A chemical approach to high Tc superconductivity

SOLID STATE

Solid State Ionics 49 ( 1991 ) 9-15 North-Holland

IONICS A chemical approach to high Tc superconductivity Akio N a k a m u r a Japan Atomic Energy Research Institute, Chemisto, Division, Tokai-mura, Naka-gun, lbaraki 319-11, Japan

A concise review is given on a new chemical approach to high Tc superconductivity recently proposed by the present author, the multivalence resonance-condensation (MVRC) model. The MVRC state of superconductivity is a Bose condensate of the resonance hybrids between two kinds of multivalence states of the chemical species (Cu ~'23+. Bi 3"4"5+, etc. ) responsible for the superconductivity, which is realized macroscopically through the self-organization (valence fluctuation-,valence ordering--*resonance-condensation) process of the electron system as the fundamental chemical bonding force. This is demonstrated to provide a possible unified picture of the superconducting state of various high T¢ systems for both the so-called "hole" and "electron" type superconductors in a symmetrical manner. In this paper, through the analysis of oxygen nonstoichiometry dependence of the superconductivity of YBa2Cu307_x, these main features of the model are delineated, emphasizing the importance of the combined defect-chemical and quantum-chemical considerations on the mixed (multi) valence of high Tc systems.

1. Introduction

Recently, the present author proposed the multivalence resonance-condensation model (MVRC model) as a possible novel origin of electron pairing and superconductivity in high Tc superconductors, and demonstrated its practical applicability to various high Tc (as well as low Tc) oxide systems and A-15 type intermetallic Nb3Ge [ 1 ]. In this paper, a concise review is given on this new chemical approach to high Tc superconductivity, supplementing briefly a new interpretation on the oxygen nonstoichiometry x dependence of Tc of YBa2Cu307_x system reported in literatures. According to the model, the basic physical picture of high Tc superconductivity is briefly summarized as follows: the multivalence resonance-condensation (MVRC) state of superconductivity is a Bose condensate of the microscopic quantum chemical resonance hybrid inside the single H O M O bond o f a trication crystal molecule of the responsible chemical species Cu (Bi, Pb, Nb, etc.) shown in fig. la. This state is realized through the self-organization process of the normal state valence electrons as the fundamental chemical bonding force, that is, valence fluctuation-.valence ordering-, resonance-condensation. Of course, in oxide systems (as shown in fig. lb),

the C u - C u ( B i - B i ) bond is an indirect one via the oxide ions ( 0 2 - ). So, the full resonance scheme is more precisely described by the one involving also the oxygen hole ( O - ) configuration; A ~ O p ~ B as shown there for ORH, designating the double resonance of the type; Cu 3+ + 2 0 - ~ - C u + + 2 0 2 - as the minimum unit [2]. Also in their normal state, depending on the nature of the hybrid MO bond between the cations and the oxygen, holes (or electrons) in the ORH (or R H H ) type conductors would exhibit a variable character ranging from the cation d ( s ) - to the oxygen 2p orbitals' character. But, the more essential point here seems that such hybrid MO bonds exist between them and indeed the charge transfer process C u 3+ + 0 2 - ~ C u 2 + "~ 0 - takes place there [3,4]. So, with these precautions in mind, in the present model, the formal valence representations [5,6] for the cations as shown in fig. la is adopted assuming the formal valence state of the oxide ion as 0 2 - . These microscopic resonances (ORH and R R H ) in fig. l a are attained by the simultaneous symmetrical paired motion of two electrons of opposite spin in opposite directions. So, if these microscopic resonances are allowed to extend throughout the whole crystal plane under the appropriate chemical and structural conditions, the systems are expected to be

0167-2738/91/$ 03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.

