High Tc superconductivity by quantum confinement

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High Tc superconductivity by quantum confinement

A. Bianconi, M. Missori

To cite this version:

A. Bianconi, M. Missori. High Tc superconductivity by quantum confinement. Journal de Physique

I, EDP Sciences, 1994, 4 (3), pp.361-365. �10.1051/jp1:1994100�. �jpa-00246912�

Classification Physics Abstracts

74.70V 74.20F 78.70D

Short Communication

High _Tc superconductivity by quantum confinement

A. Bianconi and M. Missori

Università di Rcma, Dipartimento di Fisica, P-A- Moro 2, 00185 Roma, Italy

(Received

21 December 1993, accepted 4

January1994)

Abstract. We report ^{the results of} a careful expenmental investigation of trie Cu site

configurations in the Cu02 Plane of

B12Sr2CaCu208+y

(B12212) showing ^{tbat trie} quasi 2D Fermi liquid is confined in trie stripes of width L with _a superlattice period _Àp

= 4.65a. Tbe bigh Tc superconductivity is stabilized at high temperature by tuning ^trie Fermi _energy of trie 2D electron gas to trie quantum _resonance

kfy

_" ^2jr

IL.

Trie confinement of _a 3D electron _gas in quantum _{wires con} be realized by syntbetizing Bi,Ca-Sr-Cu,O systems with _some adjacent Cu02 layers forming _a metallic slab of thickness H. In ibis _case trie amplification of trie critical temperature ^is assigned to quantization of trie wavevectors along bath trie _y and _z directions satisfying the

kfy

_" 2jr

IL

and kfz

"

mjr/H

conditions.

Tl~e presence of

polarons

in tbe n~etallic

phase

^of

B12Sr2CaCu208+y (B12212)

[1-3] ^has been

investigated by measuring

tl~e

Cu-O(apical)

distance

by

Extended

X-ray Absorption

Fine Structure

(EXAFS) experiments.

In fact tbe local structure

configurations

associated with

polarons

_con be described

by

two main

configurational

coordinates:

1)

^tl~e

sl~ortening

of tl~e

Cu-O(apical)

distance due botl~ _to Cu

displacement

fron~ tl~e

Cu02 Plane

and to tl~e movement of tl~e

apical

_oxygen, and

2)

the

tilting

of the

apicaloxygen

from (7r, 7r) ^direction as in tl~e low

temperature ortl~orhon~bic

(LTO)

like structure to the

(0,

7r) direction in tl~e low ten~perature

tetragona1phase (LTT)

hke structure [4].

The idea of the present ^{work is that}

by measuring

the distribution of the

long

and short

Cu-O(apical)

bond

lengths by EXAFS,

and the modulation

period

_{Àp =} 4.65

by

electron

diffraction,

it is

possible

to _measure the width L of the stripes of Cu sites of undistorted

domains witb LTO type structure confined between the stripes of

polarons

with the LTT

structure.

Expenmental

details have been

reported

elsewhere

[si.

^Two

Cu-O(apical)

distances

2.37 and 2.53

À

_{below Tc have been}

found,

in agreement ^with diffraction works _[3]

confirming

tl~e presence of domains witl~ different Cu site

configurations

in tl~e Cu02

plane.

Tl~e domains of the undistorted Cu sites, with tl~e LTO type structure, are associated with tl~e locus of

the itinerant states

giving

_a Fermi

liquid.

These domains form

stripes

of width L. In

figure

1

362 JOURNAL DE PHYSIQUE I N°3

4

ce

~~ 3

fi

~

~

u 2

~ 'c

ÉÎ

0 0.2 0.4 0.6 Ù-1

TN

Fig. l. The determination of tbe width of the stripes of undistorted domains _m trie Cu02 Plane

obtained by the _measure of tbe relative number

Niong/Ntot

of trie apical _oxygens witb _a long

(2.53

À)

Cu-O(apical)

distance, from EXAFS data measured ai low temperature, ^for T < Tc, _in tbe B12212

monocrystal (Tc # 84

K).

we report the _measure of L below

Tc,

obtained

by

tl~e measured values of

Nong/Ntot

in fact L

la

# >p

(Njong/Ntot)

Tl~is result allows _us to describe tl~e Cu02

plane

_as sl~own in

figure

2 wl~ere

polarons

of _area

Sp

= 4a~

= l16 À~ bave condensed in _a unidimensional

charge density

_wave

CDW, forming

tl~e

polaronic stripes

of widtl~ W

= 2a with _a LTT like structure. Tl~erefore tl~e Cu02

Plane

is decorated

by

two different Cu site structure

configurations

distributed in linear

stripes.

