Circular dichroism and bilayer splitting in the normal state of underdoped ${(\mathrm{Pb},\mathrm{Bi})}_2{\mathrm{Sr}}_2\left({\mathrm{Ca}}_x{\mathrm{Y}}_{1-x}\right){\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ and overdoped ${(\mathrm{Pb},\mathrm{Bi})}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$

We report an ARPES investigation of the circular dichroism in the first Brillouin zone (BZ) of under- and overdoped $\mathrm{Pb}\text{−}\mathrm{Bi}2212$ samples. We show that the dichroism has opposite signs for bonding and antibonding components of the bilayer-split $\mathrm{CuO}\text{−}\mathrm{band}$ and is antisymmetric with respect to reflections in both mirror planes parallel to the $c$-axis. Using this property of the energy and momentum intensity distributions we prove the existence of the bilayer splitting in the normal state of the underdoped compound and compare its value with the splitting in overdoped sample. In agreement with previous studies the magnitude of the interlayer coupling does not depend significantly on doping. We also discuss possible origins of the observed dichroism.

Figure 1

(Color online) Normal state Fermi surface maps of the UD80K and OD72K samples. White lines indicate the cuts in k-space measured with circular light. Two mirror planes are shown as dashed white lines. Black dashed lines schematically show bilayer split components not clearly resolved at room temperature.

Figure 2

Overdoped sample. EDMs taken with left- and right-hand circularly polarized light and their difference along the nodal (cut 5) direction (a–c) and along direction labeled 6 (d–f). White lines in panels (c) and (f) are the energy and momentum distributions of the dichroic signal obtained from the difference EDM by deciphering the grey scale along the cuts marked by white arrows. Results of the two-Lorentzian fitting procedure applied to the spectra shown in panels (d) and (e): ratio of the heights representing the relative bonding∕antibonding contribution to the total spectral weight (g) and dispersion of the corresponding peak positions (h). Average values of the ratios are shown as black dashed lines (g).

Figure 3

(Color online) Underdoped sample. (a, b) Difference EDM’s along the directions 1 and 2. Black arrow, MDC’s energy. (c) MDC’s taken with differently polarized light, they difference and the fitting functions. (d, e) Fitting results for the direction 1 equivalent to shown in Figs. 2g, 2h.

Figure 4

Difference EDMs illustrating antisymmetric behavior of the dichroism with respect to reflection in the mirror plane for the overdoped (a, b) and underdoped (c, d) samples. Numbers of the cuts correspond to Fig. 1. Gray scale ranges from $-{10}^5$ to ${10}^5$ counts. (e) Fermi surface calculated within the LDA approximation including relativistic effects (spin-orbit interaction). (f) Schematic picture of the momentum distribution of the dichroism on the main Fermi surface in the first Brillouin zone.