Selective hybridization between the main band and the superstructure band in the ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ superconductor

High-resolution laser-based angle-resolved photoemission measurements have been carried out on ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) and ${\mathrm{Bi}}_2{\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{CuO}}_{6+\delta }$ (Bi2201) superconductors. Unexpected hybridization between the main band and the superstructure band in Bi2212 is clearly revealed. In the momentum space where one main Fermi surface intersects with one superstructure Fermi surface, four bands are observed instead of two. The hybridization exists in both the superconducting state and the normal state, and in Bi2212 samples with different doping levels. Such a hybridization is not observed in Bi2201. This phenomenon can be understood by considering the bilayer splitting in Bi2212, the selective hybridization of two bands with peculiar combinations, and the altered matrix element effects of the hybridized bands. These observations indicate that the origin of the superstructure bands is intrinsic to the ${\mathrm{CuO}}_2$ planes. Therefore, understanding physical properties and superconductivity in Bi2212 should consider the complete Fermi surface topology which involves the main bands, the superstructure bands, and their interactions.

Figure 1

Fermi surface and band structure of Bi2212 (OP91K) measured at a temperature of 20 K by laser-based ARPES. (a) Fermi surface mapping in the first quadrant of the Brillouin zone. It is obtained by integrating the spectral weight over an energy window of $[-2,+2]$ meV with respect to the Fermi level. (b) The second derivative of the original image (a) with respect to momentum. The second derivative image helps enhance the contrast to reveal some detailed structures. (c) The second derivative image of the constant energy contour obtained by integrating the spectral weight over an energy window of $[-3,+3]$ meV with respect to a binding energy of 15 meV. (d–f) The same as panels (a)–(c) but measured in the second quadrant of the Brillouin zone. (g) Band structure along the different momentum cuts A1–A9 in the first quadrant. The location of the momentum cuts is shown by white lines in panel (b). The images are second derivative of the original band structure with respect to momentum. (h) Band structure along the different momentum cuts B1–B9 in the second quadrant. The location of the momentum cuts is shown by white lines in panel (e). The images are second derivative of the original band structure with respect to momentum. The red and yellow arrows mark the locations of the observed bands. (i) Schematic Fermi surface of Bi2212 containing the main antibonding Fermi surface (MainAB, red lines) and its first-order superstructure replicas (SSAB, yellow lines). The dashed purple box represents the mapping area of panel (a), and the dashed gray box represents the mapping area of panel (d). (j) The enlarged momentum area where the main band and the superstructure band intersect at the MS1 point. (k) Same as panel (j) by assuming hybridization of two bands.

Figure 2

Doping and temperature dependencies of Fermi surface and band hybridization in Bi2212. (a) Fermi surface and constant energy contour of underdoped Bi2212 with $T_C=64$ K (UD64K) measured in the superconducting state at 15 K (a1–a3) and the normal state at 75 K (a4–a6). Panels (a2), (a3), (a5), and (a6) are obtained by the second derivative of the original data with respect to momentum. Panels (a1), (a2), (a4), and (a5) represent the measured Fermi surface, while panels (a3) and (a6) are constant energy contours at a binding energy of 15 meV. (b) Same as panel (a) but the Fermi surface and constant energy contour are measured on an optimally doped Bi2212 with $T_C=91$ K (OP91K) in the superconducting state (20 K) and the normal state (96 K). (c) Same as panel (a) but the Fermi surface and constant energy contour are measured on an overdoped Bi2212 with $T_C=78$ K (OD78K) in the superconducting state (15 K) and the normal state (80 K).

Figure 3

Fermi surface and band structure of Bi2201 (OP32K) measured at a temperature of 20 K by laser-based ARPES. (a) Fermi surface mapping in the first quadrant of the Brillouin zone. It is obtained by integrating the spectral weight over an energy window of $[-2,+2]$ meV with respect to the Fermi level. The corresponding momentum area is marked as the dashed red box in the inset. (b) The second derivative of the original data corresponding to panel (a) with respect to momentum. (c) Constant energy contour at a binding energy of 15 meV. The image is obtained by the second derivative of the original data with respect to momentum. (d) Fermi surface mapping in the second quadrant of the Brillouin zone at 15 K. The corresponding momentum area is marked as the dashed red box in the inset. (e) The second derivative of the original data corresponding to panel (d) with respect to momentum. (f) Constant energy contour at a binding energy of 15 meV. The image is obtained by the second derivative of the original data with respect to momentum. Panels (g) and (h) show the band structure measured at 15 K. The location of the corresponding momentum cuts is shown as white lines in panels (b) and (e) labeled with A1–A9 and B1–B9. The images are obtained by the second derivative of the original data with respect to momentum. The red and yellow arrows in panel (h) mark the locations of the observed bands.

Figure 4

Schematic illustration of band hybridization and its comparison with the measured results in Bi2212. (a) Schematic Fermi surface of Bi2212 containing the main Fermi surface with bilayer splitting: Antibonding sheet (MainAB, red lines) and bonding sheet (MainBB, dashed blue lines); and first-order superstructure replicas: Antibonding sheet (SSAB, yellow lines) and bonding sheet (SSBB, dashed green lines). The dashed gray box marks the momentum area enlarged in panels (b)–(e). (b) The enlarged momentum area marked in panel (a). The main bonding and antibonding Fermi surface sheets intersect with the superstructure bonding and antibonding replicas that give rise to four crossing points labeled as A, B, C, and D. (c) Same as panel (b) but considering band hybridization at all four crossing points. (d) The measured constant energy contour at a binding energy of 15 meV at the crossing point MS1 as shown in Fig. 1. The observed four branches of sheets are marked. (e) Same as panel (b) but considering the band hybridization only at A and C crossing points.