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Electron-phonon coupling model and high-temperature superconductors
Physica C 162-164 (1989) 1527-1528 North-Holland
ELECTRON-PHONON
L.N. B ~ S K I I ,
COUPLING
MODEL
AND
HIGH-TEMPERATURE
SUPERCONDUCTORS
O.V.DOLGOV, and A.A. GOLUBOV*
P.N. Lebedev Physical Institute, Academy of Sciences of the USSR, Moscow, USSR * Institute of Solid State Physics, Academy of Sciences of the USSR, Chernogolovka, USSR The system of electrons interacting with phonons and excitons is studied. In the standard phonon model modes with 10w and high frequencies are considered, the latter being interact strongly with electrons. The combined model takes into account 10w frequency modes and excitons interacting weakly with electrons. Both models cannot explain all essential features of copper oxide superconductors.
The Fano profile of phonon lines in Raman scattering and softening of some phonon modes due to the superconductivity I, the isotope effect in La2_xSrxCuO42, the optical 3 and tunneling 4-6 data give evidence in favor of strong coupling of electrons with phonons and p o s s i b l y with some other e x c i t a t i o n s in superconducting cuprates. So the question is if the standard model of Fermi quasiparticles interacting via some boson excitations can explain the pairing in high-Tc compounds. The properties under consideration are the large ratio 2A(0)/T c (6-8 for Bi-cuprates according to the tunneling 6 and photoemission data and even more higher values for La-Sr-CuO and EuBa2Cu307 s u p e r c o n d u c t o r 4,5), the presence of isotope effect in La-ccmpounds and its negligible value in Y-, Bi- and TIcompounds, the temperature dependence of London penetration depth 6L(T) which is close to BCS dependence and suppression of NMR relaxation rate below T c without hump just below T c. We discuss firstly the phonon mechanism using Eliashberg model with ~*=0. We consider the interaction of electrons with low and high frequency modes. The formers have the energy ~I~T c and are characterized by the coupling parameter ki-0.5-2. The letters have the parameters ~ 2 = 5 T c and ~2=2. The high
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
frequency phonons determine the scattering of electrons near T c. The linear dependence of resistivity just above T c in all metallic cuprates can be explained by the scattering of e l e c t r o n s by the low frequency thermal p h o n o n s 7. This inelastic scattering can explain also the absence of the hump in the temperature dependence of NMR relaxation rate TI-I near Tc. The temperature dependencies of the reduced upper critical field along c-axis hc2=-Hc2 (T)/Tc [dHc2/dT]Tc and ~-2 (T)/8L-2 (0) are shown in Fig i, 2 by the curves SC for kl-i and ~ = 2 . They lie slightly above the BCS ones. The calculated value 0 for isotope effect is 0.2-0.3, the ratio 2A(0)/T¢ is 5-6 anddecreases with ~* growth. We consider now the excitonic mechanism in the presence of low frequency phonons, i.e. the E l i a s h b e r g model with excitations ~3 assuming ~y~3>>Tc and k3<
L.N. Bulaevskii et aL I Electron-phonon coupling model
1528
excitonic model is 3.5 and isotope effect is negligible.
¢,~. (T)
1.0
0.5
0.0 D.O
n, 5
l.O
Figure 1
Thus we come to the conclusions that the optical, tunneling and resistivity m e a s u r e m e n t s do confirm the presence of the strong electron-phonon interaction in high-Tc cuprates. H o w e v e r the s t a n d a r d e l e c t r o n p h o n o n or e l e c t r o n - e x c i t o n m o d e l s can not e x p l a i n all the e s s e n t i a l p r o p e r t i e s of compounds under consideration. The a n i s o t r o p i c p a i r i n g can solve the p r o b l e m of large ratio 2A(0)/T c (see 8) and e x p l a i n the p o s s i b l e gapless c h a r a c t e r of electronic excitations observed in the Raman s c a t t e r i n g at low energies. However, the phonon anomalies in I-V tunneling characteristics should be smoothed out over the energy scale A(T) in this case. So the a n i s o t r o p i c p a i r i n g m o d e l seems to be in disagreement with tunneling data 4-6.
T/Tc
S~(-F)/~-'<0) 1.0
i. C. Thomson and M. Cordona, Physical
$C
Properties of High-Temperature Superconductors, ed. D.M. Ginsberg (World Scientific, Singapore, 1989).
0.5.
2. M.K. Crawford, M.N. Kunchur, W.E. Farneth, E.M. McCarron and S.J. Poon, preprint 1989. 3. R.T. Collins, Z. Schleslnger et al. Phys. Rev. 39B (1989), 6571. 0.0
4. S.I. Vedeneev, I.P. Kazakov, A.P.
o
0. 5
0.0
1.0 T/Tc
Figure 2
Kir'janov, S.N. Maksimovskii, and V.A. Stepanov. JETP Lett. 47 (1988) 306.
T,.IL
5. L.N. Bulaevskii, O.V. Dolgov, I.P. Kazakov, S.N. Maksimovskii, M.O. Ptitsyn, V.A. Stepanov, and S.I. Vedenveev, Superc. Sci. Technol. 1 (1988) 205.
1.0
6. S.I. Vedeneev and V.A. Stepanov, Pis'ma ZhETF 49(1989)510. 7. G.M. Eliashberg, Pis'ma ZhETF, 98(1988)275. 8. O.V. Dolgov and A.A. Golubov, Int. Journ. Mod. Phys. IB(1988)I089.
