II. RESULTS AND DISCUSSION

Oxide MBE has yielded films with the highest structural quality and most precise layering control at the atomic-layer and we therefore adopted this approach for the synthesis of Pr_2−x Ce _x CuO_4+δ thin films. In particular it is the electron-doped cuprates system that caught our attention more than two decades ago ^{Reference Naito and Sato14} while knowing that the true challenge of this superconductor goes well beyond a perfect cation arrangement. In light of recent advancements on the comprehension of the growth of complex oxide materials ^{Reference Lee, Luo, Tung, Chang, Luo, Malshe, Gadre, Bhattacharya, Nakhmanson, Eastman, Hong, Jellinek, Morgan, Fong and Freeland80} the synthesis of high-quality Pr_2−x Ce _x CuO_4+δ thin films still remains a major challenge. In Fig. 1 we show a scheme of our oxide MBE setup used for the growth of Pr_2−x Ce _x CuO_4+δ thin films. EIES was used to monitor and control Pr and Cu fluxes and due to weak relative electron impact emission intensities of Ce dopants ^{Reference Marin, Cornejo and Arriagada81} we used a shielded quartz-crystal rate-control system for high precision rate control exclusively for Ce. The absolute deposition rate of each constituent element is shown in Fig. 2. Without limitations of generality we used ozone generated from a silent discharge ozone generator as an oxidizing agent (see Fig. 1). A constant substrate temperature of 700 °C was maintained using a custom designed resistive heater stage which is monitored by a pyrometer. The atomic structure of the Pr_2−x Ce _x CuO_4+δ thin films and Pr_2−x Ce _x CuO_4+δ–SrTiO₃ interface was investigated by means of high resolution (scanning) transmission electron microscopy (HRSTEM). A JEOL JEM-ARM 200F (JEOL Ltd., Tokyo, Japan) STEM with a spherical aberration correction, operated at 200 kV. ^{Reference von Harrach, Dona, Freitag, Soltau, Niculae and Rohde82} For atomic-scale chemical mapping, energy dispersive x-ray spectroscopy (EDS) spectral image data was acquired with an electron probe of size ∼1.0 Å, convergence angle of 18–22 mrad, and current of ∼23–68 pA. High-angle annular dark-field (HAADF) images were recorded under similar optical conditions using an annular detector with a collection range of 90–370 mrad. Spectral images were acquired as a series of frames, where the same region was scanned multiple times. Frames were spatially drift-corrected to build up spectral image data. The instantaneous dwell time on each pixel was 38.5 µs, and a typical frame was 512 × 512 pixels. Spectral image collection typically took about 10 s, yielding a total per-pixel dwell time of about 38 ms. The epitaxial character of the deposited films are evident from Fig. 3, which shows a HAADF image of the interface region of a representative Pr_2−x Ce _x CuO_4+δ sample in (110) viewing direction. Using HAADF conditions the atomic columns cause bright contrast, whereas the intensity of the maxima increases with atomic number from CuO columns via PrO, producing an additional chemical contrast. Apparently, Ce is homogeneously distributed at Pr positions as a possible superstructure remains elusive [see Fig. 3(c)]. Figure 4 shows atomic resolution HRSTEM EDS mappings of the Pr_2−x Ce _x CuO_4+δ thin films synthesized by reactive MBE. EDS mapping was performed using a JEOL JEM-ARM 200F HRSTEM (JEOL Ltd.) equipped with a Wien filter. ^{Reference Rose83} Pr and Cu maps clearly reveal the formation of the characteristic chemically ordered T′ structure. For thin TEM specimens, the EDS signal is localized to atomic columns. ^{Reference Lu, Xiong, Benthem and Jia84,Reference Allen, Findlay, Lupini, Oxley and Pennycook85} Furthermore, under such conditions, EDS x-ray counts from individual atomic columns can be approximated by a Gaussian distribution and thus be properly integrated by fitting Gaussian peaks at each atomic column position ^{Reference Lu, Romero, Lee, MacManus-Driscoll and Jia86} ; the chemical composition at the atomic column positions can then be calculated column-by-column using the Cliff–Lorimer method. ^{Reference Cliff and Lorimer87} The width of the Gaussian peak, defined as the full-width at half-maximum (FWHM), which ultimately determines the spatial resolution of the chemical mapping, is effectively determined by convoluting the electron probe with the effective EDS local ionization potential under thin specimen conditions. By selecting a small electron probe (∼1.0 Å) and an appropriately thin area on the specimen, the spatial resolution of chemical mapping can be improved. The specimen thickness for the approximation to be valid must be limited to be less than 30 nm. The selection of small electron probe and thin specimen leads, however, to significant reduction in x-ray count. This reduction can be compensated by lattice-averaging EDS maps that are related by lattice translation vectors, effectively improving the EDS counting statistics. It is intriguing to see to what extent, if any, the superconducting state is influenced by the appearance of crystallographic defects. It is worth to state that although the mean free path lengths $\ell$ vary a lot, there is little to no influence on the superconducting transition temperature seen. This becomes only prominent for very short $\ell$ , or when residual resistivity ratio RRR = ρ(300 K)/ρ(1.8 K) < 2. In that case, however, one would approach the Ioffe–Regel limit which coincides with the onset of long-range antiferromagnetic