Aspects of high temperature superconductivity

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Aspects of high temperature superconductivity

Guy Deutscher

To cite this version:

Aspects

of

_high

_temperature

_{superconductivity}

Guy

Deutscher

School of

_Physics

and

_{Astronomy, Raymond}

and

_Beverly

Sackler

_Faculty

of Exact Sciences, Tel Aviv

University,

Ramat Aviv, Tel Aviv, Israel

(Reçu

le 17 mai 1989,

accepté

le 9

_juin

₁₉₈₉₎

Résumé. 2014

Nous proposons

quelques

remarques sur les aspects

particuliers

qui

distinguent

la

phénoménologie

des nouveaux

_oxydes

à

_{haute Tc}

de celle des

_{supraconducteurs}

conventionnels. Ils _comportent une

_largeur

mesurable de la

_{région critique}

et une

_grande

sensibilité aux défauts cristallins. Une

description

cohérente du _type Landau

_Ginsburg

est

_possible

avec une courte

longueur

de _{cohérence 03BE ~} 15

Å

et une

_profondeur

de

_{pénétration}

03BB ~ 900

Å.

Cette dernière est

sensiblement

_plus

courte _{que la valeur} couramment admise, et

_implique

l’existence d’une bande de conduction assez

_large.

Abstract. 2014 We

present some remarks on

_special

features that

distinguish the phenomenology

of the new

_{high Tc}

oxides from that of the conventional

superconductors. They

include a measurable width of the critical

_region

and a

_{high sensitivity}

to

_{crystallographic}

defects. A consistent Landau

Ginsburg interpretation

it

possible,

with a short coherence

_{length 03BEab ~}

15

Å

and a

_penetration

depth 03BBL ~

900

Å.

The latter is somewhat smaller than the

_{currently accepted}

value, and

_implies

a broad band scheme.

Classification

Physics

Abstracts 74.30C - 74.40 -

74.70V

Introduction.

While the

_question

of the mechanism for

_high

_temperature

_{superconductivity}

_{is still very} much open

theoretically,

recent

_experiments

on

_samples

of

_{improved quality point}

out more and more

_clearly

to an

_ambiguous

situation. On the one

_hand,

there is

_growing

evidence for a

BCS

behavior,

with a well defined energy gap and conventional behavior of the London

penetration depth

[1].

On the other

hand,

the gap appears to _{be very sensitive} to

crystallographic

defects on the atomic scale

_judging

from the anomalous

_Josephson

behavior at

_boundaries,

which

_clearly

indicate a

_depressed

order

_parameter

_[2].

This is

_quite

_contrary

to the behavior of conventional

_{superconductors,}

where

_crystalline

defects such as

_impurities,

dislocations,

grain

boundaries do not

_modify

the

_{superconducting}

state

_except

in as much as

they

reduce the normal state mean free

_path,

reduce the coherence

_length

and enhance the

penetration depth.

But

_they

do not

_modify

the critical

_temperature

_{and the gap.}

_Accordingly,

all the fundamental data can be obtained

_{using polycrystalline,}

not

_particularly

_pure or defect free

_samples.

2852

This is not the case for the new

_{high T,}

oxides that must be studied in

_{single crystal}

form for the determination of the

_{penetration depth,}

the lower critical field

_Hc1,

_{the gap, the}

_depairing

critical current

_density

etc...

This extrinsic behavior can be understood on the basis of a short coherence

_length

[3],

_by

now well documented

_{experimentally}

[4].

Extrinsic behavior due to

_{crystallographic}

defects could also be

_interpreted

as indications that

_{superconductivity}

in the

_{high T,}

oxides is of an unconventional nature

_(d

wave

superconductivity, charge

or

_spin

transfer models

_etc...).

_Early

observation of an anomalous low

temperature

heat

_capacity

in the YBCO

_compound

received such an

_{interpretation}

_[5].

But later measurements on the Bi

_compounds

did not show this behavior

_[6]

which is

therefore not intrinsic to

_{superconductivity}

in the oxides

_[6].

In the absence of direct

_proof

of unconventional

_{superconductivity,}

we shall take the

_point

of view that their

_sensitivity

to defects is

_only

due to a short coherence

_length,

and that with this caveat their

_properties

can be

_interpreted

in the framework of the Landau

_Ginzburg

theory.

