Coherent $d$-Wave Superconducting Gap in Underdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ by Angle-Resolved Photoemission Spectroscopy

We present angle-resolved photoemission spectroscopy data on moderately underdoped ${\mathrm{La}}_{1.855}{\mathrm{Sr}}_{0.145}{\mathrm{CuO}}_4$ at temperatures below and above the superconducting transition temperature. Unlike previous studies of this material, we observe sharp spectral peaks along the entire underlying Fermi surface in the superconducting state. These peaks trace out an energy gap that follows a simple $d$-wave form, with a maximum superconducting gap of 14 meV. Our results are consistent with a single gap picture for the cuprates. Furthermore our data on the even more underdoped sample ${\mathrm{La}}_{1.895}{\mathrm{Sr}}_{0.105}{\mathrm{CuO}}_4$ also show sharp spectral peaks, even at the antinode, with a maximum superconducting gap of 26 meV.

Figure 1

ARPES intensities along momentum cuts that cross the underlying Fermi surface (FS) (a) at the node, (b)–(f) between the node and the antinode, and (g) at the antinode. The corresponding cuts 1–7 are indicated in (h). The circles in (h) are the underlying FS determined from our measurements, while the solid line is the FS from a tight-binding fit to our data. The measurements were performed on LSCO ($T_c=36\mathrm{K}$, $x=0.145$) at 12 K with $h_{\nu }=55\mathrm{eV}$.

Figure 2

(a)–(c) EDCs along the momentum cuts 1, 3, and 7 in Fig. 1h. The corresponding momentum ranges are indicated in Figs. 1a, 1c, 1g with arrows. Thick curves are EDCs at $k_F$. (d) Comparison of the EDCs at the antinode (left curve) and at the node (right curve). (e) Comparison of the EDC at the antinode with $h\nu =55\mathrm{eV}$ and an energy resolution of 17 meV (solid symbols), and the angle-integrated EDC over the momentum range marked by the arrow in Fig. 1g acquired with $h\nu =25\mathrm{eV}$ an energy resolution of 12 meV (solid line).

Figure 3

(a) and (c) Symmetrized EDCs for $x=0.145$ at various $k_F$ from the antinode (top) to the node (bottom) (each curve is offset for clarity) at 12 and 41 K, respectively. The corresponding $k_F$ from cuts 1–7 are indicated in Fig. 1h by solid circles. The $k_F$ for cuts 1, 3, and 5 are on the upper underlying FS curve, and the rest are on the lower underlying FS curve. The solid lines are fits using Eqs. (1, 2). (b) The EDCs at 12 K (solid lines) and at 41 K (dotted lines) from which the symmetrized EDCs in (a) and (c) are obtained. (d) Symmetrized EDCs for $x=0.105$ at the $k_F$ shown below the panel. (e) The superconducting gaps for $x=0.105$ (solid squares), the superconducting gaps (solid circles) and the pseudogaps for $x=0.145$ (diamonds connected with a dashed line) from the fit as a function of the underlying FS angle $\varphi$ indicated in Fig. 1h, with the dotted lines the simple $d$-wave gap ${\Delta }_{\max }|\cos (2\varphi )|$ with ${\Delta }_{\max }=13.8$ and 25.5 meV, respectively. The open circles are the gaps determined by Terashima et al. for a LSCO sample with $x=0.15$ [10]. The data were acquired with $h_{\nu }=55\mathrm{eV}$.