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Infrared reflection of epitaxial Tl2Ba2CaCu2O8 thin films in the normal and superconducting states
~
iSolid State Co~nunications, Vol. 76, No. 5, pp. 651-654, 1990. Printed in Great Britain.
0038-1098/9053.00+.00 Pergamon Press plc
INFRARED REFLECTION OF EPITAXIAL TI2Ba2CaCu208 THIN FILMS IN THE NORMAL AND SUPERCONDUCTING STATES C. M. Foster, K. F. Voss, T. W. Hagler, D. Mihallovi6# and AJ. Heeger Institute for Polymers and Organic Solids, University of California, Santa Barbara, California 93106 USA and M. M. Eddy, W.L. Olson and E.J. Smith Superconductor Technologies, Inc., 460 Ward Drive, Santa Barbara, California, 93111 USA (Received August 15, 1990 by A. A. Maradudin) For T>Tc, the frequency-dependent conductivity, a(c0), is Drude-like in the far-infrared OR) and indicates a broad absorption in the mid-IR. For T
to give the desired thickness. The films were then heated for
Measurements of the temperature (T) dependence of the infrared OR) properties of high-Tc superconductors have shown that the frequency-dependent conductivity consists of two contributions, a narrow Drude part (with width F =kB T) and a broad, T-independent mid-IR part l These studies have focused on the anomalous normal state properfes, the origin of the mid-IR absorption,and determination of the magnitude of the energy gap (2A). For YBa2Cu307.8, the IR reflectance (9~) has been interpreted in terms of the superconducting clean limit where l"=l/x<< 2A.2 Within this model, the mid-IR oscillator strength with onset at -120 cm -1 is due to a direct electronic transition of unspecified origin but distinct from the free carder contribution, and the -450 cm -I shoulder is modeled3 as a strongly-coupled Fano-type4 interference between a phonon band at 433 cm -1 and the broad mid-IR electronic absorption. Thus, neither feature is associated with the energy gap. Alternatively, the mid-lR band has been attributed (in part) to absorption resulting from the Cu-O chains, and the --450 cm -I shoulder to 2A=8kBTc. 5 In this paper, we present reflection measurements on high quality T12Ba2CaCu208 (T1-2212) films in the normal (9~n) and superconducting (~s) states and use a KramersKr6nig CKK) analysis of 9~(co) to obtain ¢~(¢0) and e(¢0), the frequency-dependent conductivity and dielectric function. In the normal state, ¢~(¢0) is Drude-like in the far-IR (I"-2.2kBT), and indicates a broad absorption in the mid-IR. For T
several minutes at 830-900oc in a thallium atmosphere ~to prevent loss of T1203). Final film thicknesses were =9000A. X-ray diffraction scans show the films are oriented with c- axis normal to the LaAIO3 substrate surface. Narrow X-ray rocking curves (as sharp as 0.3 degrees) and selectedarea electron channeling patterns indicate that the TI-2212 films are epitaxially oriented in the a-b plane. Electron channeling is observed over the whole film showing the [100] direction of the superconductor to be aligned with the [I00] direction of the substrate. The TI-2212 films have T¢ from 98K to 100K (mid-point, by ac susceptibility) and transition widths as narrow as 0.8K. At 77K, the microwave (9.55GHz) surface resistance is approximately twenty times lower than that of high purity copper. Resonators (2.SGHz) fabricated from such films perform over ten times better than equivalent resonators from normal metal even at high power levels (e.g. at 0 dbm). 