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Vibrational spectra of high-Tc superconductors YBa2Cu3OX. Evidence of interband hybridization
Journal ofA4okcular Structure, 219 (1990) 153-158 Elsevier Science Publishers B.V.. Amsterdam - Printed
153 in The Netherlands
VIBRATIONALSPECTRAOF HIGH-T,SUPERCONDUCTORS yB82%Ox. EVIDENCE OF INTERBAM)HYBRIDIZATION K.V. KRAISKAYA*, V.M. BURLAKOV, N.Y. BOLDYREV, E.I.FIRSOV, A.G. MIT’KO, E.V. PECHENfW.A. HADZHIYSKY S.I. KRASNOSVOBODTZEV*, Troltsk, Instltute of S ectrosco y, USSR Academy of Sciences, Moscow re ion, U8SR, 142082 *Lebedev 8 hyslcal Instltute, USSR Academy of Sciences, Moscow SUMMARY
IR reflectlon spectra of polycrystalllne samples YBaaCUsOx (x=6.3 and 6.6) at varlous temperatures are reported. From calculated spectra of Im[&(w)l and Im[-&-’ (w)l Is determlned that anomalous change ln reflectlvlty In the frequency region 500-700 Is due to the change In TO band cm-’ of axial Cul-01 vlbratlon integrated Intensity IE. Thls change in IX Is propozed to be connected wlth the free carrier locallzatlon on an Ion Cul wlth the consequent change of Its effective charge. The conclusion Is made about two energy bands of free carriers: one being connected wlth Cul-0, planes and the other wlth the Cul-04 chains. These two bands are well separated from each other In space but also hybrldlzed by tunneling through energy barler. The exchange of carriers between these two bands Is strongly dependent on the temperature and may contrlbute In superconductlvlty. INTRODUCTION One of the maln problem In lnvestlgatlon of recently discovered high-Tc superconductors Is a palring mechanism. The comparative study of phonon denslty of states F(w) In superconductlng (TcE90 K, x=7.0), and semlconductlng (~~6.0) samples YBa,Cu30x falled in flndlng the slgnlflcant differences In the functions F(w) in both compounds (ref. 1-3). Thls Indicates that the carriers palrlng If It Is caused by phonon medlated mechanism Is due to a small number of vlbrations glvlng too small contribution into F(w). Consequently the coupling constant a(w) of electron-phonon interactlon must be sufflclently large to compensate a small number of phonons contributing Into the effective attractlon constant h (ref. 4). But the large constant 0022.2860/90/$03.50
0 1990 Elsevier
Science
Publishers
B.V.
154
lead to significant renormalization3 of phonons. To search the evidence of phonon renormalization was the aim of this paper.
a(w)
RESULTSANDDISCUSSION For the detaIled Investigation of phonon renormalization the two samples of YBa2Cu30x compounds with x=6.3 (semiconducting sample 1) and with x=6.6 (superconducting below 12 K sample 2) were used. These ceramic samples were prepared by conventional technique. The analysis of reflectJon (Fig. 1) of sample 1 show that the TO band near 600 cm-’ attributed to Cul-01 axial vibration (ref. 5) 1s strongly asymmetric . Temperature measurements reveal the slgniflcant increase of Integrated intensity IE: of this band below 120 K - Fig.2. No significant changes in band parameters of other vibrations in. the spectrum was detected. Note that the temperature change in IX corresponding LO band 1s much smaller than that of TO band-Fig i. It is well understood now that the weakly unharmonlc vlbration has a temperature independent integrated intensity IX. Thus one should temperature variations of IX may be suppose that the observed caused either by strong anharmonic1ty effect or by temperature variations of the microscopic characteristic of vibrating particles such as effective charge e*. Let us analyse both possiblllties. r
-l
I, arbmits 10
.3
5
.4
-1
i_\
.2
Fi . jr Reflect;& Im4 -E (w)l (sample 1).
n-j1 I$;(;Lloand 2 3 6.3
L
100
200
300 7-x
Fig. 2. Temperature dependence of integrpted lntenslty IX of 600 cm phonon band.
