For a large variety of superconducting materials both experimental and theoretical lattice dynamical studies have been performed to date. The assignment of the observed infrared- and Raman-active phonon modes to the particular lattice eigenmodes is generally accepted. We will concentrate here upon the analysis of the changes of the infrared-phonon parameters (frequency and linewidth) upon entering the superconducting state which, as will be shown, may provide information on the magnitude of the superconductivity-related gap and its dependence on the superconducting transition temperature Tc

Borjesson, L.

Cardona, M.

Litvinchuk, A. P.

Thomsen, C.

English

NASA Technical Reports Server

SPECTROSCOPY OF INFRARED-ACTIVE PHONONS
IN HIGH-TEMPERATURE SUPERCONDUCTORS
A.P. Litvinchuk
Department of Physics, Chalmers University of Technology,
S-41296 GSteborg, Sweden
C. Thomsen
Institut fiir FestkSrperphysik, Technische Universith't Berlin,
Hardenbergstrafle 36, D-10623 Berlin, Federal Republic of Germany
M. Cardona
Max-Planck-Institut fiir FestkSrperforschung,
Heisenbergstrafle 1, D-70569 Stuttgart, Federal Republic of Germany
L. B6rjesson
Department of Physics, The Royal Institute of Technology,
S-10044 Stockholm, Sweden
For a large variety of superconducting materials both experimental and theo-
retical lattice dynamical studies have been performed to date. The assignment of
the observed infrared- and Raman-active phonon modes to the particular lattice
eigenmodes is generally accepted (for a reviews see Ref. [1-5]). We will concen-
trate here upon the analysis of the changes of the infrared-phonon parameters
(frequency and linewidth) upon entering the superconducting state which, as will
be shown, may provide information on the magnitude of the superconductivity-
related gap and its dependence on the superconducting transition temperature
Tc.
Effects of the superconductivity-induced infrared-phonon renormalization
were studied experimentally most intensively for Y2Ba4Cu6+nO14+,_s(n = 0,
1, and 2) superconductors with a double CuO2-1ayerin each primitive cell. An
interesting feature of the materials with single-CuO chains as structural element
(n -- 0 and 1) is the possibility to gradually modify their superconducting pro-
perties by varying the oxygen content; this allows to study the effectsof a reduced
Tc in detail even for materials of the same crystallographic structure. For n = 2,
however, the presence of the double-CuO chains fixes the oxygen content and, cor-
respondingly, To. Another possible way to investigate the effects of phonon renor-
malization and their connection to superconductivity is to study ion-substituted
superconductors knowing the effectsof the ions on the superconducting properties
of materials from independent measurements.
Superconductivity-induced phonon self-energy effects or so called phonon
anomalies were found rather soon after discoveryof YBCO superconductors [6, 7].
For a number of reasons they were studied most intensively by means of Ra-
man spectroscopy mainly because the sample requirements are easier to fulfill for
Raman then for infrared spectroscopy or neutron-scattering experiments. Pro-
nounced changes (up to 10 cm-1) of the frequencies and the linewidths of the
oxygen-related mode at about 340 cm-I were found upon cooling below the su-
perconducting transition temperature (note that even larger effects have been
reported for the T12Ba2Ca2Cu3010superconductor [8]). It is clear qualitatively
328
https://ntrs.nasa.gov/search.jsp?R=19960000264 2020-06-16T07:05:10+00:00Z
Figure 1: Calculated (af-
0 _o_ ter Zeyher and Zwicknagl
o_----_/'_'_ f [10]) imaginary (a) and real
._-1 (b) parts of the phonon
/
_l > - _' R.m.° self-energies for a super-
, e, conducting energy gap at
0 TmJ
-2 + 2A = 316 cm -1 and
°,:}E*- ,a (ol an impurity scattering rate- 0
, , , 1/(2At) = 1 (solid lines).
200 300 _oo 500 6oo Points are the experimen-
v (cmq) tal data (after Ref. [11-
1- 15] for Raman- as well as
infrared-active (after Ref.
[16])phonons. Open points
0 refer to 160 and full - to 1so
-_1_ T6 substituted materials./
+% iN
f t I
200 300 400 500 600
v (era-1)
that if the phonon energy huph is larger than the magnitude of a given super-
conducting gap 2A, one expects an additional broadening of the phonon at low
temperatures because new decay channels appear due to the possibility to break
a superconducting pair. When ht,ph < 2A one expects, on the other hand, the
phonon to narrow because of the reduction in the density of states in the gap
and hence in the number of decay channels. At the same time phonons ex-
hibit frequency hardening or softening depending on their position relative to
the superconductivity-related gap. Of course, phonons with energies close to the
gap value 2A should react most sensitively to the transition from normal to the
superconducting state. For even-parity Raman-active phonons all the features
mentioned above were calculated quantitatively by Zeyher and Zwicknagl [9, 10]
in the framework of weak BCS as well as conventional strong-coupling theory.
In Fig. 1 experimental results are shown for the superconductivity-indu-
ced changes of the phonon linewidth (a) and frequency (b) for single-chain
YBa2CuaOv, i.e., changes of the phonon parameters (zXFand At, between Tc
and T _ 0). The solid lines in the figure are the results of the calculations under
the assumption of a single isotropic gap. The only adjustable parameter in these
calculations (except, of course, of the magnitude of the superconducting gap 2A
which was assumed to be 316 cm-1 _ 39.5 meV in Fig. 1) is the electron-phonon
coupling constant which from the comparison of theoretical and experimental re-
