valence orbitals l e a d s t o a n e n h a n c e d DOS n e a r EW. 23 W i t h i n t h e s i n g l e impurity model, t h e h i g h DOS i s a s s o c i a t e d with a Kondo peak appearing n e a r E F . z¢ S i n c e we h a v e shown that the doped barriers are not d holes, we may instead c o n s i d e r o x y g e n p holes. (We cannot rule out the p o s s i b i l i t y that some of the dnL states are c o n s i e r a b l y b r o a d e n e d due to, e.g., i n t e r s i t e d i s p e r s i o n and intersect E FHowever, since these states have also O p - h o l e c h a r a c t e r , no clear d i s t i n c t i o n can be made from the p holes c o n s i d e r e d here.) Then, h y b r i d i z a t i o n b e t w e e n the localized Cud and the e x t e n d e d O p states may lead to a K o n d o - l i k e a n o m a l y near Em. This a n a l o g y is i l l u s t r a t e d in Fig. 3"for Cu (d*) and Ce (f~) systems. W h i l e U ~ 5 eV for both systems, e l e c t r o n s and holes are i n t e r c h a n g e d b e t w e e n the two cases. Further, the
Cu oxide undoped
d9*d8
d9 Matt-Hubbard or Charge-transfer gap //,////,///~ I_ _l
bare non-f or non-d DOS a t E= is p r o b a b l y at least an order o~ m a g n i t u d e s m a l l e r for the Cu oxides than for Ce. The "Kondo peak" in the Cu oxides would be located b e l o w E~, 24 which seems c o n s i s t e n t w-ilt-h th~ p - t y p e c o n d u c t i o n , Is a l t h o u g h we cannot make a d e f i n i t e s t a t e m e n t w i t h o u t k n o w l e d g e of the effect of the lattice p e r i o d i c i t y on the DOS. T a k a h a s h i et al. g have indeed o b s e r v e d by p h o t o e m i s s i o n s p e c t r o s c o p y a w e a k peak at E F for L a l . s s S r o . l s C u O > 3 . s 6 , a l t h o u g h it is not so high as Would be e x p e c t e d from the r and Zo v a l u e s tg-zl p r o b a b l y due to the limited instrumental resolution. This peak cannot be due to a dSL m u l t i p l e t c o m p o n e n t b e c a u s e u n l i k e other dSL features it was o b s e r v e d only when the sample was cooled and d i s a p p e a r e d w i t h i n a few hours. 9 The p e a k can be a s s o c i a t e d with the p r e s e n c e of holes, if samples doped with holes or o x i d a t i o n states h i g h e r than 2+ are u n s t a b l e against oxygen d e s o r p t i o n in an u l t r a - h i g h v a c u u m at least w i t h i n the p h o t o e l e c t r o n escape depth (~5 A) for hv = 21.2 eV. We s u p p o s e that Cu 3+ is indeed u n s t a b l e in v a c u u m from the fact that LaCuO3 in which the o x i d i a t i o n state of Cu is 3+ can be s y n t h e s i z e d only under high oxygen pressure. A n o t h e r p o s s i b l e e x p l a n a t i o n for the e l e c t r o n i c states around E F would be defect levels, but such an e x p l a n a t i o n has been found quite difficult. 13 In a d d i t i o n to the s i n g l e - i m p u r i t y p r o p e r t i e s d i s c u s s e d above, we have to c o n s i d e r i n t e r s i t e i n t e r a c t i o n s for the C u - i o n lattice. Such a s y s t e m can be d e s c r i b e d by the p e r i o d i c A n d e r s o n H a m i l t o n i a n , zs
H = ~ ~k~Okv t O k~ kv + ~
d9
doped
Ce metal
+ ~ • d~ d . jn n jn jn
+ (1//N) kvjn Z V k r n ( d ~ nOk~
d9~d8
fl_~f2
Kondo
Energy
/
EF
Fig. 3 S c h e m a t i c spectral d e n s i t y of states for doped and u n d o p e d Cu oxides and m e t a l l i c Ce (Ref. 24). The h a t c h e d area c o r r e p o n d s to o c c u p i e d states.
859.
+ O~ vdjn),
(I)
where < j n , j n ' l e Z / r l j n , j n ' > ~ U. For large U, this model can be reduced to the local c l u s t e r model d e s c r i b e d above as far as gross features in the p h o t o e m i s s i o n s p e c t r a are concerend, while it can also d e s c r i b e in p r i n c i p l e e l e c t r o n i c states around EF on a low e n e r g y scale and Fermi surlaces in the spirit of r e n o r m a l i z e d band theory. 2s We note that Eq. (1) also r e p r e s e n t s a n t i f e r r o m e g n e t i c c o u p l i n g b e t w e e n local spins which is an essential feature for the H u b b a r d - m o d e l studies. 6-s U n f o r t u n a t e l y , the p e r i o d i c A n d e r s o n model is too c o m p l i c a t e d even in its s i m p l e s t v e r s i o n s and its p r o p e r t i e s have not been well studied. The H u b b a r d model, on the other hand, would be useful as an e f f e c t i v e H a m i l t o n i a n for
860
ELECTRONIC STRUCTURE OF SUPERCONDUCTING Cu OXIDES
low-energy (magnetic, thermal, and transport) properties, although it should be noted that the Hubbard U is not the same as the bare U obtained here [Eq. (1)] but should be regarded as a renormalized one.