6 Critical current values of 106 A/cm2 at 77K are typical. The narrow superconducting transition width, low microwave surface resistance, and high critical currents indicate that the quaility of the films is comparable to the best YBa2Cu307.5 fdms. Reflectance measurements were made at UCSB with an IBM-Bruker 0R98) Fourier transform interferometer in a temperature controlled cryostat in the energy range from 805OO0 cm -1 (0.01-0.625 eV) and with a grating monochromator from 4800-12000 cm -1 (0.60-1.48 eV). Absolute values of ~(c0) were obtained by comparison of the T1-2212 films to a vacuum deposited l~tm thick Au mirror on a polished CaF2 substrate mounted onto the back of the sample holder. The reference and sample positions were accurately exchanged by constraining all degrees of freedom except rotation in the plane of the beam path. This orientation angle was then fixed by using relfection from the sample/reference from a HeNe laser through a long (3m) path giving an orientation angle error of <0.1 o. The samples were
651
subsequently Au-coated and measured again to estimate scattering losses. Although there were scattering losses for hco >500 cm -1, the far-IR data required no correction. In Figure 1, we show 9t(co) in the far-IR. The data were reproducible from films which showed good superconducting properties (high To, sharp transition and low microwave surface resistance). Within experimental error, the films showed ~ s = l . 0 for to<200cm -1, above which there is an onset of absorption. At higher frequencies, a series of relatively broad features are observed. For co>2500 cm -1, ~(co) is temperature independent 12. In the normal state, 9tn
(la)
OD(CO)= (1/4~)~p2x[l+(cox)2] (lb) where e,. is the high frequency dielectric constant and ~p=[41~Ne2/m ,] 1/2 is the plasma frequency (N is the density of free carriers with charge e). As shown by the dashed curves in Fig. 1, 9~n deviates below the Drude curve above -400 cm -1 indicative of the onset of a new loss channel. At higher co, the same spectral features seen in ~n are clearly present in 9~s. The fits to eqn. 1 yield flp=6250+__50 cm "l, e**= 3.5, and a scattering rate linear in T, r=1/'~=(2.13i-0.08)kBT. These values imply a de resistivity of 7001.t~-cm at 300K which decreases linearly with temperature. Both the magnitude and the slope are consistent with direct deresistivity measurements on these T1-2212 films. These values of f~p and e** are only approximate since the Drude model clearly neglects features in 9~(co) above 400cm -1. At 125K, r = 1 8 2 c m -1 ( 2 . 6 2 k B T c ) , suggesting that if 2A23.52kBTc (the BCS value) then TI-2212 is in the clean limit] A KK transform of 9t(to) was carried out to determine or(co) and c(co). Our KK program was extensively tested on Drude-Lorentz model dielectric functions to determine the best extrapolation procedure. The phase shift on reflection, 0(co), was corrected so that 0(co--**)=0; 9t s and 9~n were extrapolated as constants equal to their highest measured value. Since 9ts,n are featureless above 0.5 eV, we found that o(co) and e(co) (for to<2000 cm -1) were insensitive to high frequency extrapolations. On the low-frequency side,
2000
Z
IL)
~n(a~--0) was extrapolated using the Drude-model fits shown in Fig. 1, while ~,s(a~-~0) is fixed at unity. For regions where ks=l.0, this extrapolation yields 0(co)=-~, 6(co)=0, and e(co)<<0. We estimate that any errors in a(co) and e(co) introduced by the KK transform are <10% in the lowest 5 data points and negligible (i.e. smaller than experimental error) for higher frequencies. The o(co) of T1-2212, as determined from KK analysis of ~(co), is shown in Figure 2. At 300K, On(co) is Drude-like in the far-IR (F=480 cm -1) with pronounced shoulders suggestive of the onset of HolsteinS processes for phonon emission at appoximately 200-400 and 500-600 cm -1, and a long tail extending into the mid-IR. At 125K, the Drude contribution has sharpened (F--180 cm -1) and the phonon features have significantly weakened; however, the mid-IR absorption is essentially unchanged. For T
5000
1.00
..q
VOI. 76, No. 5
INFRARED REFLECTION OF EPITAXIAL TI2Ba2CaCu208
652
" ~ - - - - - - ~ - ' - - "- ~
-,,..-t__"
. . . .
.....................
0.90
i
~ moo
0.80 0.70 ?