10

A. Nakamura / .-I chemical approach to high 7] ~uperconductit,tty i

(

2. MVRC state of superconductivity

)

,( i¸

"L

(t

"

I I" )

(

"/ I L i

B')

(A'

B

A

RRH

0 R H :

:(1 -¸II,

11

11 (A)

(Op)

(B)

(Op)

(A)

0 R H Fig. 1. (a) Oxidized and Reduced type Resonance Hybrids (ORH and RRH) inside the tri-cation crystal molecule. Spin state (electron number); C)(0), @(1), (~)(2): (b) Full resonance scheme includingoxygenhole (O-) configuration for ORH. Large circle: cation, small circle: oxygen. in the macroscopically coherent quantum chemically resonating state with a real space electron pair corresponding to the so-called Cooper pair in k (mom e n t u m ) space in the BCS theory [7], that is, the MVRC state of superconductivity. This is demonstrated in the following for almost all the oxide superconductors reported so far and the former high 7~ record holder Nb3Ge, as is briefly summarized in table 1.

As the extensive description of the analysis is already available in reL [ 1 ], here, only its main results are delineated, taking YBa2Cu~O7 , and Nb~Ge as a paradigm and shortly mentioning on other various systems. The 90 K high 2~ system YBaeCu3Ov (.v=0) [8] with a tri-layer perovskite structure and average Cu valence of +2.33 offers the best example of the present model: Obviously, the ( b - c ) plane of this system shown in fig. 2 is nothing but the interconnected onedimensional ( I - D ' ) array of O R H of fig. la. Thus, the microscopic intramolecular resonance (A ~ B ), now provided with the intermolecular resonance via intervening oxygens which connect the Cu to the t~axis direction inside the chain, is considered to manifest itself as the macroscopic MVRC state of superconductivity (ABAB...-:~BABA-..), in which every electron moves as half of a real space electron pair, i.e., two electrons of opposite spin moving in opposite directions. We may regard the MVRC state as a Bose condensate of two bosons (A and B) strongly interacting in real space. An important aspect of this C u - O bond is its noncubic s y m m e t w around Cu: Square-planar and pyramidal configurations of oxygen around Cu in the middle chain (I) and the upper and lower 2-D square planes (II), respectively, are essential to lift the degeneracy of Cu 3d orbitals (Hund's rule), so that this multivalence state of Cu occurs inside the split single C u - O H O M O bond with the designated spin degeneracy. As is apparent in table 1, this seems to be the definitive reason why in d-electron systems, superconductivity is found only in the anisotropic 1-, 2- and 3-D systems, and not in the isotropic 3-D systems, whereas in the s-electron system (1 = 0 ) isotropic 3-D superconductivity is possible as in Ba (K, Rb) BiOs [9,10]. As is shown in fig. 3a, it is now well recognized that YBa2Cu307 ~ also exhibits the second superconductive plateau of T ~ = 5 5 - 6 0 K [11,12] with quasi-two-dimensional superconductivity [ 13,14] similar to that of single-layered La(Sr)2CuOa [ 15,16 ], double-layered La (Sr) CaCu206 [ 17 ] and multilayered T I ( B i ) - C u systems [18,19]. In this category, we could also include Pb2Sr2Y~ ,Ca,-Cu3Os [20] and YBaeCuaOs [21] with the more complex

A. Nakamura / A chemical approach to high T,. superconductivity

11

Table 1 Brief summary of the present analysis on various superconductors. Underlined cationic species denote those responsible for their superconductivity. Dimension

Systems (electron conf.)

I-D chain

Nb3Ge(4d45s I)

I-D' chain 2-D square plane

Tc ( max ) (K)

Cation orbital

Cation valence (ORH or RRH)

Valencestate (~) (~ C)

23.7

dz2a

2.25+ (ORH)

Nbl'2"3+(4d 4.3.2)

YBazCu3OT(3dl°4sI )

92

3d,2 ~,2a*

2.33 + (ORH)

Cul'23+(3d 1°.9"s)

Lal.75Sro.25CuO4 TI(Bi)-Cu-O systems

37 130 20

3dx2_y2 o* 3dx2 :,,2o*

CuL23+(3d l°'9,s) Cut'2'3+ (3d1°.9.8)

3dx2_y2 o'*

2.25+ (ORH) 2.25+ (ORH) 1.75+ (RRH)

Ndl.ssCeo.15CuO3.95

Lio.sTi2.204(3d24p 2)

2- to 3-D' network

3-D network

C u 1"2"3+(3d

TM)