We shall discuss in the

_following

whether the available data can be

_interpreted

consistently

within this

framework,

concluding

with some remarks on the

_{physical significance}

of the short coherence

_length.

Landau

_Ginzburg

_parameters

of the

_high

_T,

oxides.

The

_strongly

_{anisotropic quasi-2D}

structure of the oxides as well as their short coherence

length immediately

suggest

that non mean field behavior should be

observable,

in contrast

with conventional

_{superconducting}

metals and

_alloys.

On the reduced

_temperature

scale E =

(T, -

T)/Tc,

there should be a detectable

_temperature

_range Ec with

large

ther-modynamic

fluctuations of the order

_parameter

and

_{correspondingly}

non mean field values of the critical

_exponents.

Taking

a 3D

averaged e

of 12

Â

and a

_{thermodynamic}

critical field

_Hc

= 12.000

G,

the

Ginzburg

criterion

_{gives Ec}

of the same order as that for

_superfluid

He

[7].

Fluctuation effects are further enhanced in 2D. The measured

_7c

should then be

_{significantly depressed}

relative

to its mean field value.

Specific

heat measurements on YBCO

_samples

do

_display

fluctuation effects near

T,.

In addition to the mean field

_jump,

there is a small but definite enhancement of the heat

capacity

both above and below

_Tc,

that has been

_interpreted

as

_qualitative

evidence for a

À transition

_[8].

The available data is not

_yet

_{of sufficient accuracy} to allow a determination of critical

indices,

but is sufficient to establish that the width of the critical

_region

is indeed much

larger

than for conventional

_{superconductors,}

but smaller than that of

_superfluid

He. This is confirmed

_by

two additional sets of measurements : that of the

_{penetration depth}

which follows with

_{great accuracy}

mean _{field behavior in the entire range of} measurements,

up to 0.5 K from

_T,,

_{[9] ;}

and that of the excess

_conductivity

above

_T,,

which is in

_good

agreement

with the mean field behavior of a

_{layered superconductor}

with

_gab

= 12

_Â,

e,

= 2

Â,

also up to 0.5 K from

Tc

[10].

The

_Ginzburg

criterion can be written under the form :

where A is a numerical

coefficient,

₀₀

the flux

_{quantum, e,}

is the coherence

_{length along}

the c axis and

_Àab

the

_{penetration depth}

in the

(a, b)

_plane.

Here we have

_expressed

the condensation energy per coherent volume

( Hc/8 2 -u) . Pl using î3 = e ab . 2 ec,

and have

Equation

(1)

can be rewritten as :

The numerical factor

_{(A e c 112)}

_{is in any} case smaller than one.

_Taking

for

_{ç c}

an _{upper limit of} 5

_Â,

_{and Tc}

= 92 K

(YBCO),

_we

get

À : 900

Â.

This is smaller than the

_{currently accepted}

value À = 1 400

Â,

and

only barely compatible

with the lower end of the

_experimental

bracket of ±

500 Â

_[9].

There are indeed some

_experimental

difficulties that may lead to an overestimate of

A. For instance it is well known that anomalous low field

_penetration

and microwave

absorption

(discussed below)

are

_always

observed in the

_oxides,

even whenin

_{single crystal}

form. These effects must be due to _{the presence of weak}

_{superconducting regions,}

that are

necessarily

the sites of a

_locally

enhanced

_{penetration depth.}

We also note that

_reflectivity

measurements near the

_plasma

_edge

in YBCO lend a value of the

_plasma

_frequency

that

_corresponds

to À =

(c / lJ) p)

= 700

À

[11].

The

_point

that we are

_making

here is that a consistent Landau

_{Ginzburg description}

of the oxides

_requires

a

_{penetration depth}

somewhat smaller than the value

_{generally accepted.}

It could of course be the case that such a

_description

is not

_applicable,

but one would then have

to

_explain

the excel-mean field fit of À

_(T).

A

_large

k value indicates a

_large

effective mass, as

_pointed

out in

_[9],

and is indicative of

strong

coupling.

Conversely,

a smaller À is consistent with a broad band and weak

_coupling.

As is well

known,

the

_Orsay

school has

_argued

in favor of such a broad band

_scheme,

with the Fermi level located near the Van Hove

_singularity

of a

_quasi

2D band

_[12].

