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May 2, 2003 Superconductivity Induced Electronic Excitation and Phonon Anomalies in Trilayer Bi2Sr2Ca2Cu3O10A.V. Boris1,2, D. Munzar3, N.N. Kovaleva1,2, B. Liang1, C.T. Lin1, A. Dubroka3, A.V. Pimenov1, T. Holden1,4, B. Keimer1, Y.-L. Mathis5, and C. Bernhard1 Charge and lattice dynamics along the c axis perpendicular to the CuO2 superconducting (SC) planes have been studied in a Bi2223 crystal by infrared ellipsometry using synchrotron radiation. The far-infrared (FIR) conductivity data reveal that a strong absorption band corresponding to a transverse Josephson plasmon develops as the crystal enters the SC state. The related effect of the FIR spectral weight increase is directly opposite the spectral weight decrease observed in conventional SC‘s. This unusual effect highlights that an anomalously large energy scale beyond the FIR range can be attributed to formation of the SC condensate in high-Tc superconductors. We also observe phonon anomalies, which suggest that the Josephson currents lead to a drastic variation of the local electric field within the block of closely spaced CuO2 planes.
These far reaching implications call for further experiments on a compound where the related SW transfer is larger and therefore more easily identified. The most promising candidates are multilayer high-Tc compounds, which contain more than two CuO2 plane per unit cell. Here we present ellipsometric data of the c axis dielectric response of the trilayer compound Bi2Sr2Ca2Cu3O10 (Bi2223). The ellipsometric measurements have been performed at the infrared beamlines of the synchrotron radiation sources at ANKA in Karlsruhe, Germany and at NSLS in Brookhaven. The high brilliance of the synchrotron enables us to obtain accurate data in the FIR spectral range even on mm-sized samples.
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The National Synchrotron Light Source at Brookhaven National Laboratory in New York, is a national user research
facility funded by the U.S. Department of Energy's Office of Basic Energy Science. The NSLS operates two electron
storage rings: an X-Ray ring and a Vacuum UltraViolet (VUV) ring which provide intense light spanning the electromagnetic
spectrum from the infrared through x-rays. Each year over 2300 scientists from universities, industries and government
labs perform research at the NSLS.
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The
transition from a normal metal to a superconductor (SC) below the
critical temperature, Tc, is accompanied by a redistribution of
spectral weight (SW) for the real part of the complex optical
conductivity, σ (ω), from finite frequencies in the normal state
(NS) into a δ-function at zero frequency in the SC state that
represents the loss-free response of the SC condensate. For
classical SC's, the energy gap determines the relevant frequency
range over which the SW of the δ-function is collected, so that
noticeable changes occur only for ω< 6 Δ (Ferrell-Glover-Tinkham (FGT)
sum rule). Recently, it was found that the FGT sum rule is partially
violated for the c axis response of some of the high-Tc cuprate
compounds: the SW loss in the FIR below Tc is smaller than the
SW of
the δ-function at zero frequency. The change of the FIR-SW in the SC
state is small and hard to measure experimentally. Nevertheless, due
to its important implications, the reports on the FGT sum rule
violation have attracted considerable attention. It implies that a
very large frequency scale is involved in the SC pairing and seems
to rule out any conventional mechanism that relies exclusively on
low-frequency bosons like phonons. Instead, it supports models where
a decrease in the c axis kinetic energy below Tc provides a
significant contribution to the SC condensation energy. 
The
Figure 1 shows the real part σ1 of the c axis optical conductivity
of Bi2223 at the three different doping levels. The NS spectra are
dominated by the contributions of several IR-active phonons, the one
of the charge carriers is extremely weak. In the NS the spectra
exhibit hardly any noticeable changes. Right below Tc, however, the
spectra change appreciably. The most prominent feature is the broad
absorption band around 500 cm-1, which appears below Tc and grows
rapidly with decreasing temperature. The center of this band shifts
towards higher frequencies with increasing doping. A similar
absorption band has been previously identified in the bilayer
compounds YBa2Cu3O7-δ and Bi2Sr2CaCu2O8 where it has been attributed
to a transverse Josephson-plasma resonance (t-JPR). This can be
understood in terms of the interlayer-tunneling model, which assumes
that the CuO2 planes are weakly coupled by the Josephson currents in
the SC state. For bi- or trilayer compounds, this results in two
kinds of Josephson junctions (Josephson superlattice) with different
longitudinal plasma frequencies. Their out-of-phase oscillation
gives rise to the t-JPR, which has been assigned to the absorption
peak that develops below Tc. The SW of this feature is very large
and gives rise to a considerable increase in the FIR-SW below Tc.
Such an apparent increase in the SW is certainly not expected for
any conventional SC where the FIR-SW should be removed and
transferred to the δ-function at zero frequency (Figure 2a). Figure
2b shows a sketch of the SC induced change of the FIR conductivity
in Bi2223. The data represent a striking manifestation of the
violation of the FGT sum rule. They highlight that a significant
amount of SW is transferred from higher frequencies to the
absorption band near 500 cm-1. This result is independent of a
particular model that is used to explain the origin of the band. We
emphasize that within the Josephson superlattice model (JSM) the SW
of the t-JPR belongs to the SC condensate just as much as the one of
the δ-function at zero frequency. 
The
It is evident from Figure 1 that the formation of the t-JPR is also
associated with an anomalous temperature dependence of the phonon
modes. Particularly interesting are the contrasting T dependences of
the modes at 360 and 400 cm-1. As shown in Figure 3a, the mode at
360 cm-1 loses a significant amount of its SW below Tc, while, in
clear contrast, the latter one gains in the SW. Both phonons are
assigned to be oxygen bond-bending modes with the eigenvector
diagrams shown in Figure 3b. Their contrasting behavior, while
surprising at first, is explained by the JSM. A sketch of the charge
dynamics corresponding to the t-JPR is shown in Figure 3c where κ(ω)
denotes the charge density that alternates from one outer plane to
the other. The onset of the Josephson currents jl and j2 between the
CuO2 layers below Tc can lead to a significant change of the
dynamical local electric field inside the the trilayer, E1, inside
the spacing layer that separates the trilayers, E2, and at the outer
CuO2 layers, E3. The strength of a given phonon mode is determined
by the local field at the ions participating in the mode and by the
mode polarizability. The main difference between the oxygen
bond-bending modes is in relative phase and amplitude of the inner
and outer-plane oxygen vibrations: The mode at 360 cm-1 consists
predominantly in the vibration of the oxygens in the outer CuO2
planes (O1), the latter one involves vibrations of the oxygens in
the middle CuO2 (O4) plane. Following the simple model being
discussed here, we estimate that the average magnitude of E3 at O1
ion sites is strongly suppressed below Tc, while the magnitude of E1
inside the trilayer at O4 sites increases. The local field effect
leads to the observed contrasting behavior of the oxygen
bond-bending modes in the SC state. These phonon anomalies clearly
reflect a transition from a state exhibiting confinement (incoherent
intra-trilayer conductivity) into a state where the CuO2 planes are
Josephson coupled. They demonstrate that, in the SC state, the local
electric field can exhibit enormous variations within the unit cell.