Evidence for strong electron–phonon interaction from inelastic tunneling of Cooper pairs in c-direction in Bi2Sr2CaCu2O8 break junctions

PERGAMON

Solid State Communications 111 (1999) 513–518

Evidence for strong electron–phonon interaction from inelastic tunneling of Cooper pairs in c-direction in Bi2Sr2CaCu2O8 break junctions Ya.G. Ponomarev a, E.B. Tsokur a, M.V. Sudakova a, S.N. Tchesnokov a, M.E. Shabalin b, M.A. Lorenz c,*, M.A. Hein c, G. Mu¨ller c, H. Piel c, B.A. Aminov d a

M.V. Lomonosov Moscow State University, Faculty of Physics, 119 899 Moscow, Russia b General Physics Institute of Russian Academy of Science, 117 942 Moscow, Russia c Bergische Universita¨t Wuppertal, Fachbereich Physik, Gaußstr. 20, D-42 097 Wuppertal, Germany d Cryoelectra GmbH, Wettinerstr. 6h, D-42 287 Wuppertal, Germany Received 30 March 1999; accepted 31 March 1999 by L.V. Keldysh

Abstract A reproducible fine structure at subgap voltages in the I…U†-characteristics of Bi2 Sr2 CaCu2 O8 break junctions has been observed and investigated. The structure is detectable only in the presence of an a.c. Josephson current. The position of the dips, composing the structure in the dI=dU-characteristics, is independent of the gap parameter D, the temperature T and the geometry of the contacts. The overall form of the fine structure is in good agreement with the Raman scattering spectra of the phonon modes in this material. We attribute this structure to an inelastic (phonon assisted) tunneling of Cooper pairs, which is accompanied by the emission of coherent Raman-active optical phonons at resonance voltages Ures ˆ "vphon =2e. These results hint for strong electron–phonon interaction in this material. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. High-Tc superconductors; D. Electron–phonon interaction; D. Tunneling

Whilst the physical nature of c-axis (perpendicular to the CuO2 -planes) electron transport in High Temperature Superconductors (HTSC) is far from being clear, there is an impressive progress in the experimental studies of this phenomenon. In particular, the so-called intrinsic Josephson effect has been observed in HTSC single crystals in the c-direction [1]. Recently, specific subgap structures in the form of current peaks (resonances) were detected in the current–voltage characteristics (CVCs) of intrinsic * Corresponding author. E-mail address: [email protected] (M.A. Lorenz)

Josephson junctions in Bi2 Sr2 CaCu2 O8 (BSCCO) and Tl2 Ba2 Ca2 Cu3 O10 [2,3]. For a single contact in a stack the current peaks were observed in the range of bias voltages 212 mV # U # 12 mV. Yurgens et al. [2] proposed that the c-axis Raman-active phonons in BSCCO could stimulate dynamically assisted quasiparticle hopping thus contributing to the formation of the resonances. Helm et al. [4,5] explained the resonances by the coupling between infrared-active c-axis phonons and the a.c. Josephson current. It should be noted that the excitation of lattice vibrations by the AC Josephson current in classical Josephson junctions was investigated, experimentally and theoretically, a long time ago [6–8].

0038-1098/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00168-4

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21.3

2

4 2 1

dI/dU [arb.un.]

I [mA]

1

0 10

I [mA]

-1

-2

0

-10 -20

-60

-40

-20

0

20

0

26.4

3

20

22

24

26

28

U [mV]

2

1

U [mV]

-3

23.8

dI/dU [arb.un.]

1

P

20

40

60

U [mV] Fig. 1. CVCs of two break junctions in BSCCO single crystals at T ˆ 4:2 K. Curve 1 shows a local branching in the presence of Josephson currents, while curve 2 misses them both. The inset shows a strong branching of the CVC of another BSCCO Josephson contact in two different regions of voltage at T ˆ 4:2 K.

The major difference between HTSC and classical Josephson junctions in this respect is that for HTSC at T ˆ 4:2 K the range of frequencies of the a.c. Josephson current with sufficiently high amplitude far exceeds the range of phonon frequencies. In principle, this allows to observe resonant coupling of the a.c. Josephson current even to the high-energy phonon modes. For a Josephson junction in an optimally doped BSCCO single crystal, the gap voltage Ug ˆ 2D=e corresponding to the Riedel peak [9] at T ˆ 4:2 K is 50 mV, which results in the energy of the emitted phonons "v ˆ 2eUg ˆ 100 meV. A fine structure in the CVCs of BSCCO break junctions at bias voltages 227 mV # U # 27 mV was reported earlier [10,11] and was attributed to the peculiarities of the quasiparticle tunneling along the cdirection of BSCCO. In the present investigation it has been found that the presence of an a.c. Josephson current is essential for the emergence of this structure and that the resonances could be observed at bias voltages Ures as high as ^41 mV, provided that Ures drops into a ^2D=e-region. The main features of the observed fine structure can be explained in terms of a recently developed theoretical model [12]. In this