12.2 4.3 1.5 3.6

3dx2 y2 a 4dx2_ ,2 o" 5dx2_.~2 a 5dx2_~2 ~

3.25+ (ORH) 5.25+ (ORH) 5.25+ (ORH) 5.75 + (RRH)

Ti2"3:+(3d2"L°)

Ko.75MoO3(4d55s ~) a) Ko.75WO3(5d46s2) ") Ko.zsReO3(5dS6s2) a) A gTOsNO3 (4dl°5s I ) ~) BaPb3/4Biw403935(6sZ6p 2 )

1.0 13

4d~2 v2 o'* 6so

2.25 + (ORH) 3.25+ (ORH)

Ag L2'3+ (4d 1°'9'8) Pb2'3:+ (6s 2,1,° )

Ba3/4Ki/4BiO3(6s26p 3)

30

6sa

4.25+ (ORH)

Bi3:5+ (6s2,L°)

Mo4'5'6+(4d 2,1'°)

W4"5"6+(5d2"L°) ReS67+(5d2'L°)

a) For these systems, theoretically most optimized compositions (cation valence) shown in this table are not realized experimentally.

i

I

•

2

3

4

5

6 - Cu-O

Squore

-

Cu-O

Choin

-

Cu-O

Squore

b

Fig. 2. (b-c) plane of YBa2Cu307; trilayer type quasi-one-dimensional (1-D') superconductivity (ORH): (~(Cu 3+ (3d8);

system is obtained by combining 2-D square planes of fig. 4 as ( a - b ) , ( b - c ) and ( a - c ) planes in a 3-D manner. Fig. 3b shows the present interpretation on the variation of Tc of YBa2Cu307_x with oxygen nonstoichiometry x in terms of the average Cu valence in the chain and square planes. When x increases from 0 to 0.25, the detailed Cu valence distribution of the system is considered to change in the following manner: From

(~)) Cu 2+ (3d9); ( ~ ) Cu I+ (3d1°); ( - - ) C u 2 + - C u 3+ connection; ( ~ ) Cu ~+- C u 3+ connection; Solid ( ,-- ) and dashed ( ~-

YBa~_(Cu2+Cu3+ ) l , [ C u 3+ o s C u 0I+ 5]lO7

-) arrows: intra- and intermolecular resonances (the coupled motion of two electrons as the real-spaceelectron pair).

shown in fig. 2 to

atx=0

(1)

YBa~- (Cu2+Cu3+ )ll [Cuo.5 2+ Cuo.5 i+ ]106.75 mixed chain-square plane type structure. Further extension of the trilayer structure of fig. 2 in the upper and lower directions as I II I II I II ... gives the required two-dimensional C u - O square planes ( ( a - b ) plane) responsible for their 2-D superconductivity. This is shown in fig. 4 and the isotropic 2-D array of A and B of O R H in fig. la with the o p t i m u m average Cu valence of +2.25. We also know in table 1 that as its symmetrical counterpart, 2-D superconductivity of R R H (electron type) of fig. la is indeed realized in N d 2 _ , - C e x C u O 4 _ , . [22,23] with its opt i m u m average Cu valence of 1.75 + . A 3-D network

at x = 0 . 2 5 .

(2)

That is, with removal of oxygen in the chain, the reduction of the neighbouring Cu 3+ in the chain (I) to Cu 2+ would proceed continuously, keeping the average Cu valence in the square planes (II) constant at 2 . 5 0 + . As this reduction is completed at x = 0 . 2 5 (eq. ( 2 ) ) , trilayer type quasi-one-dimensional ( 1-D' ) superconductivity with its Tc of 90-85 K disappears at ( a r o u n d ) this composition. Then, to realize the next stable O R H type 2-D superconductivity inside the upper and lower square

12

A. Nakamura /,.t chemical approach 1o high 7~ Yuperconductn,ilv ~00 ~

,

,

,

r - -

,

,

,

yBO2 CU307_×

i ~.._.~

planes (11) shown in fig. 4, at x = 0 . 2 5 , thc system undergoes the valence redistribution reaction:

