Temperature Dependence of the Gap Size near the Brillouin-Zone Nodes of ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$ Superconductors

Although more than 20 years have passed, the identification of the superconducting order parameter in cuprates is still under debate. Here, we show that the gap size near the nodes is a good candidate for the order parameter: it scales with the critical temperature $T_c$ over a wide doping range and displays a significant temperature dependence below $T_c$ in both the underdoped and the overdoped regimes. In contrast, the gap size at the antinodes does not scale with $T_c$ in the underdoped regime and appears to be controlled by the pseudogap which persists below $T_c$.

Figure 1

Nodal ($B_{2g}$) and antinodal ($B_{1g}$) Raman response functions ${\chi }^{\prime \prime }(\omega )$ substracted from the one just above $T_c$ as a function of temperature (up to $T_c$) for two doping levels: $p=0.20$ [(a) and (b)] and 0.11 [(c) and (d)]. The insets in panels (a), (c), and (d) show the superconducting and normal Raman responses separately. The doping value $p$ is inferred from $T_c$ using equation of Presland et al. from Ref. 28: $1-T_c/95.5=82.6(p-0.16{)}^2$. The dashed lines are guides for the eyes and track the locations of the superconducting peak maxima (in bold line).

Figure 2

Temperature dependence of the nodal superconducting component for several doping levels. ${\Delta }_N$ has been normalized to its value at $T=10\mathrm{K}$. ${\Delta }_N$ values have been determined from the locations of the $B_{2g}$ (nodal) superconducting peaks in the Raman spectra of Hg-1201. The dashed line corresponds to the temperature dependence of a BCS $d$-wave gap from Ref. 25. For comparison, the temperature dependence of the antinodal gap component for $p=0.13$ is also shown.

Figure 3

Doping dependence of the $2{\Delta }_N(T=10\mathrm{K})/k_B{T}_c$ and $2{\Delta }_{\mathrm{AN}}(T=10\mathrm{K})/k_B{T}_c$ ratios deduced from the locations of the $B_{2g}$ (nodal) and $B_{1g}$ (antinodal) peaks in the Raman spectra. The $2{\Delta }_{\mathrm{PG}}/k_B{T}_c$ ratios are deduced from the extrapolations of the ${\Delta }_{\mathrm{AN}}$ at $T_c$ (for different doping levels) by using simple polynomial fits. The fits are shown in the inset where the temperature evolution of the normalized ${\Delta }_{\mathrm{AN}}(T)$ is depicted [11].