Origin of the shadow Fermi surface in $\mathrm{Bi}$-based cuprates

We used angle-resolved photoemission spectroscopy to study the shadow Fermi surface in one layer ${\mathrm{Bi}}_2{\mathrm{Sr}}_{1.6}{\mathrm{La}}_{0.4}{\mathrm{CuO}}_{6+\delta }$ and two layer ${(\mathrm{Bi},\mathrm{Pb})}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$. We find the shadow band to have the same peak width and dispersion as the main band. In addition, the shadow band/main band intensity ratio is found to be binding-energy independent. Consequently, it is concluded that the shadow bands in $\mathrm{Bi}$-based HTSC do not originate from atiferromagnetic interactions, but have a structural origin.

Figure 1

(Color online): Energy distribution maps (EDM’s) along the $(0,0)\text{−}(\pi ,\pi )$ direction for (a) underdoped $(\mathrm{Bi},\mathrm{Pb})\text{−}2212$, taken with excitation energy $55\mathrm{eV}$ at $T=30\mathrm{K}$; (c) slightly underdoped lead-free $\mathrm{Bi}\text{−}2212$, excitation energy $50\mathrm{eV}$ at $T=30\mathrm{K}$, and (d) optimally doped $\mathrm{Bi}\text{−}2201$, excitation energy $50\mathrm{eV}$ at $T=65\mathrm{K}$. Main bands (MB), shadow bands (SB), and diffraction replicas (DR) are indicated. The markers denote the dispersion as yielded by a fit (see text). (b) Fermi-surface map of an overdoped $(\mathrm{Bi},\mathrm{Pb})\text{−}2212$ $(T_c=69\mathrm{K})$ crystal at room temperature taken with excitation energy $21.2\mathrm{eV}$ (Ref. 13). The white square represents the first Brillouin zone. The main Fermi surface is emphasized by a black line in the upper right part, the shadow Fermi surface with white. The dashed line marks the regions where the EDM’s have been taken. The arrows represent $(\pi ,\pi )$ and equivalent vectors.

Figure 2

(color online): Comparison of the dispersions of SB (light circles) and MB or DR (dark squares) shown in Fig. 1 and corresponding peak widths for: (a, b) underdoped $(\mathrm{Bi},\mathrm{Pb})\text{−}2212$, (c, d) slightly underdoped $\mathrm{Bi}\text{−}2212$, and (e, f) optimally doped $\mathrm{Bi}\text{−}2201$. The dispersion of the SB have been mirrored and the curves have been shifted for better comparison. The MDC peak widths in the $\left(\mathrm{Bi},\mathrm{Pb}\right)\text{−}2212$ data are a bit broader than the other data due to different resolution settings in this case. [Inset (c)] shows a comparison of the dispersions of MB (dark) and DR (light) for the pure $\mathrm{Bi}\text{−}2212$ sample. [Inset (a)] shows the ratio of the peak areas of SB and MB as a function of temperature and [Inset (b)] as a function of energy for underdoped $\left(\mathrm{Bi},\mathrm{Pb}\right)\text{−}2212$. [Inset (d)]: energy-dependent intensity ratio for slightly underdoped $\mathrm{Bi}\text{−}2212$. [Inset (e)]: energy dependent intensity ratio of the peak areas of DR and MB for the pure $\mathrm{Bi}\text{−}2212$ sample. [Inset (f)]: energy-dependent intensity ratio of the peak areas of SB and DR for the $\mathrm{Bi}\text{−}2201$ sample.