a. bianconi- superstripes

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International Journal of Modern Physics B, Vol. 14, Nos. 29, 30 & 31 (2000) 3289-3297

World Scientific Publishing Company

3289

SUPERSTRIPES

A. BIANCONI

Unit INFM, Dipartimento di Fisica, Universit di Roma "La Sapienza", P. Aldo Moro 2, 00185

Roma, Italy; http://www.superstripes.com/

A superconducting superlattice of quantum stripes with a particular shape that gives theamplification of the critical temperature is called "superstripes". This superlattice ischaracterized by: a) the metallic stripe width L of the order of the de Broglie wavelength of

electrons at the Fermi level, L~F, and b) the hopping of pairs between the stripes larger than

the hopping of single electrons. "Superstripes" can be realized artificially to get new roomtemperature superconductors (RTS). This particular mesoscopic heterostructure at the atomiclimit has been found as a self organized network of charges, in a short time and space scale, indoped cuprate perovskites near the micro-strain quantum critical point for "superstripes"formation.

(Received Aug. 15, 2000)

1. Introduction

The design of new materials by atomic manipulation at the atomic limit for theamplification of the superconducting critical temperature can led to room temperature

superconductors (RTS) following the invention of "superstripes" in Rome in 19931.This invention provides the physical parameters to design new superconductingheterostructures intended to amplify the critical temperature described in a patent

1and

in following papers2-6

. The "superstripes" invention is based on the discovery that thesuperconductivity with high critical temperature is related to a particular heterogeneousstructure that has been found in a cuprate perovskite Bi2212, where the "superstripes"appear as a self organized network of stripes of charges in small bubbles of fewhundreds angstroms fluctuating with a time scale of 10

-12sec.

In the first part of this paper we describe how the critical temperature can bemultiplied by an "amplification factor", by making artificial "superstripes", up tohundred times larger than that of the homogeneous material. In the second part wedescribe the natural superstripes in cuprate perovskites.

2. Design of superstripes to amplify the critical temperature

The invention1

gives the key parameters for material design to get Tc amplification.Fig. 1 shows the heterostructure of superconducting stripes: "superstripes". Theheterostructure is formed by a superlattice of layers, (2) in Fig. 1. Each layer is madeof a plurality of first stripes of a first superconducting material, (3) in Fig. 1, and aplurality of second stripes with different electronic structure, (4) in Fig. 1, intercalatedto the first stripes, for their separation W, up to realize a superlattice having periodp.


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The separation W between the superconducting stripes measured in the y direction isof the order of the superconducting Pippard coherence length 0.

Figure 1. The heterogeneous structure made by a multi-layer of planes (2) where first metallic stripes(dashed stripes 3) of width L are separated by second stripes (empty stripes 4) forming a periodic potential

barrier of width W for the charge carriers in the stripes (3) with periodp.

Figure 2. The density of states N(E) of a superlattice of quantum stripes, "superstripes", as a function ofthe chemical potential E. The "shape resonance" is obtained by tuning the Fermi level, E F, at a density ofstates peak N(Em) occurring near the threshold of the m subband EF~Em. (m=2 in the figure). N(E) issuppressed in the pseudogap regions between Em


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k mL

mF

>

; 2 (1)

where kF is the wave-vector of the electrons at the Fermi level of the superconductingmaterial. More in general the condition for the "shape resonance" can be written as

E EF m

(2)

that means that the Fermi energy is tuned near a maximum of the electronic density of

the states N Em

( ) as shown in Fig. 2. Moreover in the case that the values of L

obtained by using the formula (1) are too small it is possible to use a second "shaperesonance" condition:

k G mL

mF

>

; 2 (3)

Energy

EF

kx

E2

E1 G

(b)

Energy

EF

kx

E2

E1

(a)

Figure 3. The particular case where the Fermi level is tuned near the bottom of the m=2 subband,following formula (1), panel (a), and formula (3), panel (b). The Fermi level is tuned by changing the

charge density of the stripe structure, to get the energy separation EF-E2


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The superconducting gap shows a resonance centered at the maximum of thedensity of states and a width determined by the energy cutoff for the paring interaction0. A characteristic feature of the Fermi surface of a superlattice of quantum stripes is

that it is broken and different superconducting gaps are associated with differentsegments. In fact there is a different gap "m" for each subband "m". Considering thesimple case shown in Fig. 2 and 3, where the chemical potential is tuned to thesecond "subband", two gaps appear in different portions of the Fermi surface.

10- 1

100

101

102

103

2 3 4 5 6 7 8 9100

101

102

Tc

(K)

1/

Tcn

Tc

Amplification

Figure 4. The calculated critical temperature as a function of the coupling for the pairing: Tc

for an

infinite homogeneous material and Tcn for a superlattice of quantum stripes by tuning the chemical

potential to the m shape resonance. The amplification of the critical temperature in the superstripes, fromref. 6, is shown.

