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69

HOLE

No. 10, Pp.987-989,

SUPERCONDUCTIVITY

J.E. Department

of Physics

B-019,

1989.

IN OXIDES

Hirsch and S. Tang

University

of California

December

14, 1988 by II. Suhl)

(Received

0038-1098189 $3.00 + .OO Pergamon Press plc

San Diego,

La Jolla,

CA 92093

We discuss a mechanism that can give rise to high temperature superconductivity in oxides and explain the origin of their anomalous normal state properties.

We

have

mental

recently

mechanism

electron-phonon tion

occurs

shells.’

proposed

the

idea

that

for superconductivity

interactions

through

is dominant

holes

in anions

In this paper we analyze on Copper-oxide

ture of oxide

with

nearly

this mechanism

compounds.

superconductors

work of anions

through

1 shows schematically

which

state

scribing

our

two-level

The essential

fea-

when they

conduction

occurs.

in

tem.

occurs

in

the planes.

Optical

experiments2*3

dominantly

second,

Clearly,

is possible.

process

normal

a pairing

in-

the states models

from a

by a

holes),

p?r orbital,

in-

of the two level systhe breathing

of the outer p-shell

charge

a more detailed

description

However,

by de-

of the anion

(or equivalently

are added or removed between

is obtained

p-shell

The electrons

The two level system

of freedom ion.

in these materials

of this

of the outer

system.‘,’

duce transitions

Fig.

0 and Cu orbitals

model

the state

focusing

of a net-

for the anomalous

of these materials;

that gives rise to high T, superconductivity.

A simple

filled

the CuOz planes. Conductivity

which is responsible

properties

teraction,

in some

is the existence

the relevant

polarons,’

from

when conduc-

detail for the case of oxide superconductors, attention

a funda-

distinct

this simplification

density

degree

of the an-

of this process allows us to deal

have shown that the 0

2p holes have at least 95%

p,,, character but have not dewhether it is pa or pr orbitals. However, NMR

termined

results4 on “0 BCS-like that

and ‘%u have unequivocally

superconductivity

shown that

is due to oxygen

holes

Cu is decoupled as far as superconductivity

cerned.

Since the po orbitals

the Cu d,z_g tions that

orbitals,

leaves no doubt are responsible

the in-plane predictions

p

bitals

that

the conducting

of quantum There

This chemical

calculations

is a direct

overlap

as has been established

There

is a specific

likely to be rtsponsible materials. orbital

When to the

drastically

feature

an electron the states

without

holes, in

with the

by Goddard

between

p?ror-

involving

the

by various calculations.5v6 of these

systems

hops from

of the

that

of the other

between

electron

and the other

0

electrons

pr

it will

p electrons

This is due to the large Coulomb

is

of these

the oxygen

neighboring

these anions. that

with

reside

for the unique properties

pn orbital

alter

oxygen

is in agreement

that gives rise to conduction

cation,

hybridized

of these observa-

for the superconductivity,

orbitals.

and coworkers.5

are strongly

the combination

and

is con-

on

repulsion in the

p

orbitals of the anions involved. The wave functions of all the remaining p-electrons on the anion where the electron was will contract a

p electron

as they experience

is removed

hops will expand).

This is shown schematically

This contraction ion relative to that effects

Fig.

when

in Fig. 1.

of the charge density of the O- anof the O-anion will lead to two

when the holes conduct

first, a dynamical

less repulsion

(and the ones where the electron

through

band narrowing,

pa orbitals

the p* network:

as it occurs

1: Schematic representation of the Cu ds_+ and 0 pa and pr orbitals on the CuOz planes. The holes occupy the pr orbitals and hop through their direct overlap. The dashed lines on the top 0 orbitals indicate schematically the contraction of the pu and orbital

with small

987

when the hole is on that anion.

in the z direction

will also contract.

The pr

988

HOLE SUPERCONDLJCTIVITY IN OXIDES

with the problem sential

in a simple

way, while keeping

Vol. 69, No. 10

the es-

physics.