sults was found to be 0.01-0.02 for the phonon branch. These values are in good
329
agreement with LMTO ab-initio calculations.
Note again that calculations presented in Fig. 1 were done for Raman-active
modes. It is interesting that the self-energy effect of the odd-parity infrared-active
modes could also be described by those calculations despite of the fact that for
even-parity excitations different transitions are involved in the electron-phonon
interaction (including intraband transitions). So, the superconductivity related
gap and even the electron-phonon coupling constants seem to be rather similar
for Raman- and infrared-active modes in YBa2Cu307 [16]. The only infrared data
points which do not fit into the general picture are the frequency variations of the
high-frequency apical oxygen vibration at about 600 cm-l: this mode exhibits a
frequency softening in the superconducting state instead of the predicted hard-
ening (see Fig. 1,b). It was shown recently, however, that this specific feature
could consistently be explained theoretically by taking into account the interplane
charge fluctuations of the double-plane system [17, 18].
Careful experimental investigations of various superconducting materials re-
vealed a strong dependence of the superconductivity-induced phonon self-energy
effects in YBa_Cu3OT-8 on the oxygen content 6 and the presence of impurities
even for the samples within the so called 90K-plateau (see, e.g., Ref. [19, 20]). It
is advantageous in this sense to investigate also the double-chain YBa2Cu40s su-
perconductor which is known to have an essentially fixed oxygen content because
of the presence of the double CuO-chains.
r-
= 300
_" 30 20
25
0 100 200 300 0 100 200 30_
Temperature,K Temperature,K
Figure 2: Temperature dependences of the frequencies (solid points) and
linewidths (open points) of two oxygen-related modes of the double-chain
YBa2Cu4Os. The dashed vertical lines mark the Tc (after [25]).
It was found that the self-energy effects experienced by the Bl,,(z) infrared-
phonons of the double-chain YBa2CuaOs are rather similar to those observed
330
for the single-chain YBa2Cu3Or-s and discussed above [21-23]. In Fig. 2 data
are presented for the frequency and linewidth variation upon cooling of two
phonon modes: the plane-oxygen vibration at 300 cm -_ and also the CuO-
chain mode [24] at about 500 cm -l. A pronounced narrowing of the former
upon cooling below Tc and a broadening of the latter yielded boundaries for
the magnitude of the superconducting gap: 310 cm-l<_ 2A <_ 497 cm -1 [22].
Note that similar to the single-chain YBa2Cu307_6 a frequency softening of
the high-frequency mode is evident. Remarkably, for both modes shown in
Fig. 2 the softening starts at temperatures well above Tc - a fact which is
still under discussion and may be related to the opening of the spin-related gap
above Tc in underdoped superconductors (see [1, 26] and references cited therein).
x=0.60 Figure 3: Temperature depen-
85 "_--_--_-'-_-- _ X ff_ dence of the full linewidth atthe half-maximum of the plane-
oxygen phonon
'E "-_ 0.50-._ of (Pr=Y___)Ba2Cu408 supercon-
_ -'_ ductors with frequency about 300
65 _0 _ cm -1. The curves from top to
X - bottom are offset vertically by 45,
._=
o 0__5-_2 25, 15, 10, and 0 cm -1. The
,-- _-5[- T dashed vertical lines mark the T_
--+-o 45 ._T_.
" '---,-_--_---_- for each sample (after Ref. [27]).
"_ _,'_'_ 0.20
25 , ' " ' "
0 1O0 200 300
Temperature(K)
Investigations of T¢-reduced (Pr- and Zn-substituted) double-chain
YBa2Cu40s yielded more information on the superconducting gap. Some of the
results for (Pr=Yl_=)Ba2Cu4Os are shown in Fig. 3. A narrowing upon cooling
of the phonon at 300 cm -1 for all materials with Pr-content x < 0.35 signals the
presence of the gap at higher energies. For higher Pr-contents this mode starts
to broaden below T_. This has been interpreted as a result of the creation of a
new decay channel for the plane-oxygen phonon and experimental evidence for
the shift of the corresponding gap to lower energies across the phonon frequency
[27].
Qualitatively similar results as regards to the effect of the reduction of T_
on the infrared-phonon self-energies were observed in the case of Zn-substituted
YBa2Cu4Os [28]. An important experimental finding is that for both Pr- and Zn-
331
substitute different ions within the crystallographic structure) differs by factor
of ten. As a comparison, there is no effect on the self-energies in the case of
Sr substitution for Ba within a rather wide range of concentrations, which also
does not influence the superconducting temperature To. All these facts provide
convincing evidence that the discussed effects of the infrared-active phonon of
Y2Ba4Cus+,_Oa4+n-_ are indeed superconductivity related.
Acknowledgments This work was supported by the Swedish Research
Board for Natural Sciences, the Bundesminister fiir Forschung und Technologic
under contract No. 13N5840 5 (Federal Republic of Germany) and the European
Community. Part of this work was performed by one of us (A.P.L.) under the sup-
port from the Swedish Superconductivity Consortium, Max-Planck Gesselschaft
(Miinchen, Federal Republic Germany) and Alexander von Humboldt Founda-
tion (Bonn, Federal Republic Germany). He also acknowledges the hospitality of
the Max-Planck-Institut fiir FestkSrperforschung (Stuttgart, Federal Republic of
Germany) where part of this work was performed.
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333


Spectroscopy of infrared-active phonons in high-temperature superconductors

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