n.l. saini and a. bianconi- superstripes by anomalous x-ray diffraction and angle resolved...

8/3/2019 N.L. Saini and A. Bianconi- Superstripes by Anomalous X-Ray Diffraction and Angle Resolved Photoemission in Bi2212

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International Journal of Modern Physics B, Vol. 14, Nos. 29, 30 & 31 (2000) 3649-3655 World Scientific Publishing Company

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SUPERSTRIPES BY ANOMALOUS X-RAY DIFFRACTION AND ANGLERESOLVED PHOTOEMISSION IN BI2212

N. L. SAINI, A. BIANCONI

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

Roma, Italy

We show an evidence for the superconducting stripes (superstripes) in the Bi2212 system by jointx-ray diffraction and angle resolved photoemission. The kink observed at ky=0.4 in the energydistribution curves is shown to be related to a modulation of the Cu displacement out of the oxygenplane with a wavevector Q~(0.4,0.4) that modulates the next-nearest neighbor hopping integralt'. The resulting Fermi surface reveals broken segments around the M points due to the modulationof the t', associated with modulation of the electron-lattice coupling () that depends on the micro

strain of the CuO2 plane. The present findings further enlightens the fact that the micro-strain,

controlling the electron-lattice coupling () is a critical parameter for the superstripes.

Introduction

Bi2Sr2CaCu2O8+ (Bi2212) superconductor is a particular heterostructure with threedifferent sublattices, [Bi2O2+](Sr2O2Ca){CuO2}2, i.e., the metallic bcc CuO2 layer, theinsulating rock-salt fcc Sr2O2Ca layerand the charge reservoir (CR) Bi2O2+layer. Thesuperconducting covalent bcc CuO2 layer is intercalated between insulating fcc ionicrock-salt Sr2O2Ca sublattices, rotated by 45

o. A large compressive stress is exerted onthe CuO2 plane due to the lattice mismatch with the rock-salt sublattice having strongadhesive forces from the CR substrate. The resulting micro-strain on the CuO2 planecould be defined as =2(r0-)/r0, where is the measured in plane Cu-O bondlength and r0=1.97 is the equilibrium Cu-O distance. Recently it has been shown thatthe strain plays important role in the physics of the doped perovskites1-5. Indeed theCuO2 plane shows superconducting stripes (called superstripes)

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argue the kink observed at ky=0.4 in the electron distribution curves in recent angleresolved photoemission experiments is a result of the modulation of the t' with awavevector Q~(0.4,0.4). This t' modulation is associated with a modulation of theelectron-lattice coupling () that depends on the micro strain . The anomalousdiffraction results are discussed with the calculated energy dispersion curves and thedensity of states and the Fermi surface topology, showing a good agreement with theangle resolved photoemission experiments. The results further shed light on the stripeformation mechanism driving the T c amplification in the cuprate perovskites.

Experimental details

Superconducting single crystals, grown by the travelling solvent floating zone method,were used for the measurements. X-ray diffraction measurements were made on thebeamline ID11 at the European Synchrotron Radiation Facility (ESRF), Grenoble.Different crystals with Tc ~ 84-87 K (Tc~1.2 K) were mounted in closed cyclerefrigerator and temperature was controlled within an accuracy of 1K. The diffractionpatterns were recorded sequentially at two wavelengths chosen to have a large variation inthe real part of the Cu anomalous scattering factor (f'=6.2 electrons) with no variationin the imaginary part f'': 1=1.3788 , at the rising edge of the Cu K threshold, and2=1.4086 , well below the edge. We have refined the z component values of Cuatoms independently from the structural parameters of all other atoms, withzCu (t) = c0 + c1cos(2 t) + c2 cos(4 t) (where t= y) considering two harmonics. The

details of the experiments and analysis are given elsewhere8.

Results and Discussion

Fig. 1 shows the modulation of the Cu z component determined at low temperature inthe superconducting phase (T


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the CuO4 square planes and their rhombic distortions. The strain changes the states nearthe Fermi leve l that can be described by an effective tight band model with nearneighbor hopping integral t() and next-nearest neighbor hopping integral t'(). Thelarge on site Coulomb repulsion U gives a correlated electron gas described by theHubbard term. Moreover the strain field tunes the relevant electron lattice interactiong() of the type of cooperative pseudo Jahn-Teller coupling of charges with Q2-type localmodes.

-0.5

0

0.5

1

1.5

2

0 10 20 30 40 50 60

z()

y ()

Ca

O(P)

Cu

Figure 1. Transverse modulation of the Ca ions (open diamond) in the rock-salt layer plotted with themodulation of the oxygen ions (filled symbols) in the CuO 2 plane. The open circles represent the anharmonicmodulation of the Cu ions along the z-axis, revealed by the Cu K-edge anomalous diffraction.

0

0.3

0.6

0.9

0 10 20 30 40 50 60 70 80

z()

y ()

x

Figure 2. Displacement of the Cu ion out of the oxygen plane forming a striped phase of the CuO2 plane .