\ ',~..,,,.
WAVENUMBERS (cm"])
0.60 0
500
1000
1500
WAVENUMBERS (cm- l) Figure 1: Far -IR reflectivity, ~g(to), of a T12Ba2CaCu208 film at 300K (solid), 125K (long dash), 60K (dash-dot), and 10K (short dash), compared with Drude fits to 9t(co) in the normal state. The Drude model pmmneters are (in cm -1) as follows: 300K, ~p=6200, F=470; 125K, f~p=6300, F=182..
o 0
1000
2000
W A V E N U M B E R S (cm -1) Figure 2: or(m) at 300K (short dash), 125K (dash-dot), 60K (long dash), and 10K (solid); the inset compares Os(co) at 60K (short dash), and 10K (dash-dot)with 6n-D(CO)= [an(co)-OD(co)] (solid).
Vol. 76, NO. 5
INFRARED REFLECTION OF EP ITAXIAL TI2Ba2CaCu208
with that obtained from the simple Drude fits to ~n- The lower value obtained from the Drude fit in Fig. 1 is due to ignoring the phonon oscillator strength near 100 em -1 (see inset to Fig. 2). In Figure 3, we plot e(03). At 300K, e(03) is positive below 140 cm -1, even though the sample is metallic with good superconducting properties. At 125K, e(03) is negative at low frequencies; however, there is structure below 200 cm -1 due to the phonon modes. Below Tc and in the clean limit, all the oscillator strength of the Drude conductivity collapses into 8(03).10 As a consequence, e(03) becomes 8(03)= eb- ~ps 2/O2 (3) where eb results from all contributions to (~(03) other than ~(03), and ~ps=[4~Nse2/m*] 1/2 is the plasma frequency of the supereonducting condensate. If all the Drude-carriers condense into the superconducting state, O,ps = Gp. In the inset of Fig. 3, e(03) is plotted vs. 03-2for T0 at low frequency at T=300K. The picture that has emerged from these data (and from similar results from YBa2Cu3OT.5) 2 is that of superconductivity in the clean limit with F<2A, so that absorption across the gap will be intrinsically weak. The major problem with such an interpretation is the mid-IR 1000
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0 -1000 e(O.,) -2000 -3000 -4OOO -5000
] .....
0.0
[ ...........
1.0 <
!07 cm2> ....
200 400 WAVENUMBERS (em"t)
2.0. :
600
Figure 3. e(03) at 300K (short dash), 125K (dash-dot), 60K (long dash), and 10K (solid); the insert shows es(03) vs (0-2.
653
contribution to a(03). Two explanations for the mid-IR absorption have been proposed: (i) a direct electronic transition of unspecified origin, but distinct from and unrelated to the free carrier contribution;2 (ii) a contribution from the free holes, but with an 03dependent r due to either a shake-off of the dressing of the carriers8 (which are renormalized by strong interactions with phonons, spin-waves, etc.) or to an intrinsic 03-dependence of the scattering mechanism.5,14-16 We fred (i) difficult to accept since the mid-IR band arises from and scales with the addition of carriers either by doping or photo-injection.17 Although for YBa2Cu307,5, there could be a contribution to ~(03) from the CuO chains,5 there are no such chains in the T1-22 12 structure. The second alternative would appear to be preferable. A scattering rate of the form F(T,03) = 0.6max {r~kBT, h03} has been proposed5 as arising from strong interaction of the carriers with a broad excitation spectrum such that the physics is near the boundary of the regime in which Fermi liquid theory is valid. 15 Alternatively, F(T,o) of this form has been calculated from electron-electron scattering in a system with a nested two-dimensional Fermi surface. 16 In the conventional picture9, either a shake-off of a polaron-like dressing or a frequency dependent scattering rate would require a minimum energy of 2A per excitation below Tc and thus a shift of the mid-IR contribution by at least 2A. However, in the high-To materials2, there is no shift or loss in mid-IR oscillator strength for T
References: 1. For a review, see T. Timusk and D. B. Tanner, in P h y s i c a l P r o p o e r t i e s of Hish T e m p e r a t u r e Superconductors I, e d i t e d by Donald M. Ginsberg (World Scientific, Singapore, 1989), p. 339. 2. K. Kamaras ~ a/., Phys. Rev. Lett. 64, 84 (1990).
