Superconducting electronic state in optimally doped ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{7-\delta }$ observed with laser-excited angle-resolved photoemission spectroscopy

Low-energy electronic structure of optimally doped ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{7-\delta }$ is investigated using laser-excited angle-resolved photoemission spectroscopy. The surface state and the CuO chain band that usually overlap the ${\text{CuO}}_2$ plane derived bands are not detected, thus enabling a clear observation of the bulk superconducting state. The observed bilayer splitting of the Fermi surface is $\sim 0.08{\text{Å}}^{-1}$ along $\left(0,0\right)-\left(\pi ,\pi \right)$ direction, significantly larger than ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+\delta }$. The kink structure of the band dispersion reflecting the renormalization effect at $\sim 60\text{meV}$ shows up similarly as in other hole-doped cuprates. The momentum dependence of the superconducting gap shows $d_{x^2-y^2}$-wave-like amplitude but exhibits a nonzero minimum of $\sim 12\text{meV}$ along the $\left(0,0\right)-\left(\pi ,\pi \right)$ direction. Possible origins of such an unexpected “nodeless” gap behavior are discussed.

Figure 1

(Color) [(a)–(f)] ARPES intensity images of optimally doped YBCO obtained at 5 K. (g) Schematic Fermi surfaces of YBCO in the first Brillouin zone. Red, blue, and green shaded areas indicate the $k_z$-projected Fermi surfaces of the bonding and antibonding ${\text{CuO}}_2$ bands and the CuO chain band, respectively, obtained from a band calculation (Ref. 29). The momentum cuts of the measurements for (a)–(f) are shown by black curves.

Figure 2

(Color online) (a) Band dispersions obtained from MDC fittings at nodal and off-nodal regions. Labels (e), (b), and (c) correspond to the momentum cuts shown in Fig. 1g. (b) Peak width of MDCs as a fuction of the binding energy.

Figure 3

(Color online) (a) ARPES intensity image and (b) EDCs at the off-nodal location as shown in the inset of (a). Closed circles denote the peak positions of EDCs, while the dip positions are represented by open circles. Curves are guides for eyes to show the bonding and antibonding band components. The $k_F$ position of the outer bonding band is shown by an arrow.

Figure 4

(Color online) (a) ARPES intensity image and (b) MDCs along the cut near the $\Gamma \text{-S}$ direction as shown in the inset. Circles and squares denote peak positions of the two Lorentzians obtained by fitting MDCs as shown in (b), respectively, indicating antibonding and bonding band.

Figure 5

(Color online) $k_F$ positions plotted on the Brillouin zone. Circles shows $k_F$ determined as the position where EDC peak most nearly approaches $E_F$ (see Fig. 3). Crosses represent the MDC peak positions near $E_F$ (see Fig. 4).

Figure 6

(Color online) [(a) and (c)] EDCs along the momentum cutoff and on the nodal point. The inset in (c) shows each momentum cut of the measurements. [(b) and (d)] EDCs from (a) and (c) symmetrized at $E_F$.

Figure 7

(Color online) [(a) and (b)] Comparison of EDC at $k_F$ to that at $k_x=0$ along off- and on-nodal momentum cuts, extracted from the data in Figs. 6a, 6c, respectively.

Figure 8

(Color online) (a) EDCs at $k_F$ and (b) those symmetrized at $E_F$ obtained at momentum positions (1)–(7) and (i)–(iii) as indicated in (d). (1)–(7) and (i)–(iii) are the results from two different samples (samples $A$ and $B$) along momentum cuts parallel to the $\Gamma \text{−}X$ and $\Gamma \text{−}Y$ directions, respectively. (c) Symmetrized EDCs at $k_F$ obtained from one sample (sample $C$) along momentum cuts parallel to the $\Gamma \text{-S}$ direction. Each $k_F$ position is represented by the Fermi-surface angle $\varphi$ as indicated in (d). (e) Symmetrized EDCs at the temperature of 5 and 100 K. A and B correspond to spectra at off-nodal and nodal points as shown in the inset.

Figure 9

(Color online) The gap size $\left|\Delta \right|$ plotted as a function of the Fermi-surface angle $\varphi$ obtained from four different samples $A\text{–}D$. Here, the samples $A\text{–}C$ are identical to those shown in Figs. 8a, 8b, 8c. The curve is the gap function of $d_{x^2-y^2}+is$ wave, where ${\Delta }_d=40\text{meV}$ and ${\Delta }_s=10\text{meV}$. The error bars arise from the experimental uncertainty of the EDC peak positions and the estimation of the momentum value.

Figure 10

(Color online) [(a)–(c)] Symmetrized EDCs at $k_F$ along antibonding and the bonding band Fermi sheets. Estimated gaps for respective bands are shown in (d) as a function of $\varphi$.