This scenario shows tl~at the Fermi

liquid

is confined in _a

superlattice

of quantum stripes of widtl~ L. Tl~e B12212 with two Cu02

layers

form _a

quasi

2D electron _gas. The

anisotropic superconducting

_gap bas been found to show _a maximum _m tl~e FM direction with values of the components of the Fermi wavevector kfx _"

kfy

_" 0.37

(27rla)

_[6]. For _a 2D-Fermi

liquid

confined in _a quantum stripes of width L the k-vector is

quantized

in the _y direction

(kny

=

n7r/L)

and it is evident that

kfy

is very close to

27r/L

=

1/2.7

_(27r

la),

_so the Fermi wavevector is tuned to the _{resonance n}

= 2.

The

density

of states of the

superlattice

of quantum

stripes

_{[7] is} different from the

density

of states of the 2D square

lattice,

because it shows very intense and

sharp peaks

with maxima

of the order of rive-tens times the 2D

density

of states. If the Fermi _{energy is} tuned at one of these maxima the

superconducting

critical temperature can be

pushed

_up

by

_a factor of tl~e order of 5-10.

In fact for _a standard

superconducting

metal

following

the BCS

theory

Tc

r~J 2wD

exp(-1/NOV),

wl~ere No is the

density

of states at the Fermi energy and V is tl~e electron-

phonon coupling

_constant, therefore the increase of

No imphes

_an increase of Tc. Careful band structure calculations of the cuprates

give

the

electron-phonon coupling

constant V

r~J 1-s and

the

density

of states

No

_r~J 0.15

stateslev-atom-spin showing

that

NOV

r~J 0.2. Therefore

by taking

_{wD '~~} 500 K _as the

Debye

temperature we can calculate _m first

approximation,

the

critical temperature ^of a

homogeneous

Cu02

plane

Tc _r~J 7 K

predicted by

the BCS

theory.

More refined calculations of Tc

using

the

Allen-Dynes equation give

Tc

r~J

30 K [8].

The enhancement of the critical temperature

by forming

metallic

stripes

of width L

separated by

stripes ^{of width} W _can be calculated

by following

the solution of the _gap

equation

of

Thompson and Blatt [9] ⁱⁿ a

surgie

film of _a

superconducting

metal where the Fermi level is close and above the energy of the _{n resonance.} The enhancement factor at the second _resonance

as found in the cuprates ^{should be of the order of}

exp(1/(3NoV))

r~J 5 for _a

superlattice

~ cu

~

~

z

x

LTT-liiè

_LTO-like

Fig. 2. Pictonal view of the Cu02 Plane witb the formations of stripes of width L of the undistorted lattice with LTO structure and long

Cu-O(apical)

bond, locus of the Fernù liquid and tbe stripes of widtb W locus of the polarons with trie Cu site configurations characterized the short

Cu-O(apical)

bond and LTT structure.

in

comparison

with tl~e

homogeneous Cu02 Plane.

Tl~erefore tl~e critical temperature _can be enhanced

by

tl~e confinement from the 7

(30)

K _range to tl~e 35

(150)

K _range. The

amplification

factor

depends

_on tl~e _resonance number _n and _on the

coupling

term NOV. In

figure

3 _we report ^tl~e enl~ancement factor for tl~e _case of _a

superlattice

of quantum wells _as function of the _resonance number for tl~e _case of

NOV

= 0.2 and

0.12,

calculated

by using

the

Thompson

and Blatt

approacl~.

It is tl~erefore clear tl~at tl~e

largest amplification

_is obtained

by tuning EF

at the lowest resonances.