The metallic phase can be described by the Holstein-Hubbard Hamiltonian9

H = Hel + HU + Hph + HI = t( ) ci+ c

j( )< i, j >, + t' ( ) ci

+ cj( )

> , + U ni

i ni

+0

( ) aq+ a

qq

+ g( )0( ) ci

+

i

ci a i+ + a i[ ] 0 ni

i

The first two terms describe the itinerant charges in a 2D square lattice, the CuO2 planewhere t() is the electron transfer integral between nearest-neighbor sites and t'()is the electron transfer integral between next-nearest-neighbor sites . The electrontransfer integrals t() and t'() are used to reduce the complex multi-bands electronic


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structure to an effective single band9-12. The e-ph coupling g() is driven by cooperativepseudo Jahn-Teller effect4,13. The t and t ' depend on the Cu-O bond and the latticegeometry and hence on the micro-strain. The modulation of the micro-strain is expectedto modulate the electronic structure through static and dynamic effects due tomodulation of the electron phonon coupling g(). In a previous work we have shownthat e-ph coupling with a mode , having a wavevector (0.4, 0.4) suppresses thephotoelectron spectral weight at the Fermi surface, around the M points of the Brillouinzone14. For the Bi2212 crystal the electron lattice interaction g() is larger than thecritical value for cooperative local lattice distortions due to a large micro-strain (averagestrain for the Bi2212is ~0.055>c)

4. The local lattice fluctuations get ordered in aparticular form of superstripes i.e., mesoscopic fluctuating bubbles of quantum wireswhere the chemical potential is tuned to a shape resonance4.

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0 0.1 0.2 0.3 0.4 0.5

Energy(eV)

k||

(/d)

Figure 3. Experimental energy distribution of the spectral weight in the -M direction, along with thecalculated band structure for a stripe phase involving dynamical modulation of t' with a wave vectorQ~(0.4, 0.4).

Angle resolved photoemission measurements were made using angle scanningmethod14. A tight binding fit to the experimental data gives the t() ~ 200 meV and t'()~ 60 meV. The experimental details and the Fermi surface could be found elsewhere14.Fig. 3 shows the experimental energy distribution of spectral weight in the -Mdirection. The buckling modulation in the superconducting bubbles observed by thediffraction induces a modulation of e-ph coupling g() resulting in a modulation of t'.Therefore the electronic band dispersion can be described as a modulation of t' with awavevector (0.4, 0.4). For the calculations we have considered modulation of t'between 60 meV and zero with a period of 2.5b along the diagonal direction. Thecalculated band along the -M direction is shown in Fig. 3.

One of the main outcome of the present calculations is a clear break in the dispersion(see the arrow) at k||~0.4. Signature of this kink-like structure in the dispersion wasseen in earlier measurements, however, recent measurements with high energy and


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momentum resolution have clearly shown existence this break, all over the Brillouinzone, with an energy ~5015 meV15, 16. The break is more pronounced near the -Mdirection and as a matter of fact evidently appears with two features in the energydispersion curves. The energy of the break depends on the value of the t', which differsslightly in different materials however remains in the range 40-80 meV4. There areseveral arguments to explain this anomalous break in the quasiparticle dispersionincluding the magnetic resonance mode, energy gap and charge inhomogeneityassociated with the stripe structure in the CuO2 plane (see for example ref. 15 and ref.16). The present work makes it clear that the kink like structure in the dispersion shouldbe related to the modulation of the t' above the critical micro-strain for the superstripeformation4.

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

ky

(

/)

kx

(/)

Figure 4. Calculated Fermi surface contours of the Bi2212 system near the optimum doping. The tightcalculations are made including modulation of the t' due to modulation of the CuO2 dimpling.

Fig. 4 shows calculated two-dimensional constant energy contours with differentchemical potential near the Fermi surface. The Fermi surface shows missing segmentsaround the M points (see the arrows). This is consistent with experimentally observedFermi surface14 on the Bi2212 system. Indeed the Fermi surface, measured by anglescanning photoemission shows an asymmetric suppression of spectral weight aroundM(,0) point that has been assigned to coupling of the itinerant carriers with anincommensurate modulation with a wavevector Q~(0.4,0.4) of charge and orbitalmomentum17. The good agreement between the experimental data and the calculationssuggests that the modulation of dimpling of the CuO2 plane, giving rise to dynamic

orbital wave, is at the origin of the asymmetric suppression of spectral weight aroundthe M(,0) point of the Fermi surface. The dynamic stripe fluctuations take place inbubbles of ~100-300 4, therefore the stripe wavevector Q~(0.4,0.4) could changedirection from bubble to bubble giving a symmetric distribution of kink location in theBrillouin zone as shown in experiments15.

In summary, we have studied superstripes in the Bi2212 superconductor by jointanomalous x-ray diffraction and angular resolved photoemission. The x-ray diffractionresults shows that the Cu displacement in the CuO2 plane is modulated with a


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wavevector Q~(0.4,0.4) associated with the superstripes. This modulation of theCuO2 dimpling modulates the next-nearest neighbor hopping integral t'. We havecalculated the band structure and the Fermi surface contours including the modulation oft'. The results suggests that the modulation of the t' gives rise to a clear break in thequasiparticle energy dispersion as found in angle resolved photoemission experiments.The Fermi surface reveals broken segments around the M points due to modulation ofthe t', related with modulation of the electron-lattice coupling () that depends on themicro strain. The present finding clearly demonstrates that the micro-strain, controllingthe electron-lattice coupling () is a critical parameter for the superconducting stripes(superstripes)4. This particular modulation gives rise to a superlattice of quantumstripes, where the chemical potential is tuned to a "shape resonance" at the optimumcharge density and the hopping of pairs between stripes is larger than that of singleelectrons18.