0.0 0.0
0.5
Figure 3
1.0
T/T c
ELECTRON-PHONON
L.N. B ~ S K I I ,
COUPLING
MODEL
AND
HIGH-TEMPERATURE
SUPERCONDUCTORS
O.V.DOLGOV, and A.A. GOLUBOV*
P.N. Lebedev Physical Institute, Academy of Sciences of the USSR, Moscow, USSR * Institute of Solid State Physics, Academy of Sciences of the USSR, Chernogolovka, USSR The system of electrons interacting with phonons and excitons is studied. In the standard phonon model modes with 10w and high frequencies are considered, the latter being interact strongly with electrons. The combined model takes into account 10w frequency modes and excitons interacting weakly with electrons. Both models cannot explain all essential features of copper oxide superconductors.
The Fano profile of phonon lines in Raman scattering and softening of some phonon modes due to the superconductivity I, the isotope effect in La2_xSrxCuO42, the optical 3 and tunneling 4-6 data give evidence in favor of strong coupling of electrons with phonons and p o s s i b l y with some other e x c i t a t i o n s in superconducting cuprates. So the question is if the standard model of Fermi quasiparticles interacting via some boson excitations can explain the pairing in high-Tc compounds. The properties under consideration are the large ratio 2A(0)/T c (6-8 for Bi-cuprates according to the tunneling 6 and photoemission data and even more higher values for La-Sr-CuO and EuBa2Cu307 s u p e r c o n d u c t o r 4,5), the presence of isotope effect in La-ccmpounds and its negligible value in Y-, Bi- and TIcompounds, the temperature dependence of London penetration depth 6L(T) which is close to BCS dependence and suppression of NMR relaxation rate below T c without hump just below T c. We discuss firstly the phonon mechanism using Eliashberg model with ~*=0. We consider the interaction of electrons with low and high frequency modes. The formers have the energy ~I~T c and are characterized by the coupling parameter ki-0.5-2. The letters have the parameters ~ 2 = 5 T c and ~2=2. The high
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
frequency phonons determine the scattering of electrons near T c. The linear dependence of resistivity just above T c in all metallic cuprates can be explained by the scattering of e l e c t r o n s by the low frequency thermal p h o n o n s 7. This inelastic scattering can explain also the absence of the hump in the temperature dependence of NMR relaxation rate TI-I near Tc. The temperature dependencies of the reduced upper critical field along c-axis hc2=-Hc2 (T)/Tc [dHc2/dT]Tc and ~-2 (T)/8L-2 (0) are shown in Fig i, 2 by the curves SC for kl-i and ~ = 2 . They lie slightly above the BCS ones. The calculated value 0 for isotope effect is 0.2-0.3, the ratio 2A(0)/T¢ is 5-6 anddecreases with ~* growth. We consider now the excitonic mechanism in the presence of low frequency phonons, i.e. the E l i a s h b e r g model with excitations ~3 assuming ~y~3>>Tc and k3<
L.N. Bulaevskii et aL I Electron-phonon coupling model
1528
excitonic model is 3.5 and isotope effect is negligible.
¢,~. (T)
1.0
0.5
0.0 D.O
n, 5
l.O
Figure 1
Thus we come to the conclusions that the optical, tunneling and resistivity m e a s u r e m e n t s do confirm the presence of the strong electron-phonon interaction in high-Tc cuprates. H o w e v e r the s t a n d a r d e l e c t r o n p h o n o n or e l e c t r o n - e x c i t o n m o d e l s can not e x p l a i n all the e s s e n t i a l p r o p e r t i e s of compounds under consideration. The a n i s o t r o p i c p a i r i n g can solve the p r o b l e m of large ratio 2A(0)/T c (see 8) and e x p l a i n the p o s s i b l e gapless c h a r a c t e r of electronic excitations observed in the Raman s c a t t e r i n g at low energies. However, the phonon anomalies in I-V tunneling characteristics should be smoothed out over the energy scale A(T) in this case. So the a n i s o t r o p i c p a i r i n g m o d e l seems to be in disagreement with tunneling data 4-6.
T/Tc
S~(-F)/~-'<0) 1.0
i. C. Thomson and M. Cordona, Physical
$C
Properties of High-Temperature Superconductors, ed. D.M. Ginsberg (World Scientific, Singapore, 1989).
0.5.
2. M.K. Crawford, M.N. Kunchur, W.E. Farneth, E.M. McCarron and S.J. Poon, preprint 1989. 3. R.T. Collins, Z. Schleslnger et al. Phys. Rev. 39B (1989), 6571. 0.0
4. S.I. Vedeneev, I.P. Kazakov, A.P.
o
0. 5
0.0
1.0 T/Tc
Figure 2
Kir'janov, S.N. Maksimovskii, and V.A. Stepanov. JETP Lett. 47 (1988) 306.
T,.IL
5. L.N. Bulaevskii, O.V. Dolgov, I.P. Kazakov, S.N. Maksimovskii, M.O. Ptitsyn, V.A. Stepanov, and S.I. Vedenveev, Superc. Sci. Technol. 1 (1988) 205.
1.0
6. S.I. Vedeneev and V.A. Stepanov, Pis'ma ZhETF 49(1989)510. 7. G.M. Eliashberg, Pis'ma ZhETF, 98(1988)275. 8. O.V. Dolgov and A.A. Golubov, Int. Journ. Mod. Phys. IB(1988)I089.
0.0 0.0
0.5
Figure 3
1.0
T/T c