Monotonic $d$-wave superconducting gap of the optimally doped ${\text{Bi}}_2{\text{Sr}}_{1.6}{\text{La}}_{0.4}{\text{CuO}}_6$ superconductor by laser-based angle-resolved photoemission spectroscopy

The momentum and temperature dependence of the superconducting gap and pseudogap in optimally doped ${\text{Bi}}_2{\text{Sr}}_{1.6}{\text{La}}_{0.4}{\text{CuO}}_6$ superconductor is investigated by superhigh-resolution laser-based angle-resolved photoemission spectroscopy. The measured energy gap in the superconducting state exhibits a standard $d$-wave form. Pseudogap opens above $T_c$ over a large portion of the Fermi surface with a “Fermi arc” formed near the nodal region. In the region outside of the “Fermi arc,” the pseudogap has the similar magnitude and momentum dependence as the gap in the superconducting state, which changes little with temperature and shows no abrupt change across $T_c$. These observations indicate that the pseudogap and superconducting gap are closely related and favor the picture that the pseudogap is a precursor to the superconducting gap.

Figure 1

(Color) Fermi surface of the optimally doped La-Bi2201 $\left(T_c=32\text{K}\right)$ and corresponding photoemission spectra (EDCs) on the Fermi surface at various temperatures. (a) Spectral weight as a function of two-dimensional momentum $\left(k_x,k_y\right)$ integrated over [$-5\text{meV}$, 5 meV] energy window with respect to the Fermi level $E_F$. The measured Fermi momenta are marked by red empty circles and labeled by numbers. (b) Original EDCs along the Fermi surface measured at 15 K. The symmetrized EDCs along the Fermi surface are shown in (c) for 15 K, (d) for 25 K, and (e and f) for 40 K. The numbers on panels (b)–(f) correspond to the Fermi momentum numbers in (a).

Figure 2

(Color) Energy gap along the Fermi surface measured at 15 K (solid circles), 25 K (empty circles), and 40 K (empty squares) on the optimally doped La-Bi2201 $\left(T_c=32\text{K}\right)$. The solid red line is fitted from the measured data at 15 K which gives $\Delta =15.5\text{cos}\left(2\Phi \right)$. The $\Phi$ angle is defined as shown in the bottom-right inset. The upper-right inset shows the gap size as a function of $\left|\text{cos}\left(k_{x}a\right)-\text{cos}\left(k_{y}a\right)\right|/2$ at 15 and 25 K. The pink line represents a fitted line with $\Delta =15.5\left|\text{cos}\left(k_{x}a\right)-\text{cos}\left(k_{y}a\right)\right|/2$.

Figure 3

(Color) [(a) and (b)] Temperature dependence of representative EDCs at two Fermi momenta on the Fermi surface in optimally doped La-Bi2201. The location of the Fermi momenta is indicated in the inset. Detailed temperature dependence of the symmetrized EDCs for the Fermi momentum A are shown in (c) and for the Fermi momentum B in (d). The dashed lines in (c) and (d) serve as a guide for the eyes.

Figure 4

(Color) Temperature dependence of the energy gap for two Fermi momenta A (empty squares) and B (empty circles) as indicated in insets of Figs. 3a, 3b, and also indicated in the upper-right inset, for optimally doped La-Bi2201. The dashed line indicates $T_c=32\text{K}$.