Evidence for Two Separate Energy Gaps in Underdoped High-Temperature Cuprate Superconductors from Broadband Infrared Ellipsometry

We present broadband infrared ellipsometry measurements of the $c$-axis conductivity of underdoped $R{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ ($R=\mathrm{Y}$, Nd, and La) single crystals. Our data show that separate energy scales are underlying the redistributions of spectral weight due to the normal state pseudogap and the superconducting gap. Furthermore, they provide evidence that these gaps do not share the same electronic states and do not merge on the overdoped side. Accordingly, our data are suggestive of a two gap scenario with a pseudogap that is likely extrinsic with respect to superconductivity.

Figure 1

$C$-axis conductivity of underdoped ${\mathrm{NdBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.9}$. Shown are representative spectra for (a) the PG state, (b) the SC state, and (c) the $T$ difference, $\Delta {\sigma }_{1c}={\sigma }_{1c}(T)-{\sigma }_{1c}(300\mathrm{K})$. Brown (blue) arrows mark the crossing points at ${\omega }_{\mathrm{PG}}$ (${\omega }_{\mathrm{SC}}$). The $T$ dependence of the spectral weight, $(\mathrm{SW}{)}_{\alpha }^{\beta }={\int }_{\alpha }^{\beta }{\sigma }_{1c}(\omega )d\omega$, is shown for (d) $\alpha =0$ and $\beta =800{\mathrm{cm}}^{-1}$ (regular part), (e) $\alpha =0$ and $\beta =4000{\mathrm{cm}}^{-1}$ [black squares show the regular part, while blue circles include the SC delta function $(\mathrm{SW}{)}^{\delta }$], and (f) $\alpha =1600$ and $\beta =4000{\mathrm{cm}}^{-1}$. Vertical bars show the statistical errors. The red line in (e) shows a fit to the normal state data with the function $\mathrm{SW}(T)=(\mathrm{SW}{)}_0[1-(\frac{T}{\Theta }{)}^{\beta }]$.

Figure 2

(a)–(c) $C$-axis conductivity of $R\mathrm{\text{−}}123$ ($R=\mathrm{Y}$, Nd, and La) with $p\approx 0.12$. Dotted (solid) arrows mark the transverse Josephson plasma mode (the mode near $1000{\mathrm{cm}}^{-1}$). (d) Difference spectra, $\Delta {\sigma }_{1c}={\sigma }_{1c}(10\mathrm{K})-{\sigma }_{1c}(90\mathrm{K})$.

Figure 3

(a) Phase diagram of Y-123 giving the doping dependence of $T_c$ (black stars), ${\omega }_{\mathrm{PG}}/2$ (brown circles), and ${\omega }_{\mathrm{SC}}/2$ (blue triangles). Open symbols show the corresponding gap values, ${\Delta }_{\mathrm{PG}}$ and ${\Delta }_{\mathrm{SC}}$, from Ref. 5. The dashed brown (blue) line shows a linear extrapolation of ${\omega }_{\mathrm{PG}}/2$ (${\omega }_{\mathrm{SC}}/2$). (b),(c) Difference spectra, $\Delta {\sigma }_{1c}^{\mathrm{PG}}={\sigma }_{1c}(T\approx T_c)-{\sigma }_{1c}(T\approx T^{*})$ and $\Delta {\sigma }_{1c}^{\mathrm{SC}}={\sigma }_{1c}(10\mathrm{K})-{\sigma }_{1c}(T\approx T_c)$, from which ${\omega }_{\mathrm{PG}}$ and ${\omega }_{\mathrm{SC}}$ were deduced. For clarity we removed sharp features due to $T$-dependent shifts of some phonon modes.

Figure 4

(a) $C$-axis conductivity spectra of ${\mathrm{LaBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ showing the two separate crossing points at ${\omega }_{\mathrm{PG}}$ and ${\omega }_{\mathrm{SC}}$ as marked by brown and blue arrows. (b),(c) Conductivity spectra showing the corresponding crossing points at ${\omega }_{\mathrm{PG}}$ and ${\omega }_{\mathrm{SC}}$ for Y-123 with $T_c=88$ and 75 K.