Interplay between the pseudogap and superconductivity in underdoped $\mathrm{Hg}{\mathrm{Ba}}_2\mathrm{Cu}{\mathrm{O}}_{4+\delta }$ single crystals

We report a doping-dependent electronic Raman scattering (ERS) study of $\mathrm{Hg}{\mathrm{Ba}}_2\mathrm{Cu}{\mathrm{O}}_{4+\delta }$ (Hg-1201) single crystals. We investigate the dynamics of the antinodal and nodal quasiparticles. We show that the dynamical response of the antinodal quasiparticles is strongly reduced towards the underdoped regime in both the normal and superconducting states. When probing the nodal quasiparticles, we are able to distinguish between the energy scale of the pseudogap and that of the superconducting gap. A simple model relating the suppression of the dynamical response of the antinodal quasiparticles to fluctuations related to a competing phase is proposed.

Figure 1

Raman spectra of Hg-1201 at various doping levels in $B_{1g}$ and $B_{2g}$ symmetries. Spectra are shown for temperatures below and slightly above $T_c$. The regions probed in $B_{1g}$ and $B_{2g}$ symmetries are displayed on a schematic Fermi surface for hole-doped cuprates in the upper side. Insets show the difference between the superconducting and normal states spectra, $\Delta {\chi }^{″}$ for Hg $78\mathrm{K}$ and Hg $63\mathrm{K}$ in the $B_{2g}$ symmetry.

Figure 2

Temperature dependance of the $B_{1g}$ (upper panel) and $B_{2g}$ (lower panel) spectra for Hg $63\mathrm{K}$ between room temperature and $20\mathrm{K}$. The inset shows the integrated spectral weight (SW) as a function of temperature in the $B_{2g}$ channel. It is defined as $\mathrm{SW}={\int }_{70}^{900}{\chi }^{″}\left(\omega \right)d\omega$.

Figure 3

Summary of the $B_{1g}$ superconducting peak ratio (SPR) observed by ERS in various cuprates as a function of doping $p$ (Refs. 8, 19, 21). The doping was simply deduced from the ratio $T_c∕T_{c,\max }$ assuming $p_{\mathrm{opt}}=0.16$ as in La-214 (Ref. 20).

Figure 4

Calculated spectra in the $B_{1g}$ and $B_{2g}$ symmetries in the normal and superconducting states (dotted and full lines, respectively). A $d$-wave gap has been assumed: ${\Delta }_{\mathbf{k}}={\Delta }_0(\cos k_{x}a-\cos k_{y}a)$. The normal state spectra were obtained by setting ${\Delta }_{\mathbf{k}}=0$. The corrected spectra are calculated using the renormalized vertex ${\widehat{\Gamma }}_k$ ($\beta =0.5$ and $\beta =1$, see text). The frequency dependence of the scattering rate was taken of marginal Fermi liquidlike form ${\Sigma }^{″}\left(\omega \right)={\Sigma }_0^{″}+\alpha \omega$ with $\alpha =1$. The scattering rate was introduced in the Green functions through the renormalized frequency $\tilde{\omega }=\omega -{\Sigma }^{″}\left(\omega \right)$.