We have shown that a consistent Landau

_{Ginzburg description}

of the oxides favors this later

_point

of view. More efforts should be devoted towards a definite

_experimental

determination of the

penetration depth,

and to its calcuIation in the different theoretical schemes.

Boundary

effects : low field microwave

absorption.

Low field microwave

_absorption

in the

_{high Tc}

ceramics

_[13]

and in

_{single crystals}

_[14]

_point

out to the existence of

_Josephson

_junctions

in these materials. Periodic

_absorption

lines have been observed in YBCO

_{single crystals,}

with a field

_period

that is a minimum when the field is

parallel

to a

₍₁₁₀₎

_direction,

and varies as

(cos 0 )

_{where 0}

is the

_angle

between the field and a

₍₁₁₀₎

direction. The well known

₍₁₁₀₎

twin boundaries of YBCO are thus involved. The

proposed interpretation

[14]

is a

_{periodic penetration}

of vortices in one

_junction,

or a series of

junctions, parallel

to one set of twin boundaries. But in view of the

_{high density}

of twin boundaries in the

_crystal,

it is not clear how one

_{particular boundary}

could dominate the

absorption

behavior.

Some further

_puzzling

features of these

_experiments

are :

_i)

the line

_{periodicity corresponds}

to an effective

_junction

width that is much

_larger

than the

_{expected penetration depth}

and

ii)

the threshold field

_He1J

for vortex

_penetration

has an anomalous

_temperature

_dependence.

For a conventional

_{junction :}

where

where

_Àj(r)

is the

_{penetration depth}

in the

_junction

and

_{k L (T)}

the London

_penetration

2854

Since

_{Jc (T)}

oc

_{(F, - T )}

and

_ÀL(r)

oc

_{(F, -}

T)- 1/2,

it follows that

_He1J

_(T)

oc

_{(Tc -}

T)3/4.

Instead,

the

_experiments

of

_{Blazey give}

_{Hlj (T)}

oc

_{(Tc - T)’,}

with n = 1.9 ± 0.3

_[14].

We wish to show here that this can be the behavior of a

_{composite junction composed}

of a stack of twin boundaries

_{separated by}

distances of the order of 100

_Â,

as is sometimes observed in YBCO

_grains

_[15].

_First,

it has been shown

_previously

that the critical current

across a

_boundary

in a

_{high Tc}

oxide varies near

_T,

as

(Te 2013

T)2

rather than

(Tc - T).

This is due to the short coherence

_length

which

_produces

at the

_boundary

a

_depression

of the order

parameter,

ài

oc

_{(Tc - T)}

instead of the

_{bulk à,}

oc

_{(T, -}

T)1/2

[16].

A second modification

occurs if we are

_dealing

with a stack of boundaries

_{separated by}

distances d small

_compared

to

AL-

In that case

_AL(T)

has to be

_{replaced by}

the effective

_screening

distance

_(d/2)

in

equation

(4)

[17].

With these

modification,

we obtain

_HelJ

oc

_{(T, -}

T)3/2@

in much better

agreement

with

_experiment.

The low field microwave

_absorption

in the

_{high Tc}

_{oxides appears} to be a _{very useful way} to

study

their

_{special electromagnetic properties.}

We have

_proposed

that stacks of twins can lead

to the observed behavior.

_Blazey

notes that the series of

_absorption

lines varies with

_samples

ageing

and

_temperature

_cycling

_[14],

and we remark that this is in

_keeping

with the known

mobility

of the twin boundaries in the oxides.

_They

_may

_eventually

become

_trapped

in

defectuous

_regions

of the

_{crystal, leading}

to stack formation. This

_hypothesis

needs of course

to be confirmed

_by

direct observation. Short cohérence

length

and Coulomb effects.

We have so far

_argued

that the available data on the oxides can be

_reasonably

well

_interpreted

within a Landau

_Ginsburg

_framework,

with a rather conventional London

_{penetration depth}

and a short coherence

_length.

In this last

section,

we wish to

_point

out to some

implications

of this

_{short e}

_concerning

the electron-electron interaction.

