Conductivity coherence peak in YBa2Cu3O7

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Conductivity coherence peak in YBa2Cu3O7

O. Klein, K. Holczer, G. Grüner, G. Emelchenko

To cite this version:

O. Klein, K. Holczer, G. Grüner, G. Emelchenko. Conductivity coherence peak in YBa2Cu3O7.

Journal de Physique I, EDP Sciences, 1992, 2 (5), pp.517-522. �10.1051/jp1:1992162�. �jpa-00246513�

tllassification Physics Abstracts

74.30G 74.70V 78.47

Short Communication

Conductivity coherence peak in YBa2Cu307

O. Klein

(~),

^{K. Holczer} _(~> *), ^{G. Griiner}

(~)

and G.A. Emelchenko

(~)

(~) UCLA, Department of Physics, Los Angeles, ^CA 90024, U.S.A.

(~) Academy ^of Sciences, 142432 Chemogolovka, Moscow, Russia

(Received

20 January 1992, accepted in final form 6 March

1992)

Abstract. We have measured both the surface resistance lls and the surface reactance Xs of

a YBa2Cu307 single crystal at millimeter _wave frequencies and have evaluated the conductivity

al. We observe _{a narrow} coherence peak below Tc which indicates _s-wave pairing with

a rapid opening of the single particle _gap.

Many aspects

of the

superconducting

state of the various

high

temperature

superconductors

have been

explored recently.

The temperature

dependence

of the

penetration depth,

also

as a function of

magnetic field,

is

highly suggestive

of

singlet pairing.

Photoemission and

some

optical experiments, together

with surface resistance studies indicate _a

large

_gap, well

exceeding

the weak

coupling

^{BCS limit.} These

experiments point

to _a

simple, strong coupling superconducting

state. In contrast, Raman

scattering

and

tunneling

studies _are indicative of

states in the _gap

[I].

Numerous

experiments

_{[2] on} the temperature

dependence

of the nuclear relaxation _rate

I/Ti

shows _a monotonic

drop

below

Tc,

at odds with that

expected

for _s-wave

pairing.

In this case, the relaxation _rate should

display

_a

peak

in the

superconducting

state, and this so-called

Hebel-Slichter

peak

_[3] is accounted

for,

within the framework of the BCS

theory,

_as

reflecting

case II coherence factors. The real part _al ^{of the}

complex conductivity

b _{= al} ia2 ^{is also}

expected

to

display

_case II coherence factors [4]. ^{We have shown}

recently

_[5] that _al indeed hm _a well defined

peak

below Tc at

frequencies

below the _gap

frequency

_wg

=

2A(0)/h~

in the low temperature

superconductors

Pb and Nb. We have also found that _al has _a

sharp peak just

below Tc in

B12Sr2CaCuz08

_[6], and have

suggested

that it arises _as the consequence of coherence effects.

However,

the

conductivity

_al also

displays

_a strong ^{increase above}

Tc,

and

we believe it arises from fluctuation effects due to the

strongly

two dimensional

(2D)

^character

of the material.

In YBa2Cu307 2D fluctuation effects _are less

important,

and fluctuations

leading

to _a

peak

in _{ai are} most

probably suppressed.

Indeed it has been found

recently

that _ai increases below Tc and the observations _were

interpreted

in terms of

marginal

Fermi

liquid

[7]. We have

*Pennanent address: Central Research Institute for Physics, P-O- Box 49, ^Hi 525 Budapest~ Hungary.

518 JOURNAL DE PHYSIQUE I N°5

therefore measured the finite

frequency conductivity

in this material in order to

gain

further

insight

in the

electrodynamics

of the

superconducting

state. We find _a

sharply increasing

_al

below Tc in

qualitative disagreement

with the temperature

dependence

observed

by

Nuss et al.

[7], ^{but in} agreement ^{with other}

experiments [8-10].

Single crystal samples

_were

prepared

in the standard _way, and dc

resistivity

measurements lead to a

sharp

transition at 92

K,

with _a width less than I K. Above

Tc,

the dc

resistivity

increases

linearly

with temperature ^{and with} a small _zero temperature

intercept.

The finite

frequency conductivity

_cannot be measured

directly (except

_{on very} thin films

or

powders)

due to the finite

penetration

of the

electromagnetic

radiation into the

specimen investigated.

The

only

parameter

experimentally

accessible is the surface

impedance

Za ₌

I~

+

iXs

where

lla

is the surface resistance and

Xa

the surface _reactance. To _measure

it,

_we

have

employed

_a

cavity perturbation technique~

where the

sample

is

placed

inside _{a resonant}

cavity

at either the electric _or

magnetic

field anti-node. We found similar results for the both

configurations

and the data

presented

in this _{paper were} taken with the

specimen

in the maximum of the B

field,

with the field direction

along

the

crystallographic

c-axis I.e.

probing

the

electrodynamics

in the

(ah) plane

During

the

experiment

both the characteristic

frequency fo (without

the

specimen)

_or

fa (with

the

specimen)

^and the bandwidth A

fo (and

A

fa)

_are ^monitored

during

two separate

experimental

_{runs, one} without and _one with the

sample.

