Optical conductivity and superconductivity in highly overdoped La2−xCaxCuO4 thin films

Significance Chemical substitution is widely used to modify the charge-carrier concentration (“doping”) in complex quantum materials, but the influence of the associated structural disorder on the electronic phase behavior remains poorly understood. We synthesized thin films of the high-temperature superconductor La2−xCaxCuO4 with minimal structural disorder and characterized their doping levels through measurements of the optical conductivity. We find that superconductivity with Tc = 15 to 20 K is stable up to much higher doping levels than previously found for analogous compounds with stronger disorder. The results imply that doping-induced disorder is the leading cause of the degradation of superconductivity for large carrier concentration, and they open up a previously inaccessible regime of the phase diagram of high-temperature superconductors to experimental investigation.

the thin red line corresponds to the best fit using a film-on-substrate model. (b) Corresponding spectra σ 1 (ω) and ε 1 (ω) (thick black lines) represented by the total contribution (thin red lines) of separate bands determined by the dispersion analysis. The green lines show the free charge carrier contribution and the red arrow marks the unscreened plasma frequency, ω pl ≈ 2.1 eV. Figure 1 shows representative ellipsometric angles Ψ(ω) and ∆(ω) and corresponding ε(ω) and σ 1 (ω). The ellipsometric data were fitted by point-by-point regression analysis to a film-on-substrate model, as implemented in the Woollam WVASE32 R data acquisition and analysis software [1].

II. IN-SITU RHEED MONITORING
All growth runs of La 2−x Ca x CuO 4 thin films were monitored with in situ RHEED, which provides information regarding the presence of parasitic phases, surface roughness, and crystal quality. The diffraction patterns in Fig. 2   Arrows and texts specify the operations during sample growth.
shape of the patterns suggests smooth surfaces and high crystallinity of the films examined. In addition, the superstructure reflections in between main Bragg peaks in the [1 0 0] direction serve as complementary evidence for excellent crystallinity.
Monitoring intensity oscillation of the RHEED pattern, which contains information re-garding coverage of the topmost layer, is an indispensable tool for MBE. We present the RHEED oscillation of LCCO(x=0.48) in Fig. 3(a), which exhibits a clear periodic modulation suggesting a stable layer-by-layer growth. The amplitude of the RHEED oscillation stays constant over the course of more than 20 repetitions, indicating that the thin film maintains its quality throughout the process. In Fig. 3(b), a magnified view of the RHEED oscillation is shown. We adjusted the shutter time of effusion cells such that the maximum intensity coincides with the end of copper deposition.
In addition to in situ RHEED, ex situ atomic force microscopy (AFM) can evaluate the roughness of thin film surfaces. We observed clear atomic-scale steps and terraces imprinted on the film by the surface structure of the substrate (Fig. 4), which suggests a smooth surface of our film. The average roughness of the measured area is ∼ 1 nm, which is consistent with the smooth topography and with the sharp RHEED patterns. (b) AFM topography image of the sample from an area of 5 µm × 5 µm.

III. X-RAY DIFFRACTION
We carried out θ−2θ scans along (00L) direction in order to determine c-lattice parameters and to rule out possible parasitic phases in our films. The (00L) scans of 100 u.c. Above x = 0.5, XRD (006) peaks become broader, and Laue fringes disappear, which indicates that the sample suffers from decomposition due to the solubility limit (see Fig.   6(a)). Because of the proximity to the solubility limit, the sample synthesis was challenging.
To exclude the samples that are decomposed, we used the c-lattice parameters from XRD θ-2θ scans. Samples that deviated from the systematic trend were excluded from the analysis ( Fig. 6(b)). Peak positions in XRD θ-2θ scans suggest that the c-lattice parameter sharply increases again to 13.17Å after x = 0.5 and saturates implying the decomposition into LCCO with x ∼ 0.3 and Ca-rich parasitic phases due to the excessive amount of chemical substitution. In order to demonstrate the homogeneous distribution of dopants, we carried out elementsensitive analyses via both STEM-electron energy loss spectroscopy (STEM-EELS) and STEM-energy-dispersive x-ray spectroscopy(STEM-EDXS). For STEM analyses we chose a 10 u.c.-thick LCCO (x=0.4) film. Before detailed analyses of elemental distribution, a STEM-HAADF image across the interface between the film and the substrate was obtained as presented in Fig. 7(a). The image of the representative region exhibits a coherent interface and an excellent structure of the film. Further insight was obtained using the line profile of the image (Fig. 7(b)), where the highly regular oscillatory behavior supports uniform  STEM-EDXS is another method to obtain the information regarding atomic-scale stoichiometry. The STEM-EDXS line profile was collected from the region specified in Fig. 8(a). In order to investigate decomposed samples that deviate from the systematic trend, we acquired a STEM image on the heavily doped samples with nominal x = 0.7 (Fig. 9). The sample with x = 0.7 shows extended defects that are dark in the HAADF image. These dark features in the HAADF image come from light elements that have a lower scattering cross-section with the electron beam, which is in this case Ca. Therefore, we could conclude that LCCO reached the solubility limit at x ≈0.5. In addition to the collapsing XRD curves of decomposed samples, we found another clear sign of decomposition from optical spectroscopy. The systematic evolution of optical spectra in the main text evidenced the formation of a homogeneous solid solution, nevertheless optical spectra of samples with x ≥ 0.6 exhibit an erratic trend showing a sudden suppression in σ 1 in the wide range of energy instead of the spectral weight transfer shown by samples with lower x (see Fig. 10). This again suggests decomposition for samples exceeding the solubility limit. Such a suppression has previously been reported in optical studies of nonsuperconducting overdoped bulk LSCO samples [2].