Josephson Plasma Resonance and Phonon Anomalies in Trilayer $\mathrm{B}{\mathrm{i}}_{\mathrm{2}}\mathrm{S}{\mathrm{r}}_{\mathrm{2}}\mathrm{C}{\mathrm{a}}_{\mathrm{2}}\mathrm{C}{\mathrm{u}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{10}}$

The far-infrared (FIR) $c$ axis conductivity of a Bi2223 crystal has been measured by ellipsometry. Below $T_c$ a strong absorption band develops near $500\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{1}}$, corresponding to a transverse Josephson plasmon. The related increase in FIR spectral weight leads to a giant violation of the Ferrell-Glover-Tinkham sum rule. The gain in $c$ axis kinetic energy accounts for a sizable part of the condensation energy. 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 ${\mathrm{C}\mathrm{u}\mathrm{O}}_2$ planes.

Figure 1

Real part, ${\sigma }_1(\omega )$, of the FIR $c$ axis conductivity of Bi2223.

Figure 2

Spectra of (a) $\Delta {\sigma }_1={\sigma }_1(10\mathrm{K},\omega )-{\sigma }_1(120\mathrm{K},\omega )$ and (b) $\Delta \mathrm{S}\mathrm{W}(\omega )$ [see Eq. (1)]. The phonon anomalies discussed in the text are denoted by $A$, $B$, and $C$. Inset: Upper limit of the quantity $(N_n-N_s)/{\omega }_{\mathrm{p}\mathrm{s}}^2$ defined in the text for Bi2223 with $T_c=107\mathrm{K}$ [${\omega }_{\mathrm{p}\mathrm{s}}=50\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{1}}$, error bars for $\Delta \mathrm{S}\mathrm{W}(\omega )$ are reckoned in].

Figure 3

(a) Calculated oxygen bond-bending $A_{2u}$ eigenmodes of Bi2223. (b) Relative SW changes of the phonons at $360\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{1}}$ (solid squares) and $400\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{1}}$ (open squares) with decreasing temperature, $\Delta {\mathrm{S}\mathrm{W}}_j=[{\mathrm{S}\mathrm{W}}_j(T)-{\mathrm{S}\mathrm{W}}_j(200\mathrm{K})]/{\mathrm{S}\mathrm{W}}_j(200\mathrm{K})$. ${\mathrm{S}\mathrm{W}}_j$ has been derived by fitting a sum of Lorentzian functions to the complex dielectric function. (c) Schematic representation of the model discussed in the text. The horizontal lines represent ${\mathrm{C}\mathrm{u}\mathrm{O}}_2$ (solid), Ca (dotted), SrO (dashed), and BiO (dash-dotted) planes. (d) Frequency dependent variation of the normalized local electric field due to the Josephson currents as defined in the text: $E_{\mathrm{i}\mathrm{n}\mathrm{t}}^{\star }$ (dashed line), $E_{\mathrm{i}\mathrm{n}}^{\star }$ (solid line), and $E_{\mathrm{o}\mathrm{u}\mathrm{t}}^{\star }$ (dotted line). The local fields at the sites of the particular ions participating in the eigenmodes at 360, 400, and $582\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{1}}$ are indicated by $A$, $B$, and $C$, respectively.