The bandwidth A

f

₌

fo/Q

is related to the

quality factor,

_Q> of the _resonance. We have

developed

_a

technique, employing

a feedback

configuration

where both

fo

and A

fo (and fs

and A

f,)

_can be measured to _a

high

accuracy [11].

Experimentally

_one cannot

male

an absolute measurement of the

frequency shift,

_as the

endplate

must be removed between the _runs with the

sample

in the

cavity

and _out of the

cavity.

Since the

frequency

is

proportional

to the volume of the

cavity~

it is

extremely

sensitive _to the

precise position

of the walls. However, due _to the mechanical

uncertainties~

it is not

possible

to put the

endplate

_on in

exactly

the _same

position

each

time,

and the

frequency

shift

fa fo

can be measured

only

_up to _a numerical additive constant

f~.

In other

words,

while A

fs

A

Jo

_can be evaluated

(as reassembling

does not

change

the

loss), only fs fo

+

fa

_can be

measured,

^with

f~

^unknown.

The parameters

f

^and

hi

_are related to the surface

impedance:

lla ₌

(A is

A

Jo) (la)

27

xs _#

is Jo) (ib)

where _~ is the resonator constant, ^determined

by

the

position,

^dimension and geometry ^{of the}

sample [12].

^The

conductivity

is related to the surface

impedance through

the relation

Zs ₌ I~ + iXs ₌

fi(2)

al ia2

where _po is the

permeability

of free _space.

Because of the unknown

f~,

_some

assumptions

have to be made either _on the

properties

of the normal _or

superconducting

state. The relevant

length

scale in the

superconducting

state is the

penetration depth I(T),

and _{we can use} the known _zero temperature value of

A(0)

₌ 1500 + 50

1

_{[13] to} evaluate

fa. Alternatively

_{we can assume} that in the normal state

the so-called

Hagen-Rubens limit,

_{wr <} I

applies.

In thin _{case al > a2} and

consequently

I~ ₌ Xs. As will be discussed

below,

both

assumptions

lead to similar results for _al below Tc.