The Hamiltonian

is given by’s:

0

0

H = t CC&c++ h.c.) + V C(n;r + nil)ai t

(id

where CL creates orbital,

an electron

only nearest

of spin u in an in-plane

hopping

and third term in H describe ing pn electrons

between

neighbor

The second

0

0

the coupling of the conduct-

with the other p electrons

in the oxygen

p shell. (1) from

between ference

the site parameters atomic

properties.

two electrons, in ionization

(54.9eV)

tron affinitieslo

energies9

Hamiltonian S(O,l).

= -1.47eV

for O--

and

O-,

does not exist in free space and

energy and will be larger and more dis-

from spherical

implies

symmetry

than

O-).

is stabi-

S(O,l)

small

0 close to 7r. It also implies a large band narrow(I) - tS(O,l)*. We take hopping is tef,

ing as the effective 0 = 0.88~

V = 21.leV

which determines

and w = 6.4eV.

This

choice

of magnitude energies

yields a band narrowing

of Slater

integrals however,

the 0 site of UP = 10.2eV. where

these materials,

This

the O-O

however,

5eV6; the reduction of nearby

anions.

and atomic

is because cycles

excitation

the affinities

are larger.”

UP has been estimated

probably

U on

for three-dimen-

distances

occurs through

In

around

polarization

We take this into account

we allow for the dynamics

diagonalization timate Eo(2)

interaction. of clusters

of the attractive

on the 4.site

cluster

+ E,(O)

by taking

We have shown this by

of 2, 4 and 8 sites.’ interaction

in Fig.

- 2Eo(l)

of the holes we ob-

between

2 is obtained

with E,(n)

An es-

two holes

Ui;$ =

from

the ground state en-

ergy of n holes in the cluster.

The effective hopping between clusters is easily seen to be t$$ = t!y*/2, as we have changed the length and energy scale by a factor of

bard model

3 we plot

tain attractive that

Hamiltonian

-U,(y>/t$\ for this case.

interaction

of next-nearest-neighbor range

yields

The

with nearest

neighbor

hopping

on a square

lattice:

H(‘) + h.c.) + 7 eff = - stLy*(ctcjo

(2)

Ue(;lfniTnil.

The Hamiltonian

Eq. (2) approximately

tem on a length

scale scaled by a factor

we are not interested erties.

length

models

the sys-

of 2. By multi-

and energy scale as long as

in very short

The superconducting

The

critical

model

distance/time

state obtained

temperature

will first

for

t larger than 0.5. Inclusion

hopping

attractive

We ob-

enlarges

interactions.

for the coupled clusters

the parameter The

effective

is an attractive

Hub-

increase

proximately

BCS

level

Ue** -

off at

prop-

from Eq. (2)

perature

in an attractive as a dashed

bandwidth, to what

in the repulsive

Hubbard

jUe**l/te** following

with

(shown

t$,/lUe**Ir similarly

and then occurs

Hubbard

ap-

line in Fig.

3),

decrease

as

for the Nkel temmodel.”

The

maxi-

mum T,, for jUe**I N bandwidth, will be of order of and somewhat smaller than t,ff. Our parameters are only approximate ballpark. terials

but one can see that

Erom the short

we conclude estimates

we obtain

that Ue**/te**-

with pressure

of lUe**l < bandwidth. density

than with

“Non-diagonal”

value.

The

De-

fact that

t indicates

that

T,

as nil* with the

to be reduced

due to

hole density.s,‘2 band originating

effective

from the reduced

with and without

hopping

dependent

processes7

over-

holes explains

mass m* N 1Om inferred

Drude peak in the frequency tion similarly

the BCS

T, will increase’

lap of the pa orbitals the enhanced

in these ma-

3 or 4. This regime

as we are surely in the region

of holes n until lUe**l starts

the increased

length

will be given elsewhere.