Vol. 63, No. 9
Useful d i s c u s s i o n s with Drs. B. Okai and T. Takahashi are g r a t e f u l l y acknowledged.
REFERENCES [1] H. F u k u y a m a and Y. Hasegawa, J. Phys. Soc. Jpn. (to be published); Y. H a s e g a w a and H. Fukuyama, Jpn. J. Appl. Phys. 26, L322 (1987). [2] K. Machida and M. Kato, Jpn. J. Appl. Phys. (to be published). [3] W. Weber, Phys. Rev. Lett. 5__88, 1371 (1987). [4] L. F. Mattheiss, Phys. Rev. Left. 5-6, 1024 (1987); J. Yu, A. J. Freeman, and J.-H. Xu, ibid, 1035. [5] L. F. Mattheiss and D. R. Hamann, Solid State Commun. (to be published). [6] P. W. Anderson, Science 235, 1196 (1987); G. Baskaran, Z. Zou, and P. W. Anderson, Solid Sate Commun. (to be published). [7] H. Fukuyama and K. Yoshida, Jpn. J. Appl. Phys. 26, L371 (1987). [8] H. Kamimura, Jpn. J. Appl. Phys. (to be published). [9] T. Takahashi, F. Maeda, S. Hosoya, and M. Sato, Jpn. J. Appl. Phys. 2__66, L349 (1987). [10] H. lhara, M. Hirabayashi, N. Terada, Y. Kimura, K. Senzaki, and M. Tokumoto, Jpn. J. Appl. Phys. 26, L450, L463 (1987). [11] B. Reihl, T. Rissterer, J. G. Bednorz, and K. A. Muller, Phys. Rev. B (to be published). [12] A. Fujimori, E. T a k a y a m a - M u r o m a c h i , Y. Uchida, and B. Okai, Phys. Rev. B, (to be published). [13] N. Nucker, J. Pink, B. Renker, D. Ewert, C. Politis, J. W. P. Weijs, and J. C. Fuggle, Z. Phys. B (to be published). [14] E. T a k a y a m a - M u r o m a c h i , Y. Uchida, Y. Matsui, and K. Kato, Jpn. J. Appl. Phys. 2-6, L476 (1987); E. TakayamaMuromachi, Y. Uchida, K. Yukino, T.
Tanaka, and K. Kato, ibid 26, No. 5; E. T a k a y a m a - M u r o m a c h i , Y. Uchida, M. Ishii, T. Tanaka, and K. Kato, Jpn. J. Appl. Phys. (submitted). [15] J. J. Yeh and I. Lindau, At. Data and Nucl. Data Tables 32, 1 (1985). [16] A. Fujimori, F. Minami, and S. Sugano, Phys. Rev. B29, 5225 (1984); 30, 957 (1984). [17] K. Siratori, S. Suga, M. Taniguchi, K. Soda, S. Kimura, and A. Yanase, J. Phys. Soc. Jpn. 55, 690 (1986). [18] S. Uchida, H. Takagi, K. Kishio, K. Kitazawa, K. Fueki, and S. Tanaka, Jpn. J. Appl. Phys. 26, L443 (1987). [19] W. K. Kwok, G. W. Crabtree, D. H. Hinks, D. W. Capone, J. D. Jorgensen, and K. Zhang, Phys. Rev. B35, 5343 (1987). [20] K. Kitazawa, M. Sakai, S. Uchida, H. Takagi, K. Kishio, S. Kambe, S. Tanaka, and K. Fueki, Jpn. J. Appl. Phys. 26, L342 (1987). [21] H. Takagi, S. Uchida, H. Obara, K. Kishio, K. Kitazawa, K. Fueki, and S. Tanaka, Jpn. J. Appl. Phys. 2-6, L434 (1987). [22] B. Batlogg, Physica B126, 275 (1984); K. Kitazawa, A. Katsumi, A. Toriumi, and S. Tanaka, Solid State Commun. 5-2, 459 (1984). [23] P. A. Lee, T. M. Rice, J. W. Serene, L. J. Sham, and J. W. Wilkins, Comments Cond. Mat. Phys. 12, 99 (1986). [24] N. E. Bickers, D. L. Cox, and J. W. Wilkins, Phys. Rev. Left. 54, 230 (1985). [25] J. W. Allen, J. Magn. Magn. Mater. 47~48, 168 (1985). [26] B. H. Brandow, Phys. Rev. B3__3_3, 215 (1986).