3. T. Timusk and D. B. Tanner (to be published). 4. U. Fano, Phys. Rev. B124., 1866 (1961). 5. R. T. Collins, eta/., Phys. Rev. Lett. ~ 422 (1989); Z. Schlesinger, e t a / . Phys. Rev. Lett. 65. 801 (1990). 6. L. C. Bourne, eta/., (submitted to App. Phys. Lett.).
654
INFRARED REFLECTION OF EPITAXIAL TI2Ba2CaCu208
7. T. Timusk eta/., Phys. Rev. I338. 6683 (1988). 8. T. Holstein Phys. Rev. 96, 539 (1954); Ann. Phys (N.Y.) ~ 410 (1964). 9. I. Batistic et al, Phys. Rev.B40, 6896 (1989). 1O. For a review, see M. Tinkham in FarlnfraredPropertie,s o f Solids, edited by S. S. Mitra and S. Nudelman, (Plenum, New York, 1974), p.431. 11. D. R. Harshman eta/., Phys. Rev. B 39, 851 (1989). 12. Z. Schlesinger eta/., Physica C 162- |64, 1111 (1989).
VOI. 76w NO. 5
13. N.P.Ong eta/.., in Strong Correlations in Superconductivity, Spinger Series on Solid State Science 89 (Springer Verlag, NY, 1989) p. 204. 14. H. G. Reik and D. Heese, Phys. Star. Sol. 24. 281 (1967). 15. C. M. Varma, eta/., Phys. Rev. Lett. ~ 1996 (1989); Phys. Rev. Lett. f ~ 497 (1990). 16. J. Ruvalds and A. Virosztek (to be published). 17. C. M. Foster eta/., Syn. Metals ~ 171 (1988).
iSolid State Co~nunications, Vol. 76, No. 5, pp. 651-654, 1990. Printed in Great Britain.
0038-1098/9053.00+.00 Pergamon Press plc
INFRARED REFLECTION OF EPITAXIAL TI2Ba2CaCu208 THIN FILMS IN THE NORMAL AND SUPERCONDUCTING STATES C. M. Foster, K. F. Voss, T. W. Hagler, D. Mihallovi6# and AJ. Heeger Institute for Polymers and Organic Solids, University of California, Santa Barbara, California 93106 USA and M. M. Eddy, W.L. Olson and E.J. Smith Superconductor Technologies, Inc., 460 Ward Drive, Santa Barbara, California, 93111 USA (Received August 15, 1990 by A. A. Maradudin) For T>Tc, the frequency-dependent conductivity, a(c0), is Drude-like in the far-infrared OR) and indicates a broad absorption in the mid-IR. For T
to give the desired thickness. The films were then heated for
Measurements of the temperature (T) dependence of the infrared OR) properties of high-Tc superconductors have shown that the frequency-dependent conductivity consists of two contributions, a narrow Drude part (with width F =kB T) and a broad, T-independent mid-IR part l These studies have focused on the anomalous normal state properfes, the origin of the mid-IR absorption,and determination of the magnitude of the energy gap (2A). For YBa2Cu307.8, the IR reflectance (9~) has been interpreted in terms of the superconducting clean limit where l"=l/x<< 2A.2 Within this model, the mid-IR oscillator strength with onset at -120 cm -1 is due to a direct electronic transition of unspecified origin but distinct from the free carder contribution, and the -450 cm -I shoulder is modeled3 as a strongly-coupled Fano-type4 interference between a phonon band at 433 cm -1 and the broad mid-IR electronic absorption. Thus, neither feature is associated with the energy gap. Alternatively, the mid-lR band has been attributed (in part) to absorption resulting from the Cu-O chains, and the --450 cm -I shoulder to 2A=8kBTc. 5 In this paper, we present reflection measurements on high quality T12Ba2CaCu208 (T1-2212) films in the normal (9~n) and superconducting (~s) states and use a KramersKr6nig CKK) analysis of 9~(co) to obtain ¢~(¢0) and e(¢0), the frequency-dependent conductivity and dielectric function. In the normal state, ¢~(¢0) is Drude-like in the far-IR (I"-2.2kBT), and indicates a broad absorption in the mid-IR. For T