irjq _;,,~~

~"'DC f crys:a ^~

@

.°°~~

~S~~°/~~

,

,,:. /° fi

/

'°z°... j ~~~o~~

~y~fl

o~~°o~O

~

fi

~%c

c

& ^o

~

~ ~

fi ^TIT

° °

/

~

f

~

cr

/

g

~~~~jcµ$~~ ~~°2~U~0~

o°C^fi&f~~$~f@

/

^{'c~ 92K} Rs/R~ ^"

2_cm

75 E0 85 _9C< 95 100

fe~pEiafUie (K)

Fig.I.-Temperature

dependence of the surface resistance Rs and surface reactance Xs of YBa2Cu307. Both Rs and Xs _are normalized to the value Rs

(T

= 95

K).

Inset: Temperature

dependence of the surface resistance Rs for _an YBa2Cu307 crystal and for _a high quality laser ablated film [14].

In

figure

^I we

display

the temperature

dependence

of Rs and

Xa,

both normalized to the surface resistance measured

just

above the

superconducting

transition. We have used the

Hagen-Rubens

condition to evaluate the

frequency

offset

f~.

In the normal _{state we} find that Rs and Xs have the _same temperature

dependence, confirming~

^the

validity

of the latter

assumption

in the entire measured temperature _range. Furthermore if _we

approximate

the

sample by

_an oblate

spheroid

of

semi-major

axis _a

= 0.03 _cm and semi-minor axis b

= 0.002 _cm

we can compute ^the resonator constant

[12]. Using

the measured value of the bandwidth

(Afa Afo)T=g5K

_" 3 _x

10~~,

_we calculate the normal _state surface resistance Rn ₌ 0.5 Q

using equation (16),

this results leads _to

a

resistivity

_{pn =} 100

pQ.cm (the subscript

_n refers to the normal state _or T ₌ 95 K

value).

^The

length

scale is thus determined

by

the

skin-depth

ⁱⁿ

the normal state ₌ 1.8 _pm.

Using

the

temperature dependence

of

Xs(T)

₌

wpoA(T)

_{we can}

deduce the

penetration depth

at _zero temperature. In

figure

I _{we can see} that

Xs(T)

saturates at low temperature to a value

corresponding

to _a

penetration depth

AT=75K

" 1800

1

_{+ 10$l}

in excellent agreement with other works [13]. ^{In the}

superconducting phase,

lla

drops rapidly

to _zero with

decreasing

temperature,

showing

_a

sharp

_cusp at 92

K,

in agreement ^{with the} 2~

inferred from dc measurement. We have

compared

our data below Tc with earlier measurements of

ll~(T)

_on

high quality

laser ablated films. The values obtained _on those films [14~ 15] ^have

been

reproduced by

other groups on similar films and the observed temperature

dependence

is

thought

to represent ^the intrinsic surface resistance _not influenced

by

defects _or

irregularities

in the

specimen.

In the

inset,

_we

display

the measured

lla(T)

in the

superconducting

state both for the

YBa2Cu307 crystal

and for the laser ablated film. The

experiments

_were conducted at different

frequencies f

₌ 100 GHz for the film and

f

₌ 60 GHz for the

crystal),

and _we have used the well confirmed w~

frequency dependence

_[14] of lla in the

superconducting

state

to compare both measurements. The surface resistance of the film and the

crystal

_are

similar,

giving

evidence for the

high quality

^{of the}

crystal

_we have

investigated.

520 JOURNAL DE PHYSIQUE I N°5

Y8aZ(U 307 Tc ~ ~2K

----Mmjis- eG,de*n

j₌2 jm~~ _{Ch0nq 8} Scelcc<n~

q OS z6(01/k7c~8

"n '~ ~ ~~

26(01/kTc~IO

-~ ~, O O

',

~

,O' _,

_.° '

~ .~

'_ .°~

b ^°'

i o

o

o o

o

75 e0 85 90 95 loo

temperature (K)

Fig.2.

Temperature dependence of _{al as} evaluated from

lL(T)

and

Xs(T)

shown in figure 1. The dashed line represents the Mattis-Bardeen calculation [16], the solid and dotted line

are the calculation nom reference [17] using different slope for the gap-opening.

Using

the lls and Xa measurements shown in

figure

I _we have evaluated _al and _our results obtained in the

vicinity ofTc

_are

displayed

in

figure

2. In the

figure altar (with an(T)

_oc

I/T)

is

d18played.

Several features of the observed behavior _are of

importance:

.

First,

the rise of _al above Tc is small and

comparable

to the

experimental

_accuracy, in contrast to the behavior found for Bi.

.

Second,

the

conductivity displays

_a clear

sharp peak (width

m 7

K),

with the

peak

temperature Tp =

T(almax)

well below Tc

(difference

m 3

K).

We note that at

Tp,

the surface resistance has

dropped by

_an ^order of

magnitude

from the normal state

value,

_a

signature

that the material is well into the

superconducting

state.

Those two observations _are at odds with alternative

explanations

from Olsson and Koch

[10],

that have

suggested

that the

peak

in _{al can} be attributed to _a

broadening

of the resistive

transition,

where fluctuation effects lead _to

a

peak strictly

at Tc. Our measured increase of _al is

entirely

due _to the

development

of the

superconducting

state below 2~.

Similarly

to what has been observed in the Bi

compound,

the

peak

of _al is

sharp

in clear contrast to what is

predicted by

Mattis-Bardeen for weak

coupling

^BCS

theory

[16]. ^The latter is indicated

by

the dashed-line in

figure

2. Our

findings

_are

quantitatively

different from the observations of M.C. Nuss et al. [7]1 who report a broad

peak

in

al(T)

at

frequencies

somewhat above _our measurement

frequency.

The _reason for this

disagreement

is not clear at

present. ^We note that

performing

the identical

experiment

with the _same

analysis

to the _one described

above,

led in conventional

superconductors

to _a behavior

fully

consistent with the BCS

theory

[5]. ^Recent calculations [17]

using

^{the finite} _mean ^free