For analysis of the first possibility the calculation of IX temperature dependence of anharmonic oscillator X withing the perturbation theory is sufficient. Equation of motion for such an
155
oscillator
can be written
as follows
mass, were m, w, and B are oscillator damping; 7 is anharmonlslty constant, E field, p is temperature dependent random the fluctuation dissipative analysis one titensity I(w) D(w)Z(w) I(w) = jEj2 (w-Go)2 t T2(w) ’ 3V Go= wet 3 zoo
resonant frequency and is an external electric fluctuating field. Using can obtain for spectral
(2a) (2b)
’
‘Z(W) 1 1--m-a 1 (3b) 9
rr
1
t ---. 8 m2wz (tio)2t
(W
W2
-1
Z(w) =
3 r2T2
8 m2wz (tio)*t
1
9g2
Temperature dependence of Integrated intensity is obviously determined by the factor Z(w). One can see from (2) that IZ increases with increasing temperature. Despite of classical approach to Z(w) calculation the result is sufficient for qualitative descrlptlon of IZ temperature behavlour at relatively low temperatures which is opposite to the experlmental one. Let us consider one other mechanism of temperature dependence based on temperature dependence of effective ion charge e*. of 12’ The mode effective charge Is constructed from ion effective charges through the relation Gq= e*L i iq ’
(4)
were q Is an index of normal mode, I Is an ion index and I, is the transltion matrix to the normal mode from the carteslaniqion desplacements. Before the following analytical treatment It Is worth to note that the temperature dependence of ion effective charge is determined by free carrler localization on the local ion level vibrating in axial mode mentloned above. The most probable site for this localization is Cul ions. Because of small localization radius and relatively low activation energies (100 K) there should
156
be an energy barrler between the conduction band and a locallzed levels (or band) of magnitude as large as 1 eV. Thus the temperature dependence of ion effective charge is described by equation dn -%-EL -‘= (no-n, ) ‘exp (5) w!LmwLc“&%L~L~ dt I k!r 1 of full number were no, n, and nc are the everage concentrations free localized levels and free carrier of localized levels, respectively; G and s are the Fermi level and locallzed level energies respectively, bL and tic the vibratlon frequency of particle on IL and the effective frequency of free carrier attack on the energy barrier, wLc and wcL are the tunneling probabilities of a barrier from the LL to the conduction band and In opposlt dlrection respectively, pc and p, are corresponding densities of free states. To slmpllfy the equatlon (5) we accept nc=n,; &+L,, the asymptotic wLc=wcLand pc>>pL=n, . One may simply analize behaveour of n from equation l
(no-n, ) ‘exp (-AE/kT ) = n:/p,
(6)
Note that the relation between n determined according to (6) and integrated Intensity Ic may be very complicated because of the fast exchange of carrlers between the localized and the delocalized levels. To simplify this relation one must use the approxlmatlon bazed on low rate of exchange. In this case there will be the only two types of oscillators ln the lattice connected wlth the occupied LL and free LL. They are coupled through the The linear resonant interaction causes the polarization field. redlstrlbution of oscillator intensities and do not change the full integrated intensltiy IZ,+IXZ.For this reason we use for qualitative analysis of IX the expresslon IZ = IX0 + p(n,-n,
1
,
(7)
where IZols temperature independent and p is Constant. (6) and (7) the Ix thus determined According to (5)) monotonously increases wlth decreasing temperature. As it shown on Fig. 2 there Is a nonmonotonous Increase of effective charge when This may be connected with temperature temperature decreases. dependence of energy parameters EL or U (U 1s the height of the energy barrier) caused by local transitlon lnto superconducting Flg.3 represents the IR reflectlon spectra of sample 2 state.
157
and the corresponding spectra of Imt&(w)l and ImI-E-‘(w)]. The vibrational band near 600 Cm-’ is strongly asymmetric and has the shape which is typical for Fano resonance. The presence of Fano resonance band shape 1s natural 1n weakly conducting sample 2 because of hybridization of LL with conduction band states. The LL influence the mode effective charge of axial vibration and thus this vibration and one particle lead to coupling between excitation spectrum connected with free carriers In conductlon band. The main features ti temperature dependences of TO and LO spectra are nearly the same as for the semiconducting sample 1. The main conclusion we may deduce from the results described above is the real hybridization between the CuO,- plane states and Cu-0 chati states. This hybrldlzation Is suf f lciently weak in deflclent samples, i.e. the rate of carrier exchange between the LL and plane states Is low. It is very interesting to examine the exchange rate In highly conducting material YBa,Cu,O, with high T . c In order to investigate the axial vibrational mode In highly conducting sample YBa,Cu,O, we use a single crystallme film with c-axes parallel to the film surface.