0 0

10

20

30

40

50

60

U [mV] Fig. 2. Fine structure (indicated by dashed lines) in the dI=dUcharacteristics of Josephson break junctions in BSCCO single crystals (curve P for a polycrystalline BSCCO sample) with different gap values (2D < 35 2 55 meV) at T ˆ 4:2 K. A fragment of the fine structure is shown in the inset for five contacts in different single crystals with similar gaps 2D < 50 meV at T ˆ 4:2 K.

paper we shall focus mainly on the results obtained at low Josephson current densities to avoid complications caused by nonlinear effects in the case of high Josephson current [9]. Experimental studies of tunneling in BSCCO break junctions in single crystals with different critical temperatures Tc have been carried out with current in c-direction in a wide temperature range 4:2 K # T # Tc . The technical details of break junction preparation were published in Ref. [13]. In the initial stage of the contact formation a fast reduction of the contact area takes place, causing a transition from an electrically large …L q lJ † to a small contact …L p lJ †. Here, L is the effective length of the contact, and lJ is the Josephson penetration depth, which is typically in the range of …10 2 20† mm at T ˆ 4:2 K [11]. During the transition an irreproducible and complex branching of the CVC is replaced by a reproducible local branching (Fig. 1). The effect is symmetric with respect to zero bias. As the critical Josephson current Ic decreases, the

Ya.G. Ponomarev et al. / Solid State Communications 111 (1999) 513–518 3.0 Amplitude [arb.un.]

150

2.5

I c [ µ A]

100

dI/dU [arb.un.]

2.0

50 0

0

50

100

4 3 2

150

1

H [G]

1.5

1.0 1 - H=0 2 - H=32 G

0.5

3 - H=65 G 4 - H=195 G

0.0 0

10

20

(a)

30

40

50

60

U [mV]

0.40 1.2

A res (H) / A res (0)

1 - H=1.9 G 2 - H=5.1 G

dI/dU [arb.un.]

0.35

3 - H=16 G

0.30

0.8

0.4

0.0 0.0

0.4

0.8

1.2

I c (H) / I c (0) 0.25

3 2

0.20

1

0.15 -44

(b)

-42

-40

-38

-36

-34

-32

U [mV]

Fig. 3. (a) Fine structure in the dI=dU-characteristics of a Josephson break junction in BSCCO polycrystal in different external magnetic fields at 4:2 K. The inset shows the magnetic field dependencies of the critical Josephson current Ic …H† and the amplitude of the 41 mV resonance Ares …H† for the same junction at 4:2 K. (b) The 41 mV resonance in the dI=dU-characteristics of a Josephson break junction in BSCCO polycrystal in different external magnetic fields at 4:2 K. The inset shows the dependence of the normalized amplitude of the resonance Ares …H†=Ares …0† on the normalized critical Josephson current Ic …H†=Ic …0† for different BSCCO juncions at 4:2 K: open circles, squares and triangles — 26 mV resonance, open diamonds — 41 mV resonance. The dashed line shows linear and the dotted line shows parabolic dependencies Ares …H†=Ares …0† vs Ic …H†=Ic …0†.

515

branching of the CVCs becomes less hysteretic. For small Ic -values the structure can still be observed as a well reproducible series of dips in the dI=dU-characteristics of the BSCCO junctions (Fig. 2). This allows an accurate identification of their voltage positions. A careful inspection of the fine structure (inset to Fig. 2) shows that at T ˆ 4:2 K the dips in the dI=dU-characteristics of different BSCCO break junctions occur at identical voltages within ^0:2 mV. Moreover, the form of the structure is well preserved. It should be noted that the readjusting of the contact, which often changes the CVC itself significantly, leaves the position of the dips unaffected. The strongest and most frequently observed resonances occur at Ures < …20 2 26† mV and T ˆ 4:2 K. There are additional regions of intensive branching at low bias voltages < …4 2 12† mV and close to 40 mV (Fig. 1 and Fig. 2). The position of the resonances, within experimental errors, is independent of the gap parameter (2D < 35 2 55 meV, see Fig. 2) and the critical temperature (Tc < 60 2 90 K). The fine structure was also observed in the CVCs of break junctions in polycrystalline BSCCO samples in the presence of an a.c. Josephson current (Fig. 2). The position of the dips was essentially the same as for the break junctions in the BSCCO single crystals. This agreement shows that Ures does not depend on the geometry of the investigated Josephson contacts, which rules out possible explanations of the observed structure by Fiske resonances, zero-field steps, or phase-slip centres. We have found that suppression of the Josephson current at T ˆ 4:2 K by external magnetic field H (Fig. 3(a and b)) eliminates the fine structure in the dI=dU-characteristic. The range of external magnetic field in which the suppression of the resonances takes place depends on the effective length of the contact (compare dI=dU-curves in Fig. 3(a) and (b)). There is an obvious correlation between Fraunhofer-like magnetic field dependencies of the critical Josephson current Ic and the amplitude Ares of the dips in the dI=dU-characteristic (inset to Fig. 3(a)). The amplitude Ares of the dips was taken as a distance between a local minima and a smooth background. From the measurements performed on BSCCO single crystals, whiskers and polycrystalline samples we conclude that the normalized dependence of Ares on the critical current Ic (inset to Fig. 3(b)) is close to parabolic (see Ref. [17]). Also suppression of the Josephson current by

