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Electron-phonon interactions in oxide superconductors
PHYSICAD
Physica B 186-188 (1993) 813-815 North-Holland
Electron-phonon interactions in oxide superconductors H. Rietschel, L. Pintschovius and W. Reichardt Kernforschungszentrum Karlsruhe, Institut fiir Nukleare Festk6rperphysik, P.O. Box 3640, W-7500 Karlsruhe, Germany
We present recent results on the lattice dynamics of oxide superconductors as determined by inelastic neutron-scattering experiments. Included are data on the high-Tc cuprate superconductors, for example YBa2Cu307, as well as Nb-doped SrTiO3, which is a low-Tc system (To - 1 K). Particular emphasis is laid on direct indications of electron-phonon coupling such as phonon softening by renormalization or changes in phonon frequencies when passing through Tc.
1. Introduction
It is well established that although electron pairing is the key feature of the superconducting ground state of the high-T c superconductors (HTSCs), the coupling mechanism behind this pairing remains unknown. For classical superconductors such as Pb or Nb, electronphonon coupling has been clearly identified as the dominant mechanism. The isotope effect or, in particular, the direct observation of the phonon spectrum in the frequency modulation of the energy gap are the most convincing proof of this. For HTSCs, on the other hand, there is only a marginal isotope effect, and until now no tunneling experiments performed on a HTSC have shown unambiguously a phonon modulation of the energy gap. A steadily increasing number of experimental resuits have clearly revealed the influence of the superconducting charge carriers on the phononic properties of cuprate superconductors. Examples include the pronounced kink in the phonon-dominated thermal conductivity in YBa2Cu30 7 around To, and the direct reflection of electron-phonon coupling in the phonon renormalization as observed in drastic changes in the phonon-dispersion relations when going from the undoped (insulating) to the doped (superconducting) cuprate [1]. A particularly impressive demonstration of the coupling between the superconducting electrons and the phonons in HTSCs has been provided by Raman scattering experiments [2]. On passing through T c, certain Raman-active phonons with frequencies close to 2A undergo significant frequency shifts. These
Correspondence to: H. Rietschel, Kernforschungszentrum Karlsruhe, Institut fiir Nukleare Festk6rperphysik, P.O. Box 3640, W-7500 Karlsruhe, Germany.
phonon shifts have been the subject of an extensive theoretical investigation based upon Eliashberg theory [3]. Inelastic neutron scattering experiments are a well established and proven tool in the investigation of the lattice dynamics of solids, and there is an extensive body of results for the HTSCs. For a review and further references, the reader is referred to ref. [1].
2. Results
In this paper we present recent results that supplement or complete those already published with regard to issues focusing on the following: (i) phonons in YBa2Cu307_ x related to the 340 cm l Raman-active mode and their shift on T passing To; (ii) phonons in YBa2Cu30 7 ~ related to transverse displacements of the O(1) atoms in the C u - O chains; (iii) phonons in (La, Sr)2CuO 4 related to C u - O bond-stretching vibrations in the breathing mode. In addition, we briefly discuss preliminary results on the low-To oxide superconductor Sr(Ti, Nb)O 3. 2.1. Phonon shifts across T c
The sample used was a twinned single crystal with dimensions of about 0.3 cm 3 and composition YBa3Cu307. The neutron-scattering experiments were carried out on the 2T triple-axis spectrometer at the O R P H E E reactor at Saclay. In fig. 1, we show the frequency v of the Ag(3) mode for q = 0 . 2 in the (1,0, 0)/(0, 1, 0) direction as a function of temperature. For q = 0 , this branch coincides with the 340 cm-1 Raman-active mode. A t To, a distinct shift
0921-4526/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
814
H. Rietschel et al. / Electron-phonon interactions in HTSCs 10.3
TC 1
>
10.1' 10.0
2, O, O)
160
o
200
360
T [K] Fig. 1. Frequency of the q =0.2 phonon in the branch s(arting at 340 cm-I as a function of temperature. of A v = 0.1 THz occurs. Similar measurements were performed for various q-values and also in the (0, 0, 1) direction. The detected shifts are collected in fig. 2. For q = 0, our A u lies between the Raman results of refs. [2,4]. As can be seen from fig. 2, the phonon shifts extend throughout the Brillouin zone, thus proving that the electron-phonon coupling responsible occupies an appreciable fraction of phase space. This is a very important result which corroborates the theoretical assumptions made in ref. [2].
