Observation of Bogoliubov Band Hybridization in the Optimally Doped Trilayer ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$

Using a laser-excited angle-resolved photoemission spectroscopy capable of bulk sensitive and high-energy resolution measurements, we reveal a new phenomenon of superconductors in the optimally doped trilayer ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+\delta }$. We observe a hybridization of the Bogoliubov bands derived from the inner and outer ${\mathrm{CuO}}_2$ planes with different magnitudes of energy gaps. Our data clearly exhibit the splitting of coherent peaks and the consequent enhancement of spectral gaps. These features are reproduced by model calculations, which indicate that the gap enhancement extends over a wide range of Fermi surface up to the antinode. The significant modulation of electron pairing uncovered here might be a crucial factor to achieve the highest critical temperature in the trilayer cuprates.

Figure 1

Superconducting band hybridization and spectral splitting. (a)–(h) ARPES dispersions measured deep below $T_c$ ($T=10\mathrm{K}$) in directions indicated by arrows in (i). Band dispersions determined from peak energies of spectra (EDCs) are overlapped in each image. Dotted red curves trace the secondary peaks derived from split-off of spectral weight due to the superconducting hybridization. (i) Fermi surface mapping in the superconducting state. (j)–(l) Schematics illustrating superconductivity-induced hybridization: two bands, dispersing alongside in the normal state, cross with each other in the superconducting state, and hybridization occurs. (m) ARPES spectra at $k_F$ of the inner band, extracted from (d)–(g). Double Lorentzian curves added by a slope for the secondary photoelectrons are fit to the spectrum for $\varphi =18.4°$. (n) Spectral gaps for the inner- and outer-plane bands around the node ($\varphi =0°$). Energy positions of the main and secondary coherent peaks, marked in (m), are plotted with open and filled red circles, respectively.

Figure 2

The signature of mode coupling in the band with the gap enhanced by the superconducting hybridization. (a),(b) The ARPES images and the band dispersion determined from the peak positions of spectra measured at $T=10\mathrm{K}$ for the optimally doped Bi2223 and Bi2212, respectively. The arrows indicate the energy scale of bosons, which couple to the superconducting band dispersions. The comparable values ($\sim 40\mathrm{meV}$) are estimated for all bands in Bi2223 and also in Bi2212.

Figure 3

Temperature evolution of spectral splitting across $T_c$. (a),(b) Momentum distribution curves at $-0.45\mathrm{eV}$ along light blue dotted lines in (c) and (d), respectively. Two Lorentzian functions are fit to the data. (c),(d) Band dispersion maps measured along a green arrow in the inset of (f) at $T=10\mathrm{K}$ and $T=T_c$, respectively. Dashed circle in (c) marks spectral split-off due to band hybridization. (e) Temperature scan of symmetrized EDCs at $k_F$ of the inner-plane band [magenta dashed lines in (c) and (b)] from 10 up to 118 K with a 3 K step. (f) Temperature evolution of spectral gaps estimated from energy positions of two split peaks: the main and secondary peaks [filled and open red circles in (e), respectively].

Figure 4

Model calculations for the band structure of Bi2223, which reproduce the ARPES data exhibiting the effect of superconducting band hybridization. (a1)–(a12) Each image plots the dispersion of spectral intensities extracted along magenta lines marked in (b). The $\varphi$ noted on the panels indicates the Fermi angle for the inner-layer band. The red and blue curves trace band dispersions determined from the spectral peaks. (b) Fermi surface mapping for the calculations. (c) Energy gaps for the bands in (a) determined from the spectral peaks. The original gaps without interlayer hopping are indicated with dashed curves for both the inner- and outer-plane bands. The ARPES results for gaps are also plotted with open squares.