Enhanced Superconducting Gaps in the Trilayer High-Temperature ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathbf{O}}_{10+\delta }$ Cuprate Superconductor

We report the first observation of the multilayer band splitting in the optimally doped trilayer cuprate ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$ (Bi2223) by angle-resolved photoemission spectroscopy. The observed energy bands and Fermi surfaces are originated from the outer and inner ${\mathrm{CuO}}_2$ planes (OP and IP). The OP band is overdoped with a large $d$-wave gap around the node of ${\Delta }_0\sim 43\mathrm{meV}$ while the IP is underdoped with an even large gap of ${\Delta }_0\sim 60\mathrm{meV}$. These energy gaps are much larger than those for the same doping level of the double-layer cuprates, which leads to the large $T_c$ in Bi2223. We propose possible origins of the large superconducting gaps for the OP and IP: (1) minimal influence of out-of-plane disorder and a proximity effect and (2) interlayer tunneling of Cooper pairs between the OP and IP.

Figure 1

(a),(b) Intensity plots of ARPES spectra for Bi2223 at $E=\pm 20\mathrm{meV}$ in momentum space. Two Fermi surfaces are observed corresponding to the outer ${\mathrm{CuO}}_2$ plane (OP) and inner ${\mathrm{CuO}}_2$ plane (IP). Superstructures due to the Bi-O layer modulation are indicated by SS. (c),(d) Band dispersions in the nodal direction corresponding to red arrows in (a) and (b), respectively. (e) Relative intensities of the OP and IP bands as functions of photon energy. For $h\nu =7.65\mathrm{eV}$ [(a),(c)], the OP band spectra are enhanced while for $h\nu =11.95\mathrm{eV}$ [(b),(d)], the IP band is enhanced.

Figure 2

Energy-momentum intensity plots for cuts from the nodal to the off-nodal regions for the OP band [(a1)–(a3)] and for the IP band [(b1)–(b3)]. The corresponding cuts are shown in the right panels. The photon energies, $h\nu =9\mathrm{eV}$ and 11.95 eV, enhance the OP and IP bands, respectively. (c) Momentum dependences of the energy gaps. The definition of the SC gap ${\Delta }_0$ and the antinodal gap ${\Delta }^{*}$ is shown.

Figure 3

Comparison of ${\Delta }_0$ and ${\Delta }^{*}$ between the single-, double-, and triple-layer cuprates as functions of hole concentration. Their $T_c$ are plotted by solid curves. The ${\Delta }_0$ and ${\Delta }^{*}$ values for $n=1$ and 2 have been taken from ARPES results for LSCO [24] and Bi2212 [7, 22, 23, 39, 40]. The error bars in the hole concentrations reflect uncertainties in the $k_F$ positions.

Figure 4

Correlation between ${\Delta }_0$, $-t^{\prime }/t$ at optimal doping ($x\sim 0.16$), ${\Delta }^{*}$ in the underdoped region ($x\sim 0.06$), and $T_{c,\max }$ from the single- ($n=1$) to triple-layer ($n=3$) cuprates. ${\Delta }_0$ shows the strongest correlation with $T_{c,\max }$ ($T_{c,\max }\propto {\Delta }_0$) while $-t^{\prime }/t$ and ${\Delta }^{*}$ show only weak correlation with $T_{c,\max }$. Values of $-t^{\prime }/t$ for $n=1$ and 2 have been taken from ARPES results for LSCO [27], Bi2201 [28], and Bi2212 [29]. Inset shows correlation between ${\Delta }^{*}$ and $-t^{\prime }/t$ at $x\sim 0.07$. The $-t^{\prime }/t$ values for $n=1,2$ in the inset are taken from Ref. 27 for LSCO and Refs. 29, 33 for Bi2212.