2.2. Transverse displacement modes o f the 0(1 ) chain atoms It has often been argued that in YBa2Cu30 7, the O(1) chain atoms are weakly bound and undergo large displacements perpendicular to the chain direction. Likewise it has been assumed that these atoms move in double-well potentials giving rise to enhanced electron-lattice coupling together with large anharmonicities [5]. Using inelastic neutron scattering once more, but now on an untwinned YBazCu30 7 single crystal, we investigated the transverse phonon branch
"" 0 I--
-0.1
~
i
i~ / ~ ' /
RA~
u
-0.2 0.50.'3 1~ 0~1 0.'2 0.'3 0.'4 0.'5 (o,o,.;;) (~, o, o)/(o,~;, o)
Fig. 2. Frequency shifts for various q values; the solid squares are from Raman measurements [2,4].
in the (0, 1,0) direction which is dominated by (0, 0, 1) displacements of the O(1) atoms. At the zone boundary, the displacement pattern is zig-zag like. Our main findings are that this branch is without dispersion and virtually independent of temperature in the range 50 ~< T <~300 K, and that the phonons are well defined with moderate damping. This clearly indicates that O(1) displacements cannot be considered as strongly anharmonic, but rather they behave in a normal manner. Furthermore, the relatively high frequency of this branch ( - 5 THz) shows that the O(1) atoms are not weakly bound. Thus, there should be no enhanced coupling of these transverse O(1) phonons to the free charge carriers in YBa~Cu30 7.
2.3. C u - O bond stretching vibrations in (La, Sr)2CuO 4 From single crystals of both undoped La2CuO 4 and doped Lal.9Sr0.1CuO 4 ( T c = 2 0 K ) we determined both the dispersion and linewidth of high-frequency phonons in the ( 1 , 1 , 0 ) direction polarized in the basal plane. These phonons imply C u - O bond-stretching displacements which at the zone boundary correspond to a breathing-type mode. We observe a softening of the whole branch by about 3% when going from the undoped to the doped compound, accompanied by a significant increase in linewidth. At the zone boundary ( u = 2 1 T H z ) the linewidth is about 2THz ( F W H M ) , in quantitative agreement with recent microscopic L D A calculations [6]. We think that this increase in linewidth on doping is a further clear indication of strong electron-phonon coupling in HTSCs. Finally, we turn briefly to our neutron-scattering results for SrTiO 3 and SrTi0.99Nb0.10 3. Although it is a low-T c oxide superconductor without Cu and has a 3-dimensional perovskite structure, the n-doped Sr(Ti, Nb)O 3 has one important feature in common with the cuprate superconductors, namely the low concentration, ne, of free carriers. In our SrTio.99Nb0.uO3 single crystal ( T ~ = 0 . 5 K ) , n e - 2 × 1 0 2 ° c m -3. For m e = 1, this leads to a Fermi energy of Ef/h = 27 THz and to a plasma frequency of up = 50 THz, which is of the same order of magnitude as the highest breathingtype phonons (~26THz). Thus, electronic and phononic degrees-of-freedom may be strongly hybridized so that the validity of fundamental assumptions such as Midgal's theorem or the adiabatic approximation can no longer be guaranteed. Indeed, our neutron-scattering results on Sr(Ti, Nb)O 3 single crystals revealed some very interesting features. The observed screening of the F15 (LO) branch on doping
H. Rietschel et al. / Electron-phonon interactions in HTSCs
cannot be described in terms of any RPA-type formalism with or without local field corrections, even when keeping the frequency dependence of e(q, to) (nonadiabatic description). Also, in the frequency range 16 <~ u ~<20 THz, the screened branch loses virtually all of its spectral weight. Whether or not these anomalies are caused by low-lying electronic excitations (plasmons) could be clarified by additional measurements on crystals with higher doping concentrations. Such experiments are now being prepared.
815
References [1] L. Pintschovius et al., Physica C 185-189 (1991) 156. [2] B. Friedl, C. Thomsen and M. Cardona, Phys. Rev. Lett. 65 (1990) 915. [3] R. Zeyher, Phys. Rev. B 44 (1991) 9596. [4] M. Krantz, H.J. Rosen, R.M. Macfarlane and Y.Y. Lee, Phys. Rev. B 38 (1988) 4992. [5] J.R. Hardy and J.W. Flocken, Phys. Rev. Lett. 64 (1988) 2191. [6] H. Krakauer et al., private communication.