several minutes at 830-900oc in a thallium atmosphere ~to prevent loss of T1203). Final film thicknesses were =9000A. X-ray diffraction scans show the films are oriented with c- axis normal to the LaAIO3 substrate surface. Narrow X-ray rocking curves (as sharp as 0.3 degrees) and selectedarea electron channeling patterns indicate that the TI-2212 films are epitaxially oriented in the a-b plane. Electron channeling is observed over the whole film showing the [100] direction of the superconductor to be aligned with the [I00] direction of the substrate. The TI-2212 films have T¢ from 98K to 100K (mid-point, by ac susceptibility) and transition widths as narrow as 0.8K. At 77K, the microwave (9.55GHz) surface resistance is approximately twenty times lower than that of high purity copper. Resonators (2.SGHz) fabricated from such films perform over ten times better than equivalent resonators from normal metal even at high power levels (e.g. at 0 dbm). 6 Critical current values of 106 A/cm2 at 77K are typical. The narrow superconducting transition width, low microwave surface resistance, and high critical currents indicate that the quaility of the films is comparable to the best YBa2Cu307.5 fdms. Reflectance measurements were made at UCSB with an IBM-Bruker 0R98) Fourier transform interferometer in a temperature controlled cryostat in the energy range from 805OO0 cm -1 (0.01-0.625 eV) and with a grating monochromator from 4800-12000 cm -1 (0.60-1.48 eV). Absolute values of ~(c0) were obtained by comparison of the T1-2212 films to a vacuum deposited l~tm thick Au mirror on a polished CaF2 substrate mounted onto the back of the sample holder. The reference and sample positions were accurately exchanged by constraining all degrees of freedom except rotation in the plane of the beam path. This orientation angle was then fixed by using relfection from the sample/reference from a HeNe laser through a long (3m) path giving an orientation angle error of <0.1 o. The samples were
651
subsequently Au-coated and measured again to estimate scattering losses. Although there were scattering losses for hco >500 cm -1, the far-IR data required no correction. In Figure 1, we show 9t(co) in the far-IR. The data were reproducible from films which showed good superconducting properties (high To, sharp transition and low microwave surface resistance). Within experimental error, the films showed ~ s = l . 0 for to<200cm -1, above which there is an onset of absorption. At higher frequencies, a series of relatively broad features are observed. For co>2500 cm -1, ~(co) is temperature independent 12. In the normal state, 9tn
(la)
OD(CO)= (1/4~)~p2x[l+(cox)2] (lb) where e,. is the high frequency dielectric constant and ~p=[41~Ne2/m ,] 1/2 is the plasma frequency (N is the density of free carriers with charge e). As shown by the dashed curves in Fig. 1, 9~n deviates below the Drude curve above -400 cm -1 indicative of the onset of a new loss channel. At higher co, the same spectral features seen in ~n are clearly present in 9~s. The fits to eqn. 1 yield flp=6250+__50 cm "l, e**= 3.5, and a scattering rate linear in T, r=1/'~=(2.13i-0.08)kBT. These values imply a de resistivity of 7001.t~-cm at 300K which decreases linearly with temperature. Both the magnitude and the slope are consistent with direct deresistivity measurements on these T1-2212 films. These values of f~p and e** are only approximate since the Drude model clearly neglects features in 9~(co) above 400cm -1. At 125K, r = 1 8 2 c m -1 ( 2 . 