In its

_simplest

_form,

the

_expression

for the critical

_temperature

of a BCS

_{superconductor}

is :

where

_{hw ex}

is an _{excitation energy and :}

N

_being

the normal state

_density

of states at the Fermi

_level,

_Ve,,

the attractive

_potential

that results from the

_exchange

of the excitations of

_typical

_energy

_{hw ex’}

and

_{V c *}

the effective screened Coulomb

_{repulsive potential.}

Effective

_screening

_requires

that the distance between the two members of a

Cooper

pair

at

the time where the excitation created

_by

the first one is absorbed

by

the second one, be much

larger

than a

_typical

distance

kp 1 :

This can be rewritten as

_{EF IÍúJex.}

_Now,

since the coherence

_{length eo}

is

_equal

to

(V F/ £0 .)

where

_{w g}

_{is the gap}

_frequency,

and since

_úJg

« _úJex, condition

(7)

can

_only

be fulfilled if :

In a conventional

_{superconductor,}

_lùex is a

_phonon

frequency,

(EFlh£oe,,)

is of the order of a few

_hundred,

and the bare Coulomb

_repulsion

is

_typically

reduced

_by

one order of

_magnitude.

As is well

_known,

this is the reason

_why

the condition for

superconductivity

_{Ve , >}

V c * is

met

in so _{many metals and}

_alloys.

It has

_long

been advocated that an _{effective way} to

_get

_high

_temperature

_{superconductivity}

is to raise the

_perfactor

in

_equation

_(5),

i.e. to have

_hlùex

of the order of the Fermi energy. But

it was also

_recognized

that this was not a

_{simple prescription,}

since one would then at the same time have

_{Vc* =}

_Vc

and

_accordingly

a small effective NV

[19].

There is still considerable

controversy

about the value of

_Ep

in the oxides

_(broad

or narrow

band) ;

and we do not know at all that of

_hwex,

since the mechanism for

_{superconductivity}

in the oxides is not known. But we do know from critical field measurements and

_boundary

effects

_[16]

that ) =

10

_Â,

and hence that condition

_[8]

is not well fulfilled and therefore condition

_[7]

even less.

The

_high

critical

_temperature

of the oxides and their short coherence

_length

are

experimental proofs

that a

_significant

attractive electron-electron

potential

can exist even

though

the classical Thomas Fermi

_screening

is weak

_(this

is also confirmed

_by

the small

isotope

effect).

What we don’t know is how this is achieved.

Or,

in other

_words,

electron correlation effects cannot be

_ignored

in the oxides. An

_{interesting question}

is whether the

high 7c

model based on the 2D Van Hove

_singularity

_[12],

which seems to fit well the Landau

Ginzburg description

of the

oxides,

can be made more

_quantitative

_{by including}

such correlation

effects,

and still

_give

a

_{high T,.}

Conclusions.

Superconductivity

in the oxides

_presents

_{many unusual features. Because of the short} coherence

_length,

critical behavior is observable.

_{Experimentally}

the width of the critical

region

is

_{significantly}

smaller than in

_superfluid

He ;

a coherent Landau

_{Ginzburg description}

then

_requires

a

_penetration

_depth

smaller than the

_currently

_accepted

_experimental

determination. The

_appropriate

value would be close to that

_{given by}

the London

_expression

with no mass enhancement. This would be consistent with a broad band scheme. The short coherence

_length

also favorizes

_junction

formation at extended

_{crystallographic}

defects. This

might

lead to the

_suggested

overestimate of the

_{experimentally}

determined

_penetration

depth.

The low field microwave

_absorption

features seen in twinned YBCO

_crystals

can be

explained

if one assumes the existence of

_composite

_junctions

made of stacks of twin boundaries.

_Finally,

the short coherence

_{length implies}

the existence of a mechanism that can reduce

_effectively

the Coulomb

_{repulsion, beyond}

the usual Thomas Fermi

_screening.

Acknowledgements.

I wish to thank K.

_Blazey

for

_stimulating

discussions on low field microwave

_absorption,

and for

_{communicating}

his results

_prior

to

_publication.

This article has been

_prepared

in honor of Professor

_Jacques

Friedel. 1 wish to _express to

him here my

deepest gratitude

for the marvelous time that 1 have

_spent

at

_Orsay

as one of his

students,

discovering

the richness and

_beauty

of Solid State

_Physics

under his

_leadership.

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