Physica B 186-188 (1993) 813-815 North-Holland
Electron-phonon interactions in oxide superconductors H. Rietschel, L. Pintschovius and W. Reichardt Kernforschungszentrum Karlsruhe, Institut fiir Nukleare Festk6rperphysik, P.O. Box 3640, W-7500 Karlsruhe, Germany
We present recent results on the lattice dynamics of oxide superconductors as determined by inelastic neutron-scattering experiments. Included are data on the high-Tc cuprate superconductors, for example YBa2Cu307, as well as Nb-doped SrTiO3, which is a low-Tc system (To - 1 K). Particular emphasis is laid on direct indications of electron-phonon coupling such as phonon softening by renormalization or changes in phonon frequencies when passing through Tc.
1. Introduction
It is well established that although electron pairing is the key feature of the superconducting ground state of the high-T c superconductors (HTSCs), the coupling mechanism behind this pairing remains unknown. For classical superconductors such as Pb or Nb, electronphonon coupling has been clearly identified as the dominant mechanism. The isotope effect or, in particular, the direct observation of the phonon spectrum in the frequency modulation of the energy gap are the most convincing proof of this. For HTSCs, on the other hand, there is only a marginal isotope effect, and until now no tunneling experiments performed on a HTSC have shown unambiguously a phonon modulation of the energy gap. A steadily increasing number of experimental resuits have clearly revealed the influence of the superconducting charge carriers on the phononic properties of cuprate superconductors. Examples include the pronounced kink in the phonon-dominated thermal conductivity in YBa2Cu30 7 around To, and the direct reflection of electron-phonon coupling in the phonon renormalization as observed in drastic changes in the phonon-dispersion relations when going from the undoped (insulating) to the doped (superconducting) cuprate [1]. A particularly impressive demonstration of the coupling between the superconducting electrons and the phonons in HTSCs has been provided by Raman scattering experiments [2]. On passing through T c, certain Raman-active phonons with frequencies close to 2A undergo significant frequency shifts. These
Correspondence to: H. Rietschel, Kernforschungszentrum Karlsruhe, Institut fiir Nukleare Festk6rperphysik, P.O. Box 3640, W-7500 Karlsruhe, Germany.
phonon shifts have been the subject of an extensive theoretical investigation based upon Eliashberg theory [3]. Inelastic neutron scattering experiments are a well established and proven tool in the investigation of the lattice dynamics of solids, and there is an extensive body of results for the HTSCs. For a review and further references, the reader is referred to ref. [1].
2. Results
In this paper we present recent results that supplement or complete those already published with regard to issues focusing on the following: (i) phonons in YBa2Cu307_ x related to the 340 cm l Raman-active mode and their shift on T passing To; (ii) phonons in YBa2Cu30 7 ~ related to transverse displacements of the O(1) atoms in the C u - O chains; (iii) phonons in (La, Sr)2CuO 4 related to C u - O bond-stretching vibrations in the breathing mode. In addition, we briefly discuss preliminary results on the low-To oxide superconductor Sr(Ti, Nb)O 3. 2.1. Phonon shifts across T c
The sample used was a twinned single crystal with dimensions of about 0.3 cm 3 and composition YBa3Cu307. The neutron-scattering experiments were carried out on the 2T triple-axis spectrometer at the O R P H E E reactor at Saclay. In fig. 1, we show the frequency v of the Ag(3) mode for q = 0 . 2 in the (1,0, 0)/(0, 1, 0) direction as a function of temperature. For q = 0 , this branch coincides with the 340 cm-1 Raman-active mode. A t To, a distinct shift
0921-4526/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
814
H. Rietschel et al. / Electron-phonon interactions in HTSCs 10.3
TC 1
>
10.1' 10.0
2, O, O)
160
o
200
360
T [K] Fig. 1. Frequency of the q =0.2 phonon in the branch s(arting at 340 cm-I as a function of temperature. of A v = 0.1 THz occurs. Similar measurements were performed for various q-values and also in the (0, 0, 1) direction. The detected shifts are collected in fig. 2. For q = 0, our A u lies between the Raman results of refs. [2,4]. As can be seen from fig. 2, the phonon shifts extend throughout the Brillouin zone, thus proving that the electron-phonon coupling responsible occupies an appreciable fraction of phase space. This is a very important result which corroborates the theoretical assumptions made in ref. [2].