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Ya.G. Ponomarev et al. / Solid State Communications 111 (1999) 513–518 70 T = 71.6 K 67.1 K 64.8 K

60

60.3 K

dI / dU [arb. un.]

50

54.7 K 40

46.0 K

30

40.6 K

20 4.2 K 10

0 0

10

20

30

40

U [mV] Fig. 4. Fine structure in the dI=dU-characteristics of a Josephson break junction in a BSCCO single crystal at different temperatures. The dashed lines indicate the resonance voltages Ures .

40

Ures , Ugap [mV]

A(T)/A(4.2 K)

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30 20 10 0 0

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40

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T [K] 0.0 0

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20

30

40

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60

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80

T [K] Fig. 5. Temperature dependence of the normalized amplitude A…T† of the resonances at 11:9 mV (circles), 21:1 mV (squares) and 23:8 mV (diamonds). The inset shows the gap voltage Ugap (solid circles) and the position of the resonances Ures (open symbols) in the dI=dUcharacteristics as a function of temperature.

mechanically readjusting of the contact at zero magnetic field is always accompanied by extinction of the resonances. The data presented in Fig. 3(a and b) suggest that the observed CVC branching of BSCCO contacts is caused by the a.c. Josephson current. This conclusion is confirmed by the measurements performed at elevated temperatures 4:2 K # T # Tc . In the presence of a Josephson current, the fine structure in the dI=dU-characteristics can be registered over a wide range of temperatures T , Tc (Fig. 4). In contrast to the gap feature, which shifts towards zero bias as T approches Tc , the position of the resonances stays constant within experimental errors (Fig. 4 and inset to Fig. 5). On the other hand, the amplitudes of the dips show a nontrivial temperature dependence (Fig. 5). At temperatures T , 0:6 Tc , the amplitude of the resonances hardly changes, or even increases slightly. As a result, the resonances at low bias voltage are easily detectable even at high temperatures, provided that the voltages Ures occur within a voltage interval of ^2D…T†=e. As the gap feature crosses the position of the resonances, their amplitudes decrease so rapidly that they are practically switched off one after another (inset to Fig. 5). Such a behaviour is expected if the resonances are caused by the a.c. Josephson current passing through a local maximum (Riedel peak) [9]. To estimate a characteristic energy (frequency) of the resonances we have to multiply the voltage U by the charge of a Cooper pair 2e if the resonance is caused by the a.c. Josephson current. Otherwise, in the case of inelastic quasiparticle tunneling, a single charge e should be used as the appropriate multiplier. When plotted as a function of 2eU, the fine structure reproduces the majority of phonon peaks revealed in the Raman scattering spectra of BSCCO for the Ag  Z…YY†Z)  and symmetry (scattering geomety Z…XX†Z,  the B1g -symmetry (scattering geomety Z…XY†Z) [14– 17]. A comparison of the fine structure with typical infrared-reflectivity spectra of BSCCO [18] showed no reasonable correlation. A comparison between the characteristic energies (frequencies) of the observed resonances and the Raman modes measured by several groups [14–17] is given in Table 1. The striking correlation between the position of the dips in the dI=dU-characteristics of the BSCCO Josephson break junctions and the

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517

Table 1 Characteristic energies and frequencies of Ures in comparison with phonon frequencies and assignments of the phonon Raman modes in BSCCO Present work E[meV] v [cm21 ] 7.3 12.7

58 102

16.3

130

23.0 24.0

184 192

35.3 36.4 39.7 42.3

[20]

[21]

[22]