6 2 k B T c ) , suggesting that if 2A23.52kBTc (the BCS value) then TI-2212 is in the clean limit] A KK transform of 9t(to) was carried out to determine or(co) and c(co). Our KK program was extensively tested on Drude-Lorentz model dielectric functions to determine the best extrapolation procedure. The phase shift on reflection, 0(co), was corrected so that 0(co--**)=0; 9t s and 9~n were extrapolated as constants equal to their highest measured value. Since 9ts,n are featureless above 0.5 eV, we found that o(co) and e(co) (for to<2000 cm -1) were insensitive to high frequency extrapolations. On the low-frequency side,
2000
Z
IL)
~n(a~--0) was extrapolated using the Drude-model fits shown in Fig. 1, while ~,s(a~-~0) is fixed at unity. For regions where ks=l.0, this extrapolation yields 0(co)=-~, 6(co)=0, and e(co)<<0. We estimate that any errors in a(co) and e(co) introduced by the KK transform are <10% in the lowest 5 data points and negligible (i.e. smaller than experimental error) for higher frequencies. The o(co) of T1-2212, as determined from KK analysis of ~(co), is shown in Figure 2. At 300K, On(co) is Drude-like in the far-IR (F=480 cm -1) with pronounced shoulders suggestive of the onset of HolsteinS processes for phonon emission at appoximately 200-400 and 500-600 cm -1, and a long tail extending into the mid-IR. At 125K, the Drude contribution has sharpened (F--180 cm -1) and the phonon features have significantly weakened; however, the mid-IR absorption is essentially unchanged. For T
5000
1.00
..q
VOI. 76, No. 5
INFRARED REFLECTION OF EPITAXIAL TI2Ba2CaCu208
652
" ~ - - - - - - ~ - ' - - "- ~
-,,..-t__"
. . . .
.....................
0.90
i
~ moo
0.80 0.70 ?
\ ',~..,,,.
WAVENUMBERS (cm"])
0.60 0
500
1000
1500
WAVENUMBERS (cm- l) Figure 1: Far -IR reflectivity, ~g(to), of a T12Ba2CaCu208 film at 300K (solid), 125K (long dash), 60K (dash-dot), and 10K (short dash), compared with Drude fits to 9t(co) in the normal state. The Drude model pmmneters are (in cm -1) as follows: 300K, ~p=6200, F=470; 125K, f~p=6300, F=182..
o 0
1000
2000
W A V E N U M B E R S (cm -1) Figure 2: or(m) at 300K (short dash), 125K (dash-dot), 60K (long dash), and 10K (solid); the inset compares Os(co) at 60K (short dash), and 10K (dash-dot)with 6n-D(CO)= [an(co)-OD(co)] (solid).
Vol. 76, NO. 5
INFRARED REFLECTION OF EP ITAXIAL TI2Ba2CaCu208
with that obtained from the simple Drude fits to ~n- The lower value obtained from the Drude fit in Fig. 1 is due to ignoring the phonon oscillator strength near 100 em -1 (see inset to Fig. 2). In Figure 3, we plot e(03). At 300K, e(03) is positive below 140 cm -1, even though the sample is metallic with good superconducting properties. At 125K, e(03) is negative at low frequencies; however, there is structure below 200 cm -1 due to the phonon modes. Below Tc and in the clean limit, all the oscillator strength of the Drude conductivity collapses into 8(03).10 As a consequence, e(03) becomes 8(03)= eb- ~ps 2/O2 (3) where eb results from all contributions to (~(03) other than ~(03), and ~ps=[4~Nse2/m*] 1/2 is the plasma frequency of the supereonducting condensate. If all the Drude-carriers condense into the superconducting state, O,ps = Gp. In the inset of Fig. 3, e(03) is plotted vs. 03-2for T
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0 -1000 e(O.,) -2000 -3000 -4OOO -5000
] .....