2.2. Transverse displacement modes o f the 0(1 ) chain atoms It has often been argued that in YBa2Cu30 7, the O(1) chain atoms are weakly bound and undergo large displacements perpendicular to the chain direction. Likewise it has been assumed that these atoms move in double-well potentials giving rise to enhanced electron-lattice coupling together with large anharmonicities [5]. Using inelastic neutron scattering once more, but now on an untwinned YBazCu30 7 single crystal, we investigated the transverse phonon branch
"" 0 I--
-0.1
~
i
i~ / ~ ' /
RA~
u
-0.2 0.50.'3 1~ 0~1 0.'2 0.'3 0.'4 0.'5 (o,o,.;;) (~, o, o)/(o,~;, o)
Fig. 2. Frequency shifts for various q values; the solid squares are from Raman measurements [2,4].
in the (0, 1,0) direction which is dominated by (0, 0, 1) displacements of the O(1) atoms. At the zone boundary, the displacement pattern is zig-zag like. Our main findings are that this branch is without dispersion and virtually independent of temperature in the range 50 ~< T <~300 K, and that the phonons are well defined with moderate damping. This clearly indicates that O(1) displacements cannot be considered as strongly anharmonic, but rather they behave in a normal manner. Furthermore, the relatively high frequency of this branch ( - 5 THz) shows that the O(1) atoms are not weakly bound. Thus, there should be no enhanced coupling of these transverse O(1) phonons to the free charge carriers in YBa~Cu30 7.
2.3. C u - O bond stretching vibrations in (La, Sr)2CuO 4 From single crystals of both undoped La2CuO 4 and doped Lal.9Sr0.1CuO 4 ( T c = 2 0 K ) we determined both the dispersion and linewidth of high-frequency phonons in the ( 1 , 1 , 0 ) direction polarized in the basal plane. These phonons imply C u - O bond-stretching displacements which at the zone boundary correspond to a breathing-type mode. We observe a softening of the whole branch by about 3% when going from the undoped to the doped compound, accompanied by a significant increase in linewidth. At the zone boundary ( u = 2 1 T H z ) the linewidth is about 2THz ( F W H M ) , in quantitative agreement with recent microscopic L D A calculations [6]. We think that this increase in linewidth on doping is a further clear indication of strong electron-phonon coupling in HTSCs. Finally, we turn briefly to our neutron-scattering results for SrTiO 3 and SrTi0.99Nb0.10 3. Although it is a low-T c oxide superconductor without Cu and has a 3-dimensional perovskite structure, the n-doped Sr(Ti, Nb)O 3 has one important feature in common with the cuprate superconductors, namely the low concentration, ne, of free carriers. In our SrTio.99Nb0.uO3 single crystal ( T ~ = 0 . 5 K ) , n e - 2 × 1 0 2 ° c m -3. For m e = 1, this leads to a Fermi energy of Ef/h = 27 THz and to a plasma frequency of up = 50 THz, which is of the same order of magnitude as the highest breathingtype phonons (~26THz). Thus, electronic and phononic degrees-of-freedom may be strongly hybridized so that the validity of fundamental assumptions such as Midgal's theorem or the adiabatic approximation can no longer be guaranteed. Indeed, our neutron-scattering results on Sr(Ti, Nb)O 3 single crystals revealed some very interesting features. The observed screening of the F15 (LO) branch on doping
H. Rietschel et al. / Electron-phonon interactions in HTSCs
cannot be described in terms of any RPA-type formalism with or without local field corrections, even when keeping the frequency dependence of e(q, to) (nonadiabatic description). Also, in the frequency range 16 <~ u ~<20 THz, the screened branch loses virtually all of its spectral weight. Whether or not these anomalies are caused by low-lying electronic excitations (plasmons) could be clarified by additional measurements on crystals with higher doping concentrations. Such experiments are now being prepared.
815
References [1] L. Pintschovius et al., Physica C 185-189 (1991) 156. [2] B. Friedl, C. Thomsen and M. Cardona, Phys. Rev. Lett. 65 (1990) 915. [3] R. Zeyher, Phys. Rev. B 44 (1991) 9596. [4] M. Krantz, H.J. Rosen, R.M. Macfarlane and Y.Y. Lee, Phys. Rev. B 38 (1988) 4992. [5] J.R. Hardy and J.W. Flocken, Phys. Rev. Lett. 64 (1988) 2191. [6] H. Krakauer et al., private communication.