Three energy scales in the superconducting state of hole-doped cuprates detected by electronic Raman scattering

We explore by electronic Raman scattering the superconducting state of the ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi-2212) crystal by performing a fine-tuned doping study. We find three distinct energy scales in $A_{1g}, B_{1g}$, and $B_{2g}$ symmetries which show three distinct doping dependencies. Above $p=0.22$, the three energies merge; below $p=0.12$, the $A_{1g}$ scale is no longer detectable, while the $B_{1g}$ and $B_{2g}$ scales become constant in energy. In between, the $A_{1g}$ and $B_{1g}$ scales increase monotonically with underdoping, while the $B_{2g}$ one exhibits a maximum at $p=0.16$. The three superconducting energy scales appear to be a universal feature of hole-doped cuprates. We propose that the nontrivial doping dependencies of the three scales originate from the Fermi-surface changes and reveal competing orders inside the superconducting dome.

Figure 1

Raman responses ${\chi }^{″}(\omega ,T)$ in $A_{1g}$+$B_{1g}, A_{1g}$+$B_{2g}, B_{1g}$, and $B_{2g}$ symmetries in the normal and superconducting state of Bi-2212 single crystals for selected doping levels: $p>0.22$ (OD60), $p=0.16$ (OP90), and $p=0.11$ (UD70). The insets show the Raman response at 10 K subtracted from the one at 110 K $\left[\mathrm{\Delta }{\chi }^{″}\left(\omega \right)\right]$. This allows us to determine the energies of the $B_{1g}$ and $B_{2g}$ electronic peaks.

Figure 2

$A_{1g}$ extracted electronic Raman responses in the superconducting state (10 K) and normal state (110 K) for selected doping levels of Bi-2212 single crystals. Here are shown the distinct extractions of the $A_{1g}$ Raman response: $A_{1g}^{\prime }$ and $A_{1g}^{″}$ associated, respectively, with Eqs. (1) and (2). The insets display the subtracted Raman responses at 10 K from those at 110 K. The Raman responses in (c), (f), and (i) show the sums ${\chi }_{S1}^{″}$ and $\beta {\chi }_{S2}^{″}$ related to Eqs. (1) and (2). $\beta$ was defined to make the sums merging.

Figure 3

(a) Doping evolutions of the $A_{1g}, B_{1g}$, and $B_{2g}$ energy scales in the superconducting state. The arrows pinpoint the three special doping levels: Above the $p=0.22$ (blue/gray) zone, all of the energy scales merge; at $p=0.16$, the $B_{2g}$ scale is maximum; and below $p=0.12$, the $B_{2g}$ and $B_{1g}$ scales are almost constant in energy while the $A_{1g}$ one is no longer detectable. Open circles describe the superconducting transition $T_c$ vs $p$ following the Presland-Tallon law [51]. (b) Asymmetric coefficient extracted from $A_{1g}^{\prime }$ and $A_{1g}^{″}$ superconducting peaks by a standard fit [see Eq. (4)].

Figure 4

$B_{1g}, B_{2g}$, and $A_{1g}$ Raman responses in the superconducting (red/gray) and normal (black) states of overdoped Bi-2212 single crystals, (a)–(c) for $p=0.23$ and (g)–(i) for $p=0.22$. (d)–(f) and (j)–(l) correspond, respectively, to the subtracted Raman responses at 10 K from the one at 110 K for $p=0.23$ and $p=0.22$. The dashed lines show that the locations in energy of the $B_{1g}, B_{2g}$, and $A_{1g}$ merge for each doping level above $p=0.22$.

Figure 5

$B_{1g}$ and $B_{2g}$ Raman responses $\left[{\chi }^{″}(\omega ,T)\right]$ in the superconducting (red/gray) and normal (black) states of selected underdoped Bi-2212 single crystals below $p=0.12$. The inset in each panel corresponds to the subtracted Raman response $\left[\mathrm{\Delta }{\chi }^{″}\left(\omega \right)\right]$ obtained from measurements at 10 and 110 K. We can notice that both the $B_{1g}$ and $B_{2g}$ electronic peaks are almost constant in energy below $p=0.12$. Note that the Raman spectra of the UD50 compound was obtained with a 600 g/mm diffraction grating instead of 1800 g/mm one in order to improve the signal/noise ratio and detect the $B_{1g}$ and $B_{2g}$ superconducting peaks, which become weaker in intensity with underdoping. As a consequence, the energy resolution of the UD50 compound is lower than the other doping.