Fig. 4 shows the amplification of the critical temperature that can be obtained bysuperstripes design. By tuning the chemical potential close to an artificial peak of the N(E) for the superstripes, the superconducting critical temperature shows a resonantamplification that depends on the stripe width L and the potential barrier between thestripes

4-6.

Quantum phase fluctuations that usually suppress the superconducting"condensate" in low dimension are not effective in the superstripes. In fact themesoscopic stripe width L and the periodic potential barrier give sharp peaks in thedensity of states N(Em). By increasing artificially the local density of states N(Em) thehopping of electron pairs between the stripes t N E

m

( )

2 can be made larger than the

hopping of the single electrons between the stripes tt N E t

m ( ) >2 (4)

If this condition is satisfied, the phase coherence of the superconducting phase isstabilized and quantum fluctuations, expected in low dimensional systems, do notsuppress the critical temperature for the superconductivity.

The 1D charge ordering, or stripes formation, has been considered by the scientificcommunity to be always detrimental for superconductivity. In fact T c is suppressed if


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the chemical potential is tuned in the pseudo gap region. However T c is amplified bytuning the chemical potential at the shape resonance in the "superstripes. At the first

7

and second8

conference on "Stripes and high Tc superconductivity" only two paperswere presented on "superstripes".

Seven years after the invention at the third conference held in Rome9

several paperson "superstripes" have been presented

10-15considering different scenarios for the

formation of the periodic potential barrier, but confirming the mechanism of Tcamplification in "superstripes". Some authors have shown the key role of twosuperconducting gaps for Tc amplification resulting by two bands where the chemicalpotential is tuned to the bottom of the second band as shown in panel (b) of Fig. 3

16.

Direct experimental evidence for two dispersing bands in Bi2212, as predicted inFig. 3, has been reported by several groups

17-18by using high resolution angle resolved

photoemission. These experiments give a compelling experimental evidence for the presence of a superlattice of quantum stripes with wave-vector Q(0.4,0.4) firstobserved in momentum scanning photoemission by Saini et al

19-20

( a ) ( b ) ( c )

Figure 5. The phases of the 2D electron gas in cuprates at fixed doping by changing the micro-strain: (a)

Metallic phase, quantum disorder, 0; (b) Superstripes, metallic bubbles of stripes, c


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10-12

sec as shown in panel (b) of figure 5. It was found that the detection ofsuperconducting striped phases depends on the experimental measuring time, and thefluctuation time changes from sample to sample. Therefore in some samples, with fastsuperstripes fluctuations, the striped phases are difficult to be detected.

Micro-

-strain

Temperature

Doping

QCP

(a)

(c)

(b)

Figure 6. The new phase diagram of the metallic phase for all cuprate perovskites21

as a function of

doping , temperature T, and micro-strain acting on the CuO2 plane. The phases (a), (b) and (c) in Fig. 5

appear in the (,) plane. The fluctuating bubbles of superconducting stripes, "superstripes", are formed

near the quantum critical point (QCP) for superstripes formation. Critical charge, spin, and orbitalfluctuations give the self-organized pattern of "superstripes" in a short time (~10

-12sec) and length scale

(100-300 ) in the region of micro-strain and doping defined by the bold circle centered at the QCP.

Recently it has been shown that the elastic field plays a key role for the presence of"superstripes" in cuprates

21. It was known that the critical temperature of cuprate

superconductors could be changed by applying a pressure, by atomic substitution viachemical pressure, and by the mismatch with the substrate in films, but themechanism remained mysterious. Recently it has been shown that beyond temperatureand doping a third variable is needed to define the phase diagram of cuprateperovskites: the micro-strain in the CuO2 plane as shown in Fig. 6. There is acritical micro-strain for "superstripes" formation as shown in Fig. 6. Near this criticalmicro-strain the formation of fluctuating bubbles of "superstripes" has been found indoped cuprate perovskites

21. The superstripes are due to critical charge, spin and orbital

fluctuations around this quantum critical point (QCP).The new phase diagram for all cuprates, shown in Fig. 6, depends on the charge

density (i.e., the doping), the temperature and the elastic field due to the micro-strain.

In the plane (,), at T=0K, in Fig. 6 it is possible to identify the different phases(a),(b) and (c) shown in Fig. 5. The superstripes are formed beyond the critical micro-strain for formation of superstripes that determines the quantum critical point (QCP)shown in Fig. 6. Critical charge, spin, and orbital fluctuations give the self organized bubbles of "superstripes" in the region of strain-doping defined by the gray circlecentered at the QCP in Fig. 6.