.2 .i
_*_ ---. -/,-\ \ :-r;_ imgci‘,ir----.___
R(w),2
150
\/-------
650
F 3 Reflectkofn, Im ? I&-’ (0) 1 (sample 2).
cmei
I~;(;~losnd 2
3 6.6
200
600
cd
Fig.
4. Reflection spectra two polarizations of a single crystalline film. In
The reflection spectra in two polarizations of this film are shown on FIg.4. The spectra of effective dielectric functions Im[.e(w)l and ImI-&-l(w)1 for Elc calculated for the film on SrTiO, substrate as for the bulk homogeneos material are shown on Fig.5-6 respectively. Desplte the uncertainty in determination of dielectric functions of the film in polarization Elc it Is
158
possible to make a qualitative conclusion about the presence of the hybridization. It is clear from Fig. 5 and 6 that the qualitative changes of IE with temperature are nearly the same as In the deficient samples. That means the presence of carrier exchange between the plane and chain states. The more quantitative conclusions about the value of carrlers exchange rate could be done by detail determination of ImI&(w)l from the reflectlvlty spectra (Fig.4).
I 1 I-
Irrnk&-‘(kJl -
240 K -.-.- 40 K
A
0.04 0.02 0.
200
Fig. 5. The s ectra of ImI&(w) 1 Fig.6.The spectra for E,c calculated for E,c calcu Pated for the film.
600
cm-’
of ImI-&-’ (w)l for the film.
CONCLUSION The detailed JnvestQation of temperature dependence of IR band integrated intensities leads to the conclusion about hybridization of plane and chain states. The axial Cul-01 vibration can provide a modulation of the hybrldlzation coefficient and thus makes a contribution to interband palrlng. We also may suppoze that superconductivity occures for plane carriers and that an exchange of carriers between plane states and chain states plays an important role In superconductlvity. ACKNOWLEDGEMENTS We thank Dr. V.E.Kravtsov for theoretIca calculations, G.N.Zhizhin and V.A.Yakovlev for helpful discussJons.
drs.
REFERENCES l.L.Rosta et.al., Physica C, 1988, v.153-155, 268-269 2.F.Compf et.al., Physlca C, 1988, v.153-155, 274-275 3.P.Strobel et-al., Physica c, 1988, v. 153-155, 282-283 4.G.M.Ellashberg, JETF, 1960, v.38, 966 5.P.E.Sulewski et.al., Phys.Rev. B., 1987, v. 36, p.5735-5739.
153 in The Netherlands
VIBRATIONALSPECTRAOF HIGH-T,SUPERCONDUCTORS yB82%Ox. EVIDENCE OF INTERBAM)HYBRIDIZATION K.V. KRAISKAYA*, V.M. BURLAKOV, N.Y. BOLDYREV, E.I.FIRSOV, A.G. MIT’KO, E.V. PECHENfW.A. HADZHIYSKY S.I. KRASNOSVOBODTZEV*, Troltsk, Instltute of S ectrosco y, USSR Academy of Sciences, Moscow re ion, U8SR, 142082 *Lebedev 8 hyslcal Instltute, USSR Academy of Sciences, Moscow SUMMARY
IR reflectlon spectra of polycrystalllne samples YBaaCUsOx (x=6.3 and 6.6) at varlous temperatures are reported. From calculated spectra of Im[&(w)l and Im[-&-’ (w)l Is determlned that anomalous change ln reflectlvlty In the frequency region 500-700 Is due to the change In TO band cm-’ of axial Cul-01 vlbratlon integrated Intensity IE. Thls change in IX Is propozed to be connected wlth the free carrier locallzatlon on an Ion Cul wlth the consequent change of Its effective charge. The conclusion Is made about two energy bands of free carriers: one being connected wlth Cul-0, planes and the other wlth the Cul-04 chains. These two bands are well separated from each other In space but also hybrldlzed by tunneling through energy barler. The exchange of carriers between these two bands Is strongly dependent on the temperature and may contrlbute In superconductlvlty. INTRODUCTION One of the maln problem In lnvestlgatlon of recently discovered high-Tc superconductors Is a palring mechanism. The comparative study of phonon denslty of states F(w) In superconductlng (TcE90 K, x=7.0), and semlconductlng (~~6.0) samples YBa,Cu30x falled in flndlng the slgnlflcant differences In the functions F(w) in both compounds (ref. 1-3). Thls Indicates that the carriers palrlng If It Is caused by phonon medlated mechanism Is due to a small number of vlbrations glvlng too small contribution into F(w). Consequently the coupling constant a(w) of electron-phonon interactlon must be sufflclently large to compensate a small number of phonons contributing Into the effective attractlon constant h (ref. 4). But the large constant 0022.2860/90/$03.50
0 1990 Elsevier
Science
Publishers
B.V.