Ue**/te** increasing

will increase

they are in the right

coherence

also will yield 2A/kT, larger tailed

The narrow

2. In Fig.

to obtain

t$> and U,(y) by 2 we obtain an effective Hamil-

Uo = 17eV instead of 22.5eV, which yields an effective repulsion Up = 4.9eV in our model. an attractive

the closed ones CU.

on the original

on-site

When

oxygens,

plying

yield an effective

from Born-Haber

oxides

diagonalized

denote

is s-wave.

parameters,

were obtained

U$.

cluster

tonian

respectivelv.

These

Four-site

open circles

0.7~

V and w come out to be of the right order

Note that

2:

t!yf/t = 13.

V and w vary by less than 20% for 0 in the interval to ,.’

Fig.

and E(O--)-

that this overlap is small (O--

torted

0

of 0. 0 determines

p wave-functions

The fact that O--

0

dif-

and O+*

O- does, suggests

tain

0

w and V in the site

we can obtain

of the

the

(77.4eV)

lized by Madelung

sional

0

interaction

from

From the first and second elec-

of Eq. (1) as a function

the overlap

bare

of 0+3

E(O-)-E(O)

= 8.75eV

The

Us, is estimated

at Us = 22.5eV.

E(O-)

in the Hamiltonian

0

0

0

We estimate Eq.

0

0

px

pa orbitals.

hopping.

0

0

(1)

ni,n;l

t

and t is the direct

We assume

0

0

00:+ sin hi) + Uo C

UJC(COS ,

+

from the

conductivity.‘3B’4

lead to diffusive

to the case of small polarons

mo-

and explain

vo .. 69, No.

10

HOLE SUPERCONDUCTIVITYIN OXIDES

989

lize the structure.

”

It involves charge fluctuations

atom where the hole is as opposed

same oxygen

charge fluctuations, excitations.*

out of plane polarization

This mechanism

tonic mechanisms

proposed

volved spatial separation

and Cu d-d

is also distinct

from exci-

in the past which always in-

between the conducting

and the pairing medium.16 We predict superconductivity for any anion network

on the to Cu-0

charges

through this mechanism

where conduction

occurs

through

holes in the anion outer shell and the direct hopping tween anions is appreciable. 3: Ue($/t$>

Fig.

versus t for the cluster of Fig. 2, with

Hamiltonian

Eq. (1).

iJo = 17eV,

V

21.6eV,

=

w =

6.4eV,

8 = 8%~ (solid line, left scale).

dashed line (right scale) shows T, versus

The

t obtained

from BCS for this case.

the broad absorption state properties ally enhanced behavior

at higher energies.”

Other normal

like large linear resistivity, susceptibility

and specific

of the thermopower

proportion-

heat,

and the

also follow from a narrow

band model of small polarons,

as discussed

by Scalapino

good?

Because

gens. l’ Why

it allows for more densely

Cu?

Because

be-

Why is two-dimensionality it is the smallest

packed

oxy-

cation

that

will lead to a Jahn Teller effect and a two-dimensional structure. (without

T, is lower in the three-dimensional

oxides

Cu) because of the larger O-O distance.

The es-

sential mechanism

is electronic

shell on the same

atom where the conducti~ng charge is

and is favored

by having

polarization

conduction

of the outer

by holes in closed

shell anions but not restricted to this case. We have discussed elsewhere’ the evidence suggesting that this mechanism plays an important

role also in “conventional”

su-

perconductors.

et a1.14 The other

mechanism

discussed

mechanisms

conductivity phonons,

here is distinct

proposed

in oxides.*

to explain

It does

and the cation

from

high T,

not involve

is irrelevant

except

all

super-

spins

nor

to sta.bi-

Acknowledgements National

and matching is grateful

--

Science

This work was supported

Foundation

funds from AT&T

to F. Marsiglio

by the

under NSF-DMR84-51899 Bell Laboratories.

for stimulating

J.H.

discussions.

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1988; in Proceedings

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