Superstripes have been shown to be formed by self organization in a sample ofBi2Sr2CaCu2O8.21 (Bi2122) close to the QCP. The heterogeneous phase of Bi2122 ismade of i) a charge reservoir layer (Bi2O2.21) ii) a rocksalt block (Sr2O2Ca) and iii) the


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two superconducting CuO2 planes embedded within the rocksalt layers. The rocksaltlayers induce a micro-strain on the CuO2 plane larger than the critical strain for locallattice distortions (LLD). The dynamical buckling of the Cu-O plane forms a striped pattern with a wave-vector Q~(0.4,0.4) within a short coherence length of about100-300 that gives the size of the fluctuating bubbles

20. Within the bubbles, the

modulation of the second nearest neighbor hopping integral t gives a superlattice ofquantum stripes with the formation of superlattice subbands observed by angularresolved photoemission. The Fermi level at optimum doping is at about 50-80 meVabove the bottom of the highest subband

20and it has been shown that the chemical

potential at optimum doping =0.16 is tuned to the third, m=3, "shape resonance" asshown by the DOS in Fig. 7. The peaks and minima in the DOS due to the first andsecond subband (1 and 2) according with the formula (1) are indicated in Fig. 7. Atnegative doping it is possible to see the corresponding peaks due to the formula (3).

-1 -0.5 0 0.5 1

DensityofStatesN()

Doping ()

pseudo-gap optimumdoping

(1)(2)

(3)

Figure 7. The density of states (DOS) as function of doping N() calculated for a 2D CuO2 plane where

the hopping integral t is modulated in the diagonal direction with wave-vector Q(0.4,0.4). At optimum

doping, =0.16, the chemical potential is tuned to the m=3 "shape resonance" (3) indicated by the vertical

arrow. The DOS shows the pseudo-gap in the low doping region


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"Consiglio Nazionale delle Ricerche" (CNR), and "Gruppo Nazionale di Struttura dellaMateria" (GNSM).

References

1. European Patent N. 0733271 "High Tc superconductors made by metal

heterostuctures at the atomic limit; (priority date 7 Dec 1993), published inEuropean Patent Bulletin 98/22, 1998.

2. A. Bianconi Sol. State Commun. 89, 933 (1994).3. A. Bianconi, M. Missori, N. L. Saini, H. Oyanagi, H. Yamaguchi, D. H. Ha, and Y.

Nishiara Journal of Superconductivity 8, 545-548 (1995)4. A. Perali, A. Bianconi, A. Lanzara, and N. L. Saini Solid State Communications

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(1998)7. Proc. of the First Inter. Conference on Stripes, Lattice instabilities and high

Tc Superconductivity special issue of J. of Superconductivity Vol. 10, No. 4August (1997).

8. Proc. of the Second Int. Conference on Stripes and High Tc superconduct ivi tyin "Stripes and Related Phenomena" edited by A. Bianconi and N. L. Saini,Kluwer Academic/ Plenum Publishers, New York (2000).

9. Proc. of 3rd Int. Conference on "Stripes and High Tc superconductivity" Int. J. Mod. Phys. B, World Scientific, Singapore, 2000; Book of Abstracts ofSTRIPES2000 in the web site http://www.superstripes.com/

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12. W. Hanke "Stability and single-particle excitations of the stripe phase" Bookof abstracts of the Third Int. Conference on Stripes and High TcSuperconductivity, Rome Sept 25-30 (2000) S14-IV in the web si tehttp://www. superstripes.com/

13. R. S. Markiewicz and C. Kusko "Structure of charged stripes in ordered stripearrays in the cuprates" Book of abstracts of STRIPES2000, Rome Sept 25-30(2000) No. S14 -V in the web site http://www.superstripes.com/.

14 M. Fleck, E. Pavarini, and O. K. Andersen "Electronic structure of the stripedphases in La2-x-yNdySrxCuO4" in Book of abstracts of STRIPES2000, Rome Sept25-30 (2000), S16 -VI (http://www.superstripes.com/)

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centered"inInt. J. Mod. Phys. B, World Scientific, Singapore, (2000).16. E. Piegari, A. Perali, C. Castellani, C. Di Castro, M. Grilli, and A. A. Varlamov

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Shimoyama, K. Kishio, H. Ikeda, R, Yoshizaki, Z. Hussain, H. and Z. X. ShenPhys. Rev. Lett. 85, 2581 (2000).

18 J. Mesot, M. Boehm, N. Metoki, A. Hiess, K. Kadowaki. J. C. Campuzano, A.

Kaminski, S. Rosenkranz, and M. R. Norman "Neutron (,) resonance in

underdoped Bi2212 and its relation to the electronic spectra as measured byARPES" Book of abstracts of STRIPES2000, No. S-11-V.

19. N. L. Saini, J. Avila, A. Bianconi, A. Lanzara, M. C. Asensio, S.Tajima, G. D. Gu and N. Koshizuka,Phys. Rev. Lett.79, 3464 (1997).

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A. Bianconi, N. L. Saini, S. Agrestini, D. Di Castro and G. BianconiInt. J. Mod. Phys. B, World Scientific, Singapore, (2000) this volume.

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