Observation of the Fermi surface, the band structure, and their diffraction replicas of ${\text{Sr}}_{14-x}{\text{Ca}}_x{\text{Cu}}_{24}{\text{O}}_{41}$ by angle-resolved photoemission spectroscopy

We have investigated the electronic structure of ${\text{Sr}}_{14-x}{\text{Ca}}_x{\text{Cu}}_{24}{\text{O}}_{41}$ $\left(x=0;11.5\right)$ single crystals by angle-resolved photoemission spectroscopy. A satisfactory agreement with band-structure calculations is found. The Fermi surface is observed for ${\text{Sr}}_{2.5}{\text{Ca}}_{11.5}{\text{Cu}}_{24}{\text{O}}_{41}$ from which we derive a charge carrier concentration between 0.15 and 0.2 holes per Cu atom at $T=25\text{K}$ in the ladder substructure. The chain substructures, on the other hand, act as diffraction grating for the ladder photoelectrons giving rise to incommensurate replicas of the ladder bands.

Figure 1

(Color online) Photoemission spectra of ${\text{Sr}}_{14}{\text{Cu}}_{24}{\text{O}}_{41}$ taken at room temperature with $h\nu =100\text{eV}$. (a) $k$-integrated valence band. The dispersive features in panels (b)–(d) appear on top of the smooth tail of the valence band highlighted by the dashed rectangle. Inset: crystal structure of the ladder plane. (b) Momentum distribution map of photoemission intensity at $E_B=0.4\text{eV}$ integrated over $\Delta E=0.08\text{eV}$ taken with the light polarization parallel to the ladder direction. The blue line corresponds to the tight-binding (tb) fit of LDA band-structure calculations from Ref. 10 for the bonding band. The latter is also depicted in panel (d). Green arrows mark the $k_x$ positions of the measurements in (c) and (d). (c) EDM with perpendicular polarization. Smooth background intensity from the main valence band has been subtracted. The light blue line corresponds to the antibonding band of Ref. 10. (d) Energy distribution map taken with parallel polarization compared to tb band.

Figure 2

(Color online) Electronic structure of ${\text{Sr}}_{2.5}{\text{Ca}}_{11.5}{\text{Cu}}_{24}{\text{O}}_{41}$ measured with photon energy $h\nu =100\text{eV}$ at $T=25\text{K}$ with perpendicular polarization. (a) EDM parallel to $k_z$ with perpendicular polarization. Smooth background intensity from the main valence band has been subtracted. The blue line corresponds to the calculated antibonding band of Ref. 10 and is equivalent to the light blue line of Fig. 1c. The dashed lines are copies of the main band shifted along the $k$ axes. (b) Fermi surface map obtained by integrating spectral intensity in the range $E=0–35\text{meV}$. The blue lines indicate again the band-structure calculation with the same parameters as in (a). The white rectangles highlight regions with possible higher order diffraction replicas. The green arrow marks the $k_x$ position of (a). [(c) and (d)] Momentum distribution curves parallel to $k_z$. Solid lines indicate principle bands, dashed lines their first, and dotted lines their second replica. The arrows of the same color in each panel have equal lengths.

Figure 3

(Color online) (a) Intensity ratio of main band (MB) and replica for left and right halves (ratios 1 and 2) of the Brillouin zone as a function of temperature. Intensities are obtained from Lorentzian fitting of MDC cuts. (b) Low-energy angle-integrated spectral weight for ${\text{Sr}}_{14}{\text{Cu}}_{24}{\text{O}}_{41}$ and ${\text{Sr}}_{2.5}{\text{Ca}}_{11.5}{\text{Cu}}_{24}{\text{O}}_{41}$ (without background subtraction).