(0)

rc

10~

0.5('u 1+ (1) + 0 . 5 C u ~+ (I1) ,0.5Cu ~ ' ( I ) + 0 . 5 ( ' u : + ( l l )

(3)

and adjusts the average Cu valence in the square planes ( I I ) from 2.5(}+ in eq. (2) to the o p t i m u m + 2 . 2 5 in tile next eq. (4): 0 I

0

Y B a ~ ( ( ' u i ~ ( ' u i ~,~)n[Cu e+]~O'`~>

25

{4) As .\ further increases fi'om 0.25 to 0,50, similarly Io the case of 0_
CU IPlones)

20

,'

. • 2+ , ~,+ " i~ " I~ B a 2 ( ( u l s ( u B . ~ ) u [ ( u,~ ( u//5 ]10,,

at v = 0 . 5 0 .

10 o

05

io x

Fig. 3. (a) Variations of transition temperature 1~ and roomtemperature resistivity p with oxygen nonstoichiomel~' x in YBa2Cu307 ~system).(+) (T~)and(A) ( p ) : r e f . [ l l ] : ( • ) ( T,.): ref. [ 12]. (b) Variations of the average Cu valence in the chain and square planes with oxygen nonstoichiomet~, .,c in YBa2Cu3OT_ • system deduced from the present analysis.

(i,j)

1

2

3

4

5

6

1

2

3 4 5 6

! --0

Fig. 4. Square plane for ORH-type two-dimensional (2-D) superconductivity. ( Meanings of the symbols are the same as in fig.

(5)

This assures the onset o f the second broad l~ ( 6 0 55 K) plateau around 0.25-
b

at.\-=0.25.

-(b)

at.v=0.50.

(6

But, as seen in fig. 3a. this second superconductive plateau may extend to x = 0 . 5 6 region. This is because the valence redistribution reaction eq. (3) a r o u n d x = 0 . 5 0 (as well as a r o u n d x = 0 . 2 5 ) i s more or less the gradual one, and in that case, even the reduction of Cu n 2 ~ to Cu -~~°+ range in tile square planes is not expected to reduce 7~ o f the system significantly, in view of the well known Sr content dependence o f 7~. in La: ,Sr,CuO4 system [24]. The present interpretation is in line with the conclusion o b t a i n e d by Cava et al. [12] from the crystallographic analysis that the two plateau regions o f 7~ of YBa2Cu~O7 , system correspond well to those of the average Cu valence in the square planes. As for the application of the model to non-oxide systems, as shown schematically in fig. 5, the former high 7",. record holder, A-1 5-type intermetallic Nb~Ge appears to provide the another clearest example o f the present model. O n e - d i m e n s i o n a l i t y around Nb

13

A. Nakamura / A chemical approach to high Tc superconductivity

High

Tc of

Nb3Ge

1 D Extension

of ORH

:

[ NbZ25*(4d275)]6375*Ge(4S24p24p4 4dZ.Zst75Nb 2z5÷ ~

(4d275) ...., , dx,.

/,,/ i/

dyz • n-

,/"",

',', ~x

",,',

',', '

',

. Nb z.zS*

NbzzS*

(4d275) ~i"~

d x,. "',,,",

dxz

,/ ""illll/ / ij

.Tr

S.C. Bond dxz " 7r

(0.75 [e'])

,//'/'

,, ', ,

dyz. 7r

/ J

Fig. 5. The present valencebond description of one-dimensional (l-D) high T~superconductivity in Nb3Ge.