154
lead to significant renormalization3 of phonons. To search the evidence of phonon renormalization was the aim of this paper.
a(w)
RESULTSANDDISCUSSION For the detaIled Investigation of phonon renormalization the two samples of YBa2Cu30x compounds with x=6.3 (semiconducting sample 1) and with x=6.6 (superconducting below 12 K sample 2) were used. These ceramic samples were prepared by conventional technique. The analysis of reflectJon (Fig. 1) of sample 1 show that the TO band near 600 cm-’ attributed to Cul-01 axial vibration (ref. 5) 1s strongly asymmetric . Temperature measurements reveal the slgniflcant increase of Integrated intensity IE: of this band below 120 K - Fig.2. No significant changes in band parameters of other vibrations in. the spectrum was detected. Note that the temperature change in IX corresponding LO band 1s much smaller than that of TO band-Fig i. It is well understood now that the weakly unharmonlc vlbration has a temperature independent integrated intensity IX. Thus one should temperature variations of IX may be suppose that the observed caused either by strong anharmonic1ty effect or by temperature variations of the microscopic characteristic of vibrating particles such as effective charge e*. Let us analyse both possiblllties. r
-l
I, arbmits 10
.3
5
.4
-1
i_\
.2
Fi . jr Reflect;& Im4 -E (w)l (sample 1).
n-j1 I$;(;Lloand 2 3 6.3
L
100
200
300 7-x
Fig. 2. Temperature dependence of integrpted lntenslty IX of 600 cm phonon band.
For analysis of the first possibility the calculation of IX temperature dependence of anharmonic oscillator X withing the perturbation theory is sufficient. Equation of motion for such an
155
oscillator
can be written
as follows
mass, were m, w, and B are oscillator damping; 7 is anharmonlslty constant, E field, p is temperature dependent random the fluctuation dissipative analysis one titensity I(w) D(w)Z(w) I(w) = jEj2 (w-Go)2 t T2(w) ’ 3V Go= wet 3 zoo
resonant frequency and is an external electric fluctuating field. Using can obtain for spectral
(2a) (2b)
’
‘Z(W) 1 1--m-a 1 (3b) 9
rr
1
t ---. 8 m2wz (tio)2t
(W
W2
-1
Z(w) =
3 r2T2
8 m2wz (tio)*t
1
9g2
Temperature dependence of Integrated intensity is obviously determined by the factor Z(w). One can see from (2) that IZ increases with increasing temperature. Despite of classical approach to Z(w) calculation the result is sufficient for qualitative descrlptlon of IZ temperature behavlour at relatively low temperatures which is opposite to the experlmental one. Let us consider one other mechanism of temperature dependence based on temperature dependence of effective ion charge e*. of 12’ The mode effective charge Is constructed from ion effective charges through the relation Gq= e*L i iq ’
(4)
were q Is an index of normal mode, I Is an ion index and I, is the transltion matrix to the normal mode from the carteslaniqion desplacements. Before the following analytical treatment It Is worth to note that the temperature dependence of ion effective charge is determined by free carrler localization on the local ion level vibrating in axial mode mentloned above. The most probable site for this localization is Cul ions. Because of small localization radius and relatively low activation energies (100 K) there should
156
be an energy barrler between the conduction band and a locallzed levels (or band) of magnitude as large as 1 eV. Thus the temperature dependence of ion effective charge is described by equation dn -%-EL -‘= (no-n, ) ‘exp (5) w!LmwLc“&%L~L~ dt I k!r 1 of full number were no, n, and nc are the everage concentrations free localized levels and free carrier of localized levels, respectively; G and s are the Fermi level and locallzed level energies respectively, bL and tic the vibratlon frequency of particle on IL and the effective frequency of free carrier attack on the energy barrier, wLc and wcL are the tunneling probabilities of a barrier from the LL to the conduction band and In opposlt dlrection respectively, pc and p, are corresponding densities of free states. To slmpllfy the equatlon (5) we accept nc=n,; &+L,, the asymptotic wLc=wcLand pc>>pL=n, . One may simply analize behaveour of n from equation l
(no-n, ) ‘exp (-AE/kT ) = n:/p,
(6)
Note that the relation between n determined according to (6) and integrated Intensity Ic may be very complicated because of the fast exchange of carrlers between the localized and the delocalized levels. To simplify this relation one must use the approxlmatlon bazed on low rate of exchange. In this case there will be the only two types of oscillators ln the lattice connected wlth the occupied LL and free LL. They are coupled through the The linear resonant interaction causes the polarization field. redlstrlbution of oscillator intensities and do not change the full integrated intensltiy IZ,+IXZ.For this reason we use for qualitative analysis of IX the expresslon IZ = IX0 + p(n,-n,
1
,
(7)
where IZols temperature independent and p is Constant. (6) and (7) the Ix thus determined According to (5)) monotonously increases wlth decreasing temperature. As it shown on Fig. 2 there Is a nonmonotonous Increase of effective charge when This may be connected with temperature temperature decreases. dependence of energy parameters EL or U (U 1s the height of the energy barrier) caused by local transitlon lnto superconducting Flg.3 represents the IR reflectlon spectra of sample 2 state.
