Momentum and temperature dependence of renormalization effects in the high-temperature superconductor $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$

We present a detailed angle-resolved photoemission (ARPES) study of the low-energy electronic structure of $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ and show that the ARPES spectrum generally contains contribution from two components, of which the prevailing one is hugely overdoped, while the other retains superconductivity and represents the bulk properties. The doping level of the overdoped surface component turns out to be weakly dependent on the oxygen stoichiometry, always remaining close to $x\sim 0.3$. By suppressing the overdoped component, we clearly show that the other one develops a superconducting gap consistent with a $d$-wave symmetry. As in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$, the superconducting component is marked by the unusual renormalization which is strongly enhanced at antinodes and vanishes above $T_C$, supporting the universality of the conclusion regarding the magnetic origin of the unusual renormalization in high-$T_C$ superconductors.

Figure 1

(Color online). Experimental band structure of untwinned $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.85}$, $T_C=90\mathrm{K}$. The left panel contains two experimental FS maps measured along the $\Gamma \text{−}$X and $\Gamma \text{−}$Y directions and the tight-binding fit to them. (a)–(d) Energy-momentum intensity maps at various $k_x$ values indicated in the FS map, $h\nu =50\mathrm{eV}$. The projection of $k_y$ for these spectra was held constant; its value is denoted by arrows with corresponding lettering on the FS map. (e)–(h) Similar measurements, taken after rotating the sample by 90° around the $\Gamma$ point, $h\nu =55\mathrm{eV}$. The image (e) is the sum of spectra measured with circularly polarized light of left and right helicities. The other spectra were measured with linearly polarized light.

Figure 2

Coexistence of superconducting and metallic components. (a) Experimental spectrum comprising the contribution from normal and superconducting states for $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.85}$, $k_y=0.63\pi ∕b$, $T=30\mathrm{K}$, $h\nu =55\mathrm{eV}$. (b) Model image, to explain the spectrum as a superposition of the signals from superconducting and overdoped (metallic) bilayers. The bottommost image is the spectrum of the superconducting phase, middle, the metallic, and the topmost image their sum. (c) Schematic structure of the cleaved crystal. The doping of the $\mathrm{Cu}{\mathrm{O}}_2$ bilayer nearest to the surface is modified due to disturbed chains (CuO and BaO layers), while the next bilayer remains unimpaired and retains superconductivity.

Figure 3

Temperature dependence of the superconducting feature for $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.9}$. The right hand image shows evolution of the EDCs integrated in a small momentum window. The EDCs corresponding to 28 and $50\mathrm{K}$ have been omitted as they practically overlap with the $18\mathrm{K}$ one. The integration range is delimited by a dashed rectangle plotted on top of the $50\mathrm{K}$ spectrum. The black curves on top of the $18\mathrm{K}$ spectrum trace the dispersions of the overdoped antibonding band (the upper one) and the superconducting feature (the lower one).

Figure 4

(Color online) Experimental band structure of untwinned $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.4}$, $T_C=35\mathrm{K}$. The data layout is the same as in Fig. 1; all spectra were recorded at $30\mathrm{K}$. The FS map and the separate cuts (b)–(h) were measured with linear polarization and $h\nu =50\mathrm{eV}$. For the image (a) linearly polarized light with $h\nu =55\mathrm{eV}$ was used.

Figure 5

Superconducting component. (a)–(d) Opening of a superconducting gap and enhancement of the band renormalization effects when approaching the antinodal point. Symbols in the image (d) denote the peak and the dip positions extracted from the EDC’s comprising this data set. (e) Extracted value of the superconducting gap. (f)–(i) Evolution of the spectral weight and the leading edge gap (j) as a function of temperature. The spectra were measured from a freshly cleaved $\left({\mathrm{Y}}_{1-x}{\mathrm{Ca}}_x\right)\mathrm{Ba}{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$, ($x=0.15\pm 0.03$, $T_C=77\mathrm{K}$) using linearly polarized light, $h\nu =50\mathrm{eV}$.