in this system is already enough to lift the degeneracy of 4d orbitals of Nb(4d45s j). As the bond strength between the direct d - d orbitals [25] is judged to be in the order shown there, first, the lowest-lying dxz (or dyz ) ~ MO bond will be filled by two electrons and unite the neighboring Nb firmly in the z direction in a I-D manner. Here, due to the noncubic Ge configuration around Nb, the role of d,~and dyz MO bond exchanges alternately in every N b Nb connection. Then, for the superconductive HOMO bond, we should proceed to the second-lowest-lying dz2 a MO bond. I-D extension of the completely intermingled resonating state A(A' ) ~ B ( B ' ) or ORH ( R R H ) in fig. l a to the upper and lower directions gives the average electron concentration of 0.75 (1.25) in this superconductive bond. If the ORH (hole) type is chosen as the more plausible one, this gives the average electron number of 2.75 ( = 2 . 0 + 0 . 7 5 ) per Nb, in other words, the average Nb valence of 2.25+ ( = 5 . 0 - 2 . 7 5 ) . Then, by donating these remaining 2.25 electrons from Nb to Ge (4s24p 2 ), the perfectly isoelectronic configuration (4d 275) results between Nb and Ge as shown in fig. 5. As the system would like to adopt such an electronic state most willingly, it seems enough reasonable to relate this fact to the highest Tc of 23.7 K of Nb3Ge [26] among all the metallic and intermetallic superconductors reported so far. This is the answer of the present model to the

role of 1-D chain structure and the well-known empirical valence rule (Matthias' rule [27]) in A-15 type intermetallic superconductors. Results of the present analysis are briefly summarized in table 1 in the order of increasing dimensionality of the systems. Table 1 demonstrates the practical applicability of the present model in reproducing the optimum valence states of various types of superconductors with at least nine kinds of multivalent-type "soft valence" cations responsible for the respective superconductivity.

3. Nature and mechanism of superconductive transition Fig. 6 depicts the schematic scenario for the onset of (high To) superconductivity in the present model. From the above analysis, the optimum valence states of superconductivity are + 0.33 in trilayer type 1-D' systems and _+0.25 in other 1-, 2- and 3-D systems from the intermediate valence state (~) of the responsible chemical species. Here, + and - refer to the ORH (hole) and RRH (electron) type superconductors. The system may approach these particular superconductive valence states either from the magnetic insulator side (La2CuO4, YBa2Cu306) or from the metallic oxide side (BaPbO3, ReO3) by chemical

A. Nakamura / A chemu'al approach to high 7] superconductmilr

14

LaeCu04 ,YBa2OusO e . . . . (Magnetic insulators)

Melal/Insulator Trans Region

~

- ReOs , BaPbO s IMetollic Oxides)

A(A') or B{B') Dynamic Valence Exchange(?alence Disproportionotion) A ; 2Cu2+ (lI)+Cus+ (I)~2Qjs+(ll)+Ou 1+ (I); B Disordered

MV State : Valence

Fluctuation

: EN=Ea(e×c=ton)+Eo{CDW)* EN(phonon) Ordered A B state

Valence il J = E s

MVRC

Ordering [N

Slate : Resonance- Condensation Es= E s (MVRC) * E s (phonon)

Fig. 6. Schematic scenario |'on lhc onset of (high ;[) superconductivity.

doping of aliovalent oxides a n d / o r oxygen nonstoichiometry, etc. Thereby, their electronic state would be naturally destabilized significantly, driven just to the middle of the so-called m e t a l / i n s u l a t o r transition region and totally disturbed their initial stable chemical state in either the magnetic order or the covalent metallic bond. In this sense, we could regard the electron syslem in the normal state of these superconductors as a metastable or even unstable one, and therefore we could further define the whole process leading to superconductivity as a kind o f the sell'organizational a n d / o r the synergetical process of the normal state valence electrons seeking an alternative stable chemical bond due to its intrinsic nature as the chemical b o n d i n g force. Referring to figs. 1, 2 and 4, to restabilize the system, the electron system first exerts a d y n a m i c valence exchange: ( A ( A ' ) ~ B ( B ' ) or ~ice versa and generates the multivalence state. Then, using the induced electron (~)-hole O attractive interactions mside and between the chains (planes) (we denote the former and the latter as E, (exciton) and E, ( C D W ) , respectively) as the ordering energy o f the process. the high t e m p e r a t u r e disordered multivalence state with lots of thermally fluctuating unsymmetrical electron and spin configurations (valence fluctuation [6] ) will start to order gradually with decreasing temperature, competing against the thermal agitation of the system, i.e., E N ( p h o n o n ) . As the temperature is further lowered and the thermal agitation of the system becomes sufficiently weak, the ordering reaches a critical level a r o u n d which the