0.0
[ ...........
1.0 <
!07 cm2> ....
200 400 WAVENUMBERS (em"t)
2.0. :
600
Figure 3. e(03) at 300K (short dash), 125K (dash-dot), 60K (long dash), and 10K (solid); the insert shows es(03) vs (0-2.
653
contribution to a(03). Two explanations for the mid-IR absorption have been proposed: (i) a direct electronic transition of unspecified origin, but distinct from and unrelated to the free carrier contribution;2 (ii) a contribution from the free holes, but with an 03dependent r due to either a shake-off of the dressing of the carriers8 (which are renormalized by strong interactions with phonons, spin-waves, etc.) or to an intrinsic 03-dependence of the scattering mechanism.5,14-16 We fred (i) difficult to accept since the mid-IR band arises from and scales with the addition of carriers either by doping or photo-injection.17 Although for YBa2Cu307,5, there could be a contribution to ~(03) from the CuO chains,5 there are no such chains in the T1-22 12 structure. The second alternative would appear to be preferable. A scattering rate of the form F(T,03) = 0.6max {r~kBT, h03} has been proposed5 as arising from strong interaction of the carriers with a broad excitation spectrum such that the physics is near the boundary of the regime in which Fermi liquid theory is valid. 15 Alternatively, F(T,o) of this form has been calculated from electron-electron scattering in a system with a nested two-dimensional Fermi surface. 16 In the conventional picture9, either a shake-off of a polaron-like dressing or a frequency dependent scattering rate would require a minimum energy of 2A per excitation below Tc and thus a shift of the mid-IR contribution by at least 2A. However, in the high-To materials2, there is no shift or loss in mid-IR oscillator strength for T
References: 1. For a review, see T. Timusk and D. B. Tanner, in P h y s i c a l P r o p o e r t i e s of Hish T e m p e r a t u r e Superconductors I, e d i t e d by Donald M. Ginsberg (World Scientific, Singapore, 1989), p. 339. 2. K. Kamaras ~ a/., Phys. Rev. Lett. 64, 84 (1990).
3. T. Timusk and D. B. Tanner (to be published). 4. U. Fano, Phys. Rev. B124., 1866 (1961). 5. R. T. Collins, eta/., Phys. Rev. Lett. ~ 422 (1989); Z. Schlesinger, e t a / . Phys. Rev. Lett. 65. 801 (1990). 6. L. C. Bourne, eta/., (submitted to App. Phys. Lett.).
654
INFRARED REFLECTION OF EPITAXIAL TI2Ba2CaCu208
7. T. Timusk eta/., Phys. Rev. I338. 6683 (1988). 8. T. Holstein Phys. Rev. 96, 539 (1954); Ann. Phys (N.Y.) ~ 410 (1964). 9. I. Batistic et al, Phys. Rev.B40, 6896 (1989). 1O. For a review, see M. Tinkham in FarlnfraredPropertie,s o f Solids, edited by S. S. Mitra and S. Nudelman, (Plenum, New York, 1974), p.431. 11. D. R. Harshman eta/., Phys. Rev. B 39, 851 (1989). 12. Z. Schlesinger eta/., Physica C 162- |64, 1111 (1989).
VOI. 76w NO. 5
13. N.P.Ong eta/.., in Strong Correlations in Superconductivity, Spinger Series on Solid State Science 89 (Springer Verlag, NY, 1989) p. 204. 14. H. G. Reik and D. Heese, Phys. Star. Sol. 24. 281 (1967). 15. C. M. Varma, eta/., Phys. Rev. Lett. ~ 1996 (1989); Phys. Rev. Lett. f ~ 497 (1990). 16. J. Ruvalds and A. Virosztek (to be published). 17. C. M. Foster eta/., Syn. Metals ~ 171 (1988).