70

~o

50

N~V=0.12

t

40

/

b- 30

20

N V=0.2

0

2 3 4 5 6

n

Fig. 3. Trie ratio of trie cntical temperature Tc» for _a quantum well, with the Fermi energy tuned

ai the _{n resonance} normalized to trie bulk cntical temperature Tccc for superconducting menais with

different coupling constants NOV, calculated by _usmg tbe Thompson and Blatt approach.

364 JOURNAL DE PHYSIQUE I N°3

The 3D

superconducting

state _is stabilized

by

_a

superlattice

where tl~e distance between the wells _{or wires} is less _or of the order of the

superconducting

coherence

length (o

_[10]. In fact in _a

superlattice

is

possible

to rise Tc

by

quantum confinement but in _a

single

quantum

well,

_as

proposed by

Thompson and

Blatt, proximity

effects and fluctuations will suppress the

superconducting phase

and Tc.

Recently Lagues

et al.

il Ii reported

l~igh Tc

superconductivity

in _a Bi-Sr-Ca-Cu-O system witl~ 8

Cu02 layers. Following

tl~e present idea for tl~e enl~ancement of Tc

by

quantum _con- finement _{we propose} tl~at in tl~e 8

layers compound

_a three dimensional

(3D)

Fermi

liquid

is confined in quantum wires _as shown in

figure

4. In fact

by increasing

the number of

layers

we expect to form _a 3D Fermi

liquid

due to the

hopping

between the

neighbor planes.

Eacl~

quantum wire will bave _an effective tl~ickness H

given by

tl~e slab of the 8 Cu02

layers

in the _z direction and width L in the y direction determined

by

the superstructure. ^{For this} quantum ^{wire the k} vector will be

quantized

in two directions _y and _z. The enhancement of Tc in _a

superlattice

^of quantum wires is

expected

where kF is tuned to the

quantized

values

kzm

=

m7r/H

and

kny

₌ n7r

IL,

while _m the

quasi

2D electron _gas in _a

single layer compound

the

quantization

was

only along

the _y direction.

z

l~ _{W-~~ L-t~}

~

y

~

~~ Fz

Fig. 4. Pictorial view of the superlattice of quantum _wires ^that _cari ^{be realized} by tumng ^{the Fermi} level of _a 3D electron gas ^to the _resonance conditions

kfy

#

2jr/L

and kfz

#

2jr/H.

References

[Ii Bianconi A., Delta Longa S., Misson M, Pettiti I. and Pompa M., Lattice Elfects _m High-Tc Superconductors, Y. Bar-Yam, T. Egami, J. Mustre de Leon and A.R. Bishop Eds. (World Scientific Pub., Singapore, 1992) _p. 95.

[2] ^Bianconi A., Phase Separation in Cuprate Superconductors, K-A- Müller Ed.

(World

Scientific Pub., Singapore, 1992) _p. 125.

[3] Beskrovnyi A.I., Dlouhà M., Jiràk Z. and Vratislav S., Physica C 171

(1990)

19;

Beskrovnyi A.I., Dlouhà M., Jiràk Z., Vratislav S. and Pollert E., Physica C 166

(1990)

79.

[4] ^Axe J-D-, Moudden A.H., Hohlwem D.H., Cox D.E., Mohanty K-M-, Moodenbaugh A.R. and Xu Y., Phys. Rev. Lett. 62 (1989) 2751.

[Si ^Biancom A., Misson M., Oyanagi H., Yamaguci H., Ha D.H. and Della Longa S., to be published.

[6] Shen Z.-X et ai., Phys. Rev. Lett. 70

(1993)

1553;

Dessau D.S. et ai., Phys. Rev. Lett. 71

(1993)

2781.

[7]Bastard

G., Wave Mechamcs Applied to Semiconductor Heterostructures

(Les

Editions de

Physique, Les fJlis, France, 1988).

[8] Pickett W-E-, J. Phys. Chem. Solids 53

(1992)

1533.

[9] Thompson C.J. and Blatt J-N-, Phys. Lett. 5

(1963)

6.

[loi

Frick M. and Schneider T., Z. Phys. Condensed Matter 88

(1992)

123.

iii]

Lagues M.E. et al., Science 262

(1993)

1850.