157
and the corresponding spectra of Imt&(w)l and ImI-E-‘(w)]. The vibrational band near 600 Cm-’ is strongly asymmetric and has the shape which is typical for Fano resonance. The presence of Fano resonance band shape 1s natural 1n weakly conducting sample 2 because of hybridization of LL with conduction band states. The LL influence the mode effective charge of axial vibration and thus this vibration and one particle lead to coupling between excitation spectrum connected with free carriers In conductlon band. The main features ti temperature dependences of TO and LO spectra are nearly the same as for the semiconducting sample 1. The main conclusion we may deduce from the results described above is the real hybridization between the CuO,- plane states and Cu-0 chati states. This hybrldlzation Is suf f lciently weak in deflclent samples, i.e. the rate of carrier exchange between the LL and plane states Is low. It is very interesting to examine the exchange rate In highly conducting material YBa,Cu,O, with high T . c In order to investigate the axial vibrational mode In highly conducting sample YBa,Cu,O, we use a single crystallme film with c-axes parallel to the film surface.
.2 .i
_*_ ---. -/,-\ \ :-r;_ imgci‘,ir----.___
R(w),2
150
\/-------
650
F 3 Reflectkofn, Im ? I&-’ (0) 1 (sample 2).
cmei
I~;(;~losnd 2
3 6.6
200
600
cd
Fig.
4. Reflection spectra two polarizations of a single crystalline film. In
The reflection spectra in two polarizations of this film are shown on FIg.4. The spectra of effective dielectric functions Im[.e(w)l and ImI-&-l(w)1 for Elc calculated for the film on SrTiO, substrate as for the bulk homogeneos material are shown on Fig.5-6 respectively. Desplte the uncertainty in determination of dielectric functions of the film in polarization Elc it Is
158
possible to make a qualitative conclusion about the presence of the hybridization. It is clear from Fig. 5 and 6 that the qualitative changes of IE with temperature are nearly the same as In the deficient samples. That means the presence of carrier exchange between the plane and chain states. The more quantitative conclusions about the value of carrlers exchange rate could be done by detail determination of ImI&(w)l from the reflectlvlty spectra (Fig.4).
I 1 I-
Irrnk&-‘(kJl -
240 K -.-.- 40 K
A
0.04 0.02 0.
200
Fig. 5. The s ectra of ImI&(w) 1 Fig.6.The spectra for E,c calculated for E,c calcu Pated for the film.
600
cm-’
of ImI-&-’ (w)l for the film.
CONCLUSION The detailed JnvestQation of temperature dependence of IR band integrated intensities leads to the conclusion about hybridization of plane and chain states. The axial Cul-01 vibration can provide a modulation of the hybrldlzation coefficient and thus makes a contribution to interband palrlng. We also may suppoze that superconductivity occures for plane carriers and that an exchange of carriers between plane states and chain states plays an important role In superconductlvity. ACKNOWLEDGEMENTS We thank Dr. V.E.Kravtsov for theoretIca calculations, G.N.Zhizhin and V.A.Yakovlev for helpful discussJons.
drs.
REFERENCES l.L.Rosta et.al., Physica C, 1988, v.153-155, 268-269 2.F.Compf et.al., Physlca C, 1988, v.153-155, 274-275 3.P.Strobel et-al., Physica c, 1988, v. 153-155, 282-283 4.G.M.Ellashberg, JETF, 1960, v.38, 966 5.P.E.Sulewski et.al., Phys.Rev. B., 1987, v. 36, p.5735-5739.