Acknowledgements

The authors would like to acknowledge experimental support of ESRF beamline staffduring the experiments. This work is supported by "Istituto Nazionale di Fisica dellaMateria" (INFM) in the frame of the progetto "Stripes", by the "Ministero dell'Universite della Ricerca Scientifica" (MURST) Programmi di Ricerca Scientifica di RilevanteInteresse Nazionale coordinated by R. Ferro, and by "Progetto 5% Superconduttivit ofConsiglio Nazionale delle Ricerche" (CNR).

References

1. A. Bianconi S. Agrestini, G. Bianconi, D. Di Castro and N. L. Saini, in"Stripes and Related Phenomena", Edited by A. Bianconi and N. L. Saini,(Kluwer Academic-Plenum Publisher, New York, 2000). pag. 9.

2. N. L. Saini, A. Bianconi and Y. Oyanagi J. of Phys. Soc. Jpn. , to bepublished(2000) ; N. L. Saini, A. Bianconi A. Lanzara, S. Agrestini D. DiCastro and Y. Oyanagi Int. J. Modern Physics B,to be published (2000)

3. A. Bianconi, D. Di Castro, N. L. Saini and G. Bianconi in Phase transitionsand self-organization in electronic and molecular networks, edited by M. F.Thorpe and J. C. Phillips, (Kluwer Academic/Plenum Publisher, 2000)Fundamental Materials Research Series; Proc. of the meeting at Cambridge11-14 July, 2000)

4. A. Bianconi, N. L. Saini S. Agrestini, D. Di Castro and G. Bianconi, Int. J.Mod. PhysicsThis volume

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6. A. Bianconi, European Patent N. 0733271 "High Tc superconductors made bymetal heterostuctures at the atomic limit" (priority date 7 Dec 1993),published in European Patent Bulletin 98/22, May 27 1998)

7. A. Bianconi, A. Valletta, A. Perali, and N. L. Saini Physica C 296, 269(1998).


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8. A. Bianconi, M. Lusignoli, N.L. Saini, P. Bordet, . Kvick, P.G. RadaelliPhys. Rev. B 54, 4310 (1996).

9. F. Becca, M. Tarquini, M. Grilli, and C. Di Castro Phys. Rev. B 54 , 12443(1996).

10. R. Raimondi, J.H. Jefferson, and L.F. Feiner Phys. Rev. B 53, 8774 (1996);L.F. Feiner, J.H. Jefferson, R. Raimondi Phys. Rev. B 53, 8751 (1996)

11. F. V. Kusmartsev, D. Di Castro, G. Bianconi & A. Bianconi Physics LettersA 275, 117 (2000); F. V. KusmartsevJ. de Physique IV 9 , Pr10-321 (1999);F. V. Kusmartsev Phys. Rev. Lett. 84 , 530 (2000); ibidem 84 , 5026 (2000).

12. E. L. Nagaev Sov. Jour. JEPT Lett. 16, 558 (1972); V. A. Kaschin and E. L.Nagaev Zh. Exp. Teor. Phys. 66. 2105 (1974); E. L. Nagaev, A. I.Podelshchikov and V. E. Zil'berwarg J. Phys. Condensed Matter 10, 9823

(1998).13. G. I. Bersuker and J. B. Goodenough Physica C274, 267 (1997).14. N. L. Saini, J. Avila, A. Bianconi, A. Lanzara, M. C. Asensio, S. Tajima,

G. D. Gu and N. Koshizuka, Phys. Rev. Lett. 79, 3467 (1997).15. P.V. Bogdanov, A. Lanzara, S.A. Kellar, X.J. Zhou, E.D. Lu, W.J. Zheng,

G. Gu, J.-I. Shimoyama, K. Kishio, H. Ikeda, R. Yoshizaki, Z. Hussain andZ.X. Shen, Phys. Rev. Lett. 85, 2581 (2000); A. Lanzara et al, privatecommunication, book of abstracts of STRIPES2000 (http://superstripes.com/)

16. A. Kaminski, M. Randeria, J. C. Campuzano, M. R. Norman, H. Fretwell, J.Mesot, T. Sato, T. Takahashi, K. Kadowaki, cond-mat/0004482 (2000).

17. N.L. Saini, A. Bianconi, A. Lanzara, J. Avila, M.C. Asensio, S. Tajima,G.D. Gu and N. Koshizuka, Physica C341-348, 2071 (2000).

18. A. Bianconi, Physica C 235-240 , 269 (1994); A. Bianconi Sol. StateCommun. 91 , 1 (1994) .

n.l. saini and a. bianconi- superstripes by anomalous x-ray diffraction and angle resolved...

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