[23]

v [cm21 ] Assignment

122 133 156 184 219

Bi Bi Sr Cu (Sr,Cu) b

282 291 318 338

282 a 296 313

OCu OBi

47.6 52.8

381 422

391

58.5 64.5 75.1 80.1 82.7

468 516 601 641 662

469

OSr

631 659

OBi OBi

OCu

63 108 a 121 132 141 187 190 264 a 289 a 293 327 339 a 359 394 426 a 459 469 518 593 a 632 663

Bi Sr Sr Sr Cu Cu

63 100 a 120

Bi Sr Sr

165 190

Cu Cu

OCu OSr OCu OSr

275 a 293

OCu OBi

59 105 117 129 145 175 195

Bi (Bi/Sr) c Sr …Bi=Sr†c Cu Cu …Bi=Sr†c

287 a 294 323

OCu …OBi OSr †c …OBi OSr †c

353 395 409

…OBi OSr †c …OBi OSr †c OCu

326 a

OCu OCu

434

OSr

463

OCu

463

OBi

OBi OBi OBi

625

OSr

627 656

OSr OSr

a

B1g-symmetry. Modes induced by orthorhombic distortion. c Disorder-induced modes. b

phonon peaks in the Raman scattering spectra suggests that the local branching of the CVCs could be produced by a strong coupling of the a.c. Josephson current to the Raman-active optical phonon modes. This conclusion is consistent with the theoretical model proposed in Ref. [12]. It is in agreement with the statement that the Raman-active (even) phonons in HTSC interact with electrons more strongly than the infrared-active (odd) phonons [19], and that the Raman-active c-axis phonons contribute to dynamically assisted inelastic tunneling in cdirection [20]. Following the mode assignment presented in Table 1, our experimental results show that the whole range of the optical Raman-active phonon modes can be activated, starting from the low-energy cation Ag modes …7 2 24† meV (main vibrations of Bi, Sr and Cu) to the highest-energy Ag -mode < 80 meV. Recent publications about the effect of doping [16,17,21] and oxygen-isotope effect [22] on Raman scattering in BSCCO showed clearly that this high-energy mode should be assigned to the vibration of the apical

oxygen in the Sr–O layers. Unfortunately, up to now there is a controversy in the assignment of the Raman-active modes at <(40, 42, 48 and 52) meV (see Table 1) which correspond to strong resonances in the CVCs of BSCCO break junctions. Their energy is close to the 2D-value for optimally doped BSCCO samples and there are some indications that these modes could be attributed, at least partly, to oxygen vibrations in the CuO2 -planes [23]. In accordance with the results of Raman spectroscopy [24], the position of the resonances is independent of the doping level. In addition, we observed a similar fine structure in Bi2 Sr2 Ca2 Cu3 O10 samples with Ures close to those of the 2212-samples, which is again in agreement with Raman measurements [25]. Preliminary results which we have obtained on overdoped Bi2 Sr22x Lax CuO6 samples (Tc ˆ 19 K, D…4:2K† ˆ 10 meV) are indicative of the existence of resonances corresponding to the low-energy cation Ag -modes, some of which show strong phonon-softening effects [26,27]. The above mentioned properties of the observed resonances

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give a direct evidence for the strong electron–phonon interaction in BSCCO. We should finally emphasize an important consequence of the coupling between Josephson tunneling and phonon generation at high Josephson currents. The branching of the CVCs is then very strong and the generation of nonequilibrium phonons causes strong depairing effects in the contact region. As a result, the quasiparticle branch of the CVC is often trapped by the resonance. This effect can be stabilized due to the existence of the Riedel peak, because the emission of nonequilibrium coherent phonons reaches its maximum when the gap voltage Ugap coincides with Ures . In conclusion, we have observed a subgap structure in the CVCs of BSCCO break junctions caused by the interaction of the a.c. Josephson current with optical Raman-active phonons in the range of energies up to <80 meV. The observed inelastic (phonon assisted) tunneling of Cooper pairs is accompanied by the emission of coherent nonequilibrium phonons, which produce a strong depairing effect in the contact region. The amplitude of the resonances is strongly influenced by the Riedel peak singularity. Acknowledgements The authors are indebted to E.G. Maksimov for many useful discussions and for detailed explanations of the calculations in Ref. [17]. We would like to thank N.V. Zavaritsky, T.E. Os’kina, Yu.D. Tretyakov, A. Krapf, W. Kraak and J. Pommer for providing high quality BSCCO lamellar crystals. Further we acknowledge important and stimulating discussions with L.M. Fisher, V.Z. Kresin, M.U. Kupriyanov, V.N. Zavaritsky, R. Zaitsev, G. Gu¨ntherodt and L. Gasparov. This work was supported in part by the ISC on High Temperature Superconductivity (Russia) under the contract number 96118 (project DELTA) and by RFBR (Russia) under the contract number N96-02-18170a.

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