system can no longer sustain its A ( A ' ) - B ( B ' ) type compressed normal state. The system drops almost spontaneously into the most stable macroscopically coherent M V R C state of superconductivity, changing the chemical bond from basically the electrostatically bound excitonic and C D W - t y p e compressed one to the completely uniform strong resonance bond. Accordingly, in the present model, the basic ke.~ requisite for the onset of high -l', superconductivity is judged to increase the chemical bonding force of the superconductive H O M O bond to obtain the higher resonance-condensation energy .I (the delocatization energy of the electron system ). Bishop et al. [28] measured the sound velocity o f single crystals (La, Sr)e('uO4 and "YBa2Cu.4)7 and found an anomalously strong hardening of the bulk modulus below 7~ which cannot be explained by the standard t h e r m o d y n a m i c s of the BCS theory for the both systems. This result seems to give a supporting evidence lbr the drastic change o f the nature o f the chemical bond to the much stronger uniform resonance bond below T, suggested by the present model.

4. Discussion

.As is apparent in the lbrcgoing, a major advantage o f the present model is that it can indeed reproduce the o p t i m u m valence states for the onset o f superconductivity in various superconductors in a straightforward way (table 1). This enables us to visualize a possible unified clear-cut chemical piclure o1" (high 7~ ) superconductivit}, for both the socalled hole ( O R H ) and electron ( R R H ) type superconductors in a symmetrical manner. Thus, the present model is expected to be useful in the experimental search for new superconductors by filling up the frustrating deep gap between theory and experiment of superconductivity. So, it is of some value to s u m m a r i z e here briefly what the present model suggests for such experimental efforts: ( 1 ) To adjust the valence states o f the responsible chemical species at the o p t i m u m values of _+0.33 for trilayer type ID systems and _+0.25 for other l-, 2- and 3-D systems from the intermediate valence state. (2) To check for other than s-electron systems

A. Nakamura / A chemical approach to high T+.superconductivity w h e t h e r the system has e n o u g h a n i s o t r o p y to prov i d e the split single H O M O b o n d . ( 3 ) To m a k e the system h a v e the s t r o n g e r c h e m ical b o n d (EN) o f the H O M O b o n d a n d t h e r e f o r e the higher r e s o n a n c e - c o n d e n s a t i o n energy ( J ) . T h e next step o f the p r e s e n t m o d e l is its theoretical f o r m u l a t i o n a c c o r d i n g to the a b o v e m e n t i o n e d q u a l i t a t i v e scenario. T h e s e are n o w in progress and will be r e p o r t e d in s u b s e q u e n t papers.

5. Conclusions In this paper, the a u t h o r gave a concise r e v i e w o f a n e w c h e m i c a l a p p r o a c h to high Tc s u p e r c o n d u c tivity, the m u l t i v a l e n c e r e s o n a n c e - c o n d e n s a t i o n ( M V R C ) m o d e l , the M V R C state o f s u p e r c o n d u c tivity is a m a c r o s c o p i c a l l y c o h e r e n t q u a n t u m - c h e m ically r e s o n a t i n g state with real space electron pair. We could regard the M V R C state m o r e straightforwardly as a Bose c o n d e n s a t e o f two b o s o n s A ( A ' ) and B ( B ' ) in fig. l a strongly interacting in real space. T h i s state is realized t h r o u g h the self-organization process o f the electron system as the f u n d a m e n t a l c h e m i c a l b o n d i n g force, that is, v a l e n c e fluctualion-+valence ordering-, resonance-condensation. T h i s was d e m o n s t r a t e d to p r o v i d e a possible unified c h e m i c a l picture o f the s u p e r c o n d u c t i n g state o f v a r i o u s o x i d e s u p e r c o n d u c t o r s and A-15 type intermetallic N b 3 G e for b o t h the so-called hole ( O R H ) and electron ( R R H ) type s u p e r c o n d u c t o r s in a symm e t r i c a l m a n n e r . Thus, the M V R C m o d e l is exp e c t e d to be useful in b o t h the search for new sup e r c o n d u c t o r s and the c o n s t r u c t i o n o f a new m i c r o s c o p i c theory o f s u p e r c o n d u c t i v i t y .

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