Temperature evolution of correlation strength in the superconducting state of high-$T_c$ cuprates

We have performed an angle-resolved photoemission study of the nodal quasiparticle spectra of the high-$T_c$ cuprate trilayer ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$ ($T_c\sim 110$ K). The spectral weight $Z$ of the nodal quasiparticle increases with decreasing temperature across $T_c$. Such a temperature dependence is qualitatively similar to that of the coherence peak intensity in the antinodal region of various high-$T_c$ cuprates, although the nodal spectral weight remains finite and large above $T_c$. We attribute this observation to the reduction of electron correlation strength in going from the normal metallic state to the superconducting state, a characteristic behavior of a superconductor with strong electron correlation.

Figure 1

ARPES spectra of Bi2223 in the nodal direction at various temperatures. (a) Intensity plots in energy-momentum space along the nodal direction (see the inset to the 120 K data). OP and IP denote the outer and inner quasiparticle bands, respectively. (b) Quasiparticle (QP) band dispersions for the IP and OP bands deduced from the MDC peak positions.

Figure 2

ARPES spectra of Bi2223 integrated along the nodal direction including both the IP and OP bands. (a) Raw data. (b) Spectra divided by the Fermi-Dirac function. (c) Spectra in (b) divided by the spectrum at 160 K. (d) Temperature dependence of the spectral weight intensity within 80 meV from $E_F$ (normalized to the 160 K data).

Figure 3

Spectral weight $Z_{k_F}\left(\varepsilon \right)$ for the IP and OP bands of Bi2223 deduced from the MDC peak area and the QP velocity $v_k^{*}\left(\varepsilon \right)$. In order to extract the MDC area for the IP and OP bands separately, MDC data in Fig. 1 were fitted to two Lorentzians. (a) and (b) MDC area with the same intensity normalization as Fig. 2. (c) and (d) MDC area divided by the Fermi-Dirac function convoluted with a Gaussian. (e) and (f) $Z_{k_F}\left(\epsilon \right)={\int }_{-\infty }^{\infty }A(\mathbf{k},0)d\mathbf{k}\times v_k^{*}\left(\varepsilon \right)$, where $v_k^{*}\left(\varepsilon \right)$ has been deduced from the slope of the QP dispersions shown in Fig. 1. The dip at $E_F$ in the 10 K data, particularly for the IP band, arises because the cut direction was slightly off node due to small misalignment.

Figure 4

EDCs of Bi2223 at $k_F$ on the node. (a) and (b) Temperature dependence of the EDCs at $k_F$. (c) and (d) Symmetrized EDCs at $k_F$. The area of the Lorentzian centered at $E_F$ gives $Z\left(0\right)$.

Figure 5

Spectral weight at $E_F, Z_{k_F}\left(0\right)$, for the OP and IP bands of Bi2223 derived from MDCs and EDCs (under the assumption of a Fermi liquid) plotted as functions of temperature. $Z_{k_F}\left(0\right)$ for Bi2212 ($T_c=91$ K) deduced from the EDCs in Ref. [11] is also plotted.