Universal versus Material-Dependent Two-Gap Behaviors of the High-$T_c$ Cuprate Superconductors: Angle-Resolved Photoemission Study of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$

We have investigated the doping and temperature dependences of the pseudogap and superconducting gap in the single-layer cuprate ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ by angle-resolved photoemission spectroscopy. The results clearly exhibit two distinct energy and temperature scales, namely, the gap around ($\pi$, 0) of magnitude ${\Delta }^{*}$ and the gap around the node characterized by the $d$-wave order parameter ${\Delta }_0$. In comparison with Bi2212 having higher $T_c$’s, ${\Delta }_0$ is smaller, while ${\Delta }^{*}$ and $T^{*}$ are similar. This result suggests that ${\Delta }^{*}$ and $T^{*}$ are approximately material-independent properties of a single ${\mathrm{CuO}}_2$ plane, in contrast to the material-dependent ${\Delta }_0$, representing the pairing strength.

Figure 1

ARPES intensity plot of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO). (a1)–(a3), (b1)–(b3), and (c1)–(c3): Band image plots in energy-momentum ($E\mathrm{\text{−}}k$) space for $x=0.15$, 0.07 and 0.03, respectively. Energy dispersions determined by MDC’s peaks and leading edge midpoints (LEM) are shown by red dots and blue dots, respectively. (a4),(b4), and (c4): Spectral weight mapping at $E_F$ in momentum space for each doping level. Red dots indicate Fermi momenta $k_F$. White dotted lines indicate the antiferromagnetic Brillouin zone (AMF BZ). (d)–(f): EDC’s at $k_F$ for each doping level. Black lines correspond to antinodal EDC’s and vertical bars represent energy position of the antinode gap.

Figure 2

Momentum dependence of the energy gap at $T=20\mathrm{K}$ in LSCO with various doping levels. (a): Leading edge midpoints (LEM) ${\Delta }_{\mathrm{LEM}}$ relative to that at the node. Vertical arrows represents the boundary of the AFM BZ. Inset shows LEM near the node for $x=0.07$ below and above $T_c$ ($=14\mathrm{K}$). (b): Comparison of the peak position (${\Delta }_{\mathrm{peak}}$) and ${\Delta }_{\mathrm{LEM}}$ for $x=0.15$, indicating the relationship ${\Delta }_{\mathrm{peak}}\simeq 2.2{\Delta }_{\mathrm{LEM}}$. (c): Doping dependence of ${\Delta }^{*}$ and ${\Delta }_0$ obtained by assuming the relation in panel (b).

Figure 3

Momentum dependence of the energy gap for $x=0.15$ at various temperatures. (a1)–(a4): EDC’s at $k_F$ in the nodal to the antinodal directions. (b): Momentum dependence of ${\Delta }_{\mathrm{LEM}}$ along the Fermi surface for $x=0.15$ at various temperatures. Inset shows the temperature dependence of ${\Delta }^{*}$ and ${\Delta }_0$ with the assumption $\Delta =2.2{\Delta }_{\mathrm{LEM}}$, as in Fig. 2. The $d$-wave BCS gap ${\Delta }_{\mathrm{BCS}}$ ($=4.3k_B{T}_c/2$) is also plotted for comparison.

Figure 4

Doping dependence of the characteristic energies (${\Delta }^{*}$, ${\Delta }_0$) and temperatures ($T^{*}$, $T_c$) for single-layer cuprates (LSCO, Bi2201) (a) and double-layer cuprates Bi2212 (b). Gap energies $\Delta$ and temperatures $T$ have been scaled as $2\Delta =4.3k_{B}T$ in both panels. Parameter values have been taken from NMR results for Bi2201 [33], and ARPES for Bi2212 [4, 10, 11, 34, 35].