Correlation of high-Tc superconductivity with density of states peaks

PhysicaC 162-164 (1989) 1655-1656 No~h-HoRand

CORRELATION

R.S.

OF H I G H - T c S U P E R C O N D U C T I V I T Y

M A R K I E W I C Z a'c and B.C.

WITH DENSITY

OF STATES

G I E S S E N b'c

Depts. of P h y s i c s (a) and C h e m i s t r y (b), ann~ N o r t h e a s t e r n U n i v e r s i t y , Boston, M A 02115, USA"

some

recognized

time that

or,

hole

oxide

either

as

CuO 2

La2_xSrxCUO4,

doping. 5

as

a

Recently,

a

of T c w i t h d o p i n g

the d a t a 6,7

[For

the

density

found

new

a peak,

n, the n u m b e r

plane.

been

by

same

the

density

so

that

of

this

assumption

Ref.

n

Ref.

the

The

adjusting

In

this

agrees

simple once e.g., the

of

of h o l e s density it

for

this

is

that Tc

on

can

n

of

of

direct

the both

=

states that

hole-hole

two-dimensional

1

(dos)

and as

a

effect,

because

of,

hopping, 9-II van

of

Hove

in p a r t by D O D - S D I O

under

the

by

1

The

of

to of

Fermi with

insensitive ~;

a

for

by

was

chosen

so t h a t

a

change as

n-values.

i0

predicts

ground

state

is

to

an

(N

Formula particular

~

can

in

V.

and

can

= 1

0) is

value

of

compensated

at the

formula

from IGC Corp.

be For

60 meV,

A = N V = 0.56

McMillan-type

for the shift

respect

in

tcu_o

to_ O has

insulator

to the

change

and

higher

half-filling.

(Cu-O

(direct O-O

but

Ref.

liquid

(Cu-O

eV

AE

i0,

to a c c o u n t

peak

eV

1.2

values Ref.

band

correlations,

=

antiferromagnetic near

of us I0 to

and to_ O = 1.2 eV

from

N

band

CuO 2

AE = 5.2

tCu_O

dos

the

one

strong

calculation

a subcontract

0921--4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)

by

and

a model

coupled

increased

that

A Supported

Fig.

BCS-like

potential

from

bare parameters

are t a k e n been

pairing

a

unstable

observed stage

a

(i)

calculated

separation),

The

band.]

be u n d e r s t o o d

realized

structure

hopping).

material).

to the h a l f - f i l l e d

believe

dependence number

x

seen

from h a l f

in

from

obtained

describe

with

consistency

be

representation,

corresponds We

+

is the dos

hopping),

at n =

1

V

the

the

t h a t the L a 2 _ x S r x C U O 4 data p e a k s =

is

with

noting

(n

where

have

by

1.15

~ e -1/NV,

data

for

curve

T c = 1.14

all

peak

away

formula

were

and

solid

calculated

here

the

can

The

occurs

Tc

given

materials

7.

6,

filling. shows

(vHs)

renormalized

mass,

that

layer

of

that

effective

double-Cu

of h o l e s p e r CuO 2

values

assuming

the

in Fig. 1 as T c

data

singularity

copper oxide a d e n s i t y of

has

in o t h e r h i g h - T c m a t e r i a l s . 6-

8 We r e p l o t against

has

of s u c c e s s i v e

in

of h o l e

seen

the

shows

similar variation been

of

of n u m b e r

layers, I-4 function

it

Tc

superconductors a function

now,

(c),

Institute

Barnett

The v a r i a t i o n of T_ w i t h hole concentration in the superconductors can ~readily be u n d e r s t o o d in t e r m s of s t a t e s p e a k s p l i t by i n t e r l a y e r interaction.

For

PEAKS

Fig. V

i,

adjusted dos

peak.

provide

a

R.S. Markiewicz and B. C G iessen / Correlation o f high-To superconductivity

1656

150

,

shows

,

copper

To(K) I00

~~ +

• °y

the

oxide

described

by

value

6E.

the o

that

of

Tc(n)

curves

for

superconductors Eq.

I,

(For

splitting would

varying the

all

can

be

only

the

L a 2 _ x S r x C U O 4,

have

to

be

due

to

I

_I+o-

~l +

intercell

+

large and

coupling.

splitting

it may

be

is that

In this rather too

case,

the

surprising,

is

smaller

in

this material.)

0

oJ': ........

I

Note that I

i .....

1.2 n 1.4

1.6

........

fit,

but

at

the

i.e.,

cost

The

differences

among

of

xSrxCuO4 ,

YBa2Cu307_ 6

Tl-families) shown

in

in

I.

compounds,

In

accounting

it for

is

axis

is

induced

In the

properly

Amer. 21 to

2.

H. Ihara, (1988).

3.

P. Haldar, et al., 1198 (1988).

Science

241,

4.

A.W. Sleight, S c i e n c e 24~, (1988), S. Nakajima, et Physica C 158, 471 (1989).

1519 al.,

5.

J.B. T o r r a n c e et al., Phys. Rev. Lett. 61, 1127 (1988).

6.

Y.J. Uemura, et al., Phys. Lett. 62, 2317 (1989).

7.

W. U r l a n d and F. Tietz, Commun. 69, 995 (1989).

8.

M.H. Whangbo, D.B. Kang, and C.C. Torardi, Physica C 158, 371 (1989).

9.

R.S. Markiewicz, to be published, J.Phys. Cond. Matt.

i0.

R.S. Markiewicz,

ii.

E.B. Phys.

et al, N a t u r e ~ 4 ,

510

Rev.

Sol. St.

a

the

conduction

two-Cu-layer by

high-T c of

6E.

into

is two

Fig.

1

Stechel and D.R. Jennison, Rev. B38, 4632, 8873

(1988).

this

system

band 2

unpublished.

coupling)

result

for

separated

R.M. Hazen, p r e s e n t e d at Phys. Soc. M a r c h Meeting, 25 March, 1988.

even if c-

the

coupling sub-bands

i.

interlayer to

intercell

to

split

that

(three-dimensional

by

explain

a

layered

intracell

negligible.

superconductors

and

of

known

essential

dispersion

can

intercalation

is

d e s c r i b e the Fermi surfaces, effects

model

explained

of

graphite

compounds, 12

Bi

studies

family

present

(La 2_

the

easily

the

i) --

REFERENCES

various

i n t e r l a y e r coupling,

Fig.

closely-related

coupling

and

are m o s t

by d i f f e r e n c e s as

the

superconductors

coupling

e l e c t r o n s u p e r c o n d u c t i v i t y as well.

of

a d d i t i o n a l parameters. families

interlayer

the vHs p e a k can shift

to n < 1 (see d o t t e d line in Fig.

Fig. i. T c vs hole c o n c e n t r a t i o n for copper oxide superconductors. Data: x = La2_xSrxCuO4; O = YBa2Cu307-6 and o t h e r 2-Cu l a y e r m a t e r i a l s ; • = 3-Cu l a y e r s --all from Ref. 6; + = Bi 2-Cu layer m a t e r i a l s , from Ref. 7. Lines = theoretical fits w i t h 6E = 0 (solid line); 40 m e V (dashed line); 160 m e V (dot-dash), and 600 m e V (dotted), and o t h e r p a r a m e t e r s as d i s c u s s e d in text.

better

if the

is large enough,

12.

R.S. Markiewicz Giessen, Mod. Phys. 723 (1989).

and Lett.

B.C. B. ~,