Polarization effects in photoemission disentangle the origin of the shadow bands in Bi-based superconductors

Angle-resolved photoemission spectroscopy has been used to investigate the origin of the shadow bands present at the Fermi surface of bismuth-based superconductors. Momentum distribution curves along the $\Gamma Y$ high-symmetry direction and Fermi surface maps measured on ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) single crystals with two different doping levels have revealed that the shadow bands and the main bands have different initial state symmetry. This result implies that the orthorhombicity exhibited by these materials cannot be responsible for their emergence at the Fermi surface.

Figure 1

Scheme representing the four quadrants of the Bi2212 tetragonal Brillouin zone sampled. ${\Gamma }_1$ corresponds to normal emission in our measurements and the line along ${\Gamma }_{1}Y{\Gamma }_2$ corresponds to the measured polar scans. The theory for a two holelike FS adjusted from the measurements on an overdoped Bi2212 single crystal (Ref. 1) has been included as main bands (gray lines), their umklapps (dotted gray lines), shadow bands (black lines), and their umklapps (dashed black lines).

Figure 2

(Color online) Experimental realization of the two geometry detection modes. (a) Even configuration: the direction of the outgoing electrons $\left({\vec{k}}_e\right)$ is in the plane $\left(\rho \right)$ formed by the normal to the surface $\vec{n}$, and the potential vector $\vec{A}$. When measuring in a mirror plane of the sample, only even initial states will be detected. (b) Odd geometry: the direction of the outgoing electrons $\left({\vec{k}}_e\right)$ is in the plane $\left(\epsilon \right)$, perpendicular to that formed by $\vec{n}$ and $\left(\vec{A}\right)$, therefore only odd initial states are accessible.

Figure 3

Polar scans along the ${\Gamma }_{1}Y{\Gamma }_2$ high-symmetry direction for photon energies $h\nu =26.8$, 32, and 38 eV in the even (a) and odd (b) detection geometries for the Bi2212 underdoped $T_c=60\mathrm{K}$ sample. Vertical lines correspond to the position of the main band (MB), umklapp bands (UB), shadow bands (SB), and their umklapps (USB), respectively.

Figure 4

(Color online) Fermi surface map of a Bi2212 sample measured at $h\nu =32\mathrm{eV}$ in the even detection geometry for the Brillouin zone region depicted in Fig. 1. The theoretically expected Fermi surface has been included for both SB (MB) yellow (purple) solid lines and their respective umklapps bands as dashed yellow (purple) lines.

Figure 5

(Color online) Photointensity map of a quadrant of the first Brillouin zone Fermi surface of the optimally doped Bi2212 sample measured at $h\nu =32\mathrm{eV}$ in the odd detection geometry. The theoretical Fermi surface has been included using the same line criteria as in Fig. 4.