path

effects

£/~fo

=

[14])

^{and the}

two-dimensionality,

^lead to al

(T)

similar to that shown _on the dashed-line. These calculations _were also

performed

_[18] for

larger

_gap

values,

but still

keeping

the weak

coupling

formalism

intact,

and _one finds _a

gradual sharpening

of the

conductivity peak

with

increasing

2A(0)/kBTc.

A

large

^{value of the}

2A(0)/kBTc

_m 8 10

gives

_a

good description

of _our results

~

~~°2~~3~7 I

T~⁼ 92K

.

o II 5 THz R-T

A 0 2 ip; PC Hcrmei .: _~

6 ,Z 5 I"; ^.

.

z - Z 6 _.

1 .

~ _. '

. )

.

I .

' A'

A'

>

~

AljY~

~"~ j

0 0

lT~

Fig.3.

Temperature dependence of _al measured by _us. Also displayed _on the figure is _al measured at optical frequencies [19] ^and

1/Tl

_[2], the solid line is the extrapolation at optical frequency of the

theoretical

curve in figure 2.

in the temperature _{range near} Tc. Thus the

sharpness

^{of the}

peak

^{reflects the faster} increase of A below

Tc,

and the fit indicates that the _{gap opens}

significantly

faster than the

weak-coupling

prediction.

In

figure

3 _{we compare our} results with

experiments

conducted at

optical frequencies together

with the calculated [18] temperature

dependence using

the parameter

2A(0) /kBTc.

As

expected

the coherence

peak disappears

at

high frequencies,

and

consequently

we argue that both sets of data _are in full agreement ^with

singlet pairing,

^{and that} the

optical

results [19] cannot be

taken _as evidence for _an unusual

pairing

mechanisms.

We have also

displayed

in

figure

3 the inverse nuclear relaxation rate

I/Tl

measured [2]

on the Cu and O sites in

YBa2Cu307.

As noted

earlier,

_no coherence

peak

is

found,

and

the behavior is

qualitatively

different from the _one observed in

al(T).

The _reasons for this difference _are not clear at

present,

^{however there} are several

important

distinctions between the information

provided by

the

conductivity

and

by

the nuclear relaxation rate.

First,

the

conductivity

reflects

charge

excitations at q = 01 while NMR

probes

the local

spin

fluctuation and

consequently

is

proportional

to the momentum

integral

of the _response function.

Secondly,

the contribution of

anti-ferromagnetic

fluctuations is known to be

important

for the

particular Cu(2)

site. In the _case of the

O(2,3) site, experiments

_are

usually performed

in

high magnetic

field. The dominant

absorption

_process involved in the relaxation of the O nuclear

spin,

is the electron

spin flip

_[4]

(the

contact term of the

hyperfine

interaction is

dominant)

which

implies

that the

quasi-particle spectral density

function is

probed

at the electronic Larmor

frequency

instead of the nuclear Larmor

frequency

_[20]. In consequencei

high magnetic

field NMR

(typically

7

Tesla)

is

probing

the BCS _response function at

higher

_energy

(8 cm~~)

than the present

conductivity

measurement

(2 cm~~)

^and as mentioned

earlieri

_an increase in the

probing frequency

_smears out the

height

of the coherence

peak.

Conductivity experiments

in

high magnetic

field

(up

to 2

Tesla)

_are in progress and the results will be

published

elsewhere

[21].

522 JOURNAL DE PHYSIQUE I N°5

Acknowledgqments.

We wish _to thank D.

Scalapino,

P. Littlewood and Z.

Schlesinger

for useful discussions. This research _was

supported by

^{the INCOR} _program ^{of the}

University

of California.

References

ii]

Batlogg B., Physica B 169

(1991)

7. For _a recent review of the experimental state of affairs.

[2] ^Hammel P-C-, Takigawa M-, HefIner R-H-, Fisk Z. and Ott K-C-, Phys. Rev. Lent. 63

(1989)

1992.

[3] ^{Hebel L-C- and Slichter} C-P-, Phys. Rev. 113

(1959)

1504.

[4] Schriefler J-R-, Theory of Superconductivity

(Addison-Wesley,

NY, 1988) cf. textbook p.75.

[5] Holczer K., Klein O. and Gr6ner G., Solid State Commun. 78

(1991)

875.

[6] Holczer K., Forro L., Mihily L. and Gr6ner G., Phys. Rev. Lent. 67

(1991)

152.

[7] ^Nuss M-C-, Mankiewich P-M-, O'malley M-L-, Westerwick E-H- and Littlewood P-B-, Phys. Rev.

Lent. 66

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[10] ^{Olsson H-K-} and Koch R-H-, Physica C185

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[11] ^Donovan S., Klein O., Holczer K. and Grfiner G., J. Appl. Phys., to be published.

[12] ^Klein O., Donovan S., Holczer K- and Griiner G., J- Appl. Phys., to be published.

[13] Harshman D-R-, Aeppli G., Ansaldo E-J-, Batlogg B., Brewer J-H-, Carolan J-F-, Caka R-J- and Celio M., Phys- Rev. B 36

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[15] ^Cooke D-W-, Gray E-R-, Javadi H-H-S-, Houlton R-J-, Klein N., Miller G., Orbach S., Pie] H., Drabeck L., Grfiner G., Josefowicz J-Y-, Rensch D-B- and Krajenbrink F., Solid State Commun.

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[17] Chang J-J- and Scalapino D-J-, Phys. ^Rev. B 40

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[18] Scalapino D-J-, Private Communication.

[19] ^Collins R-T-, Schlesinger Z., Holtzberg F., Fetid C., Welp U., Crabtree G-W-, Liu J-Z- and Fang Y., Phys. Rev. B 43

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[20] ^{This difference is}

insignificant

for _a metal, Where the density of _states

N(w)

is constant around the Fermi _energy, but not for _a superconductor where

N(w)

is singular at the gap value.

[21] ^{Awasthi A-M-} et al., Phys. Rev. B., to be published.