order as concentration of occupied apical sites increases. ^{Reference Kojima, Krockenberger, Yamauchi, Miyazaki, Hiraishi, Koda, Kadono, Kumai, Yamamoto, Ikeda and Naito88} In Fig. 5, we show the temperature dependence of the magnetization taken zero-field-cooled (ZFC) and field-cooled-cooling (FCC) modes. The diamagnetic signal at 1.8 K for the films with RRR ≥ 8 is −8.4 memu in ZFC mode, whereas it is significantly weaker for Pr_2−x Ce _x CuO_4+δ thin films with RRR ≈ 4. The continuous variation of the diamagnetic signal originating from the superconducting states of Pr_2−x Ce _x CuO_4+δ may allow for two interpretations. One is that the amount of the superconducting condensate depends on the amount of available carriers that could form the superconducting instability at the Fermi surface. As Pr_2−x Ce _x CuO_4+δ with small RRR values are less conducting than films with large RRR values, a reduced superconducting volume appears as a reasonable explanation. Another assumption is that Pr_2−x Ce _x CuO_4+δ films with small RRR have a higher concentration of defects or impurity states, thus the scattering probability is enhanced. ^{Reference Finkelman, Sachs, Droulers, Butch, Paglione, Bach, Greene and Dagan89} These defects may persist into the superconducting state and form localized nonsuperconducting clusters that allow for penetration of the magnetic field. We now turn to the question on how the observed changes in $\ell$ are reflected in the Hall coefficient R _H which is shown in Fig. 6. For small $\ell \approx 12.6\;{\rm{nm}}$ , the Hall coefficient is negative over the entire temperature range measured. This is not surprising as for decades it is believed that such behavior is intrinsic to electron doped cuprate superconductors. It is also known that the Fermi surface of so-called electron doped cuprates is hole-like, not electron like, as shown by angle-resolved photoemission spectroscopy (ARPES) experiments. ^{Reference King, Shen, Dessau, Wells, Spicer, Arko, Marshall, DiCarlo, Loeser, Park, Ratner, Peng, Li and Greene90} Also shown in Fig. 6 is the Hall coefficient for a Pr_2−x Ce _x CuO_4+δ thin film with $\ell \approx 75.8\;{\rm{nm}}$ . Its temperature dependency is quite different from the previous one. In contrast to the Pr_2−x Ce _x CuO_4+δ with $\ell \approx 12.6\;{\rm{nm}}$ , this Hall coefficient is positive at low temperatures. ^{Reference Brinkmann, Rex, Stief, Bach and Westerholt91} Generally, the Hall coefficient is proportional to $\mathop {\int {{\tau ^2}\left( {\bf{k}} \right){\partial ^2}/\partial {k_i}\partial {k_j}{\bf{S}}{\rm{d}}{\bf{k}}} }\nolimits^$ and one requires detailed knowledge of the topology of the underlying Fermi surface S. Changing the sign of the Hall coefficient points to significant modifications at the Fermi surface either by shape or by matrix elements of the scattering time $\tau \left( {\bf{k}} \right)$ . Comparing the superconducting transition temperatures (inset of Fig. 6) for Pr_2−x Ce _x CuO_4+δ with $\ell \approx 12.6\;{\rm{nm}}$ and 75.8 nm emphasizes that there is no change at all. Instead, the only noticeable change stems from the enhancement of $\ell$ and that in turn promotes a scenario where the scattering time of hole-like charge carriers is enhanced and that this enhancement is driven by annealing. In particular, the annealing process is known to trigger the evacuation of occupied apical sites in electron-doped cuprates ^{Reference Krockenberger, Yamamoto, Tsukada, Mitsuhashi and Naito19,Reference Radaelli, Jorgensen, Schultz, Peng and Greene92–Reference Schultz, Jorgensen, Peng and Greene95} and these occupied apical sites have been found to enhance the antiferromagnetic correlation length. ^{Reference Krockenberger, Eleazer, Irie and Yamamoto96} The influence of the antiferromagnetic correlation length on the mean-free path length can be seen in Fig. 7 where the residual resistivity ratio of Pr_2−x Ce _x CuO_4+δ thin films is plotted as a function of the annealing temperature. This RRR value can be enhanced by progressively increasing the annealing temperature while keeping in mind that one must obey the thermodynamic limit set by the decomposition of Pr_2−x Ce _x CuO_4+δ. On the other hand, however, if the annealing process time exceeds certain limitations, oxygen defects will emerge within the CuO₂ planes and superconducting transition temperature T _c inevitably decreases. For optimally annealed Pr_2−x Ce _x CuO_4+δ, as T _c remains constant and one is left therefore with the criteria of the mean-free path length to determine defect concentrations. Scattering processes initiated by such defects not only influence the normal state electron correlations but also the superconducting state. In Fig. 8 we plot the normalized magnetoresistance of Pr_2−x Ce _x CuO_4+δ thin films with $\ell = 97$ and 24 nm. For $\ell = 97\;{\rm{nm}}$ , the upper critical field H _c2 value is certainly smaller than that observed for Pr_2−x Ce _x CuO_4+δ with $\ell = 24\;{\rm{nm}}$ and this result points toward an intrinsically clean superconductor having a longer coherence length ξ_GL when compared to superconducting Pr_2−x Ce _x CuO_4+δ with $\ell = 24\;{\rm{nm}}$ . This result appears to be in contrast to reports showing that electron-doped cuprate superconductors are intrinsically in the dirty limit. ^{Reference Dagan, Beck and Greene97}

FIG. 1.

Reactive molecular beam epitaxy setup for the synthesis of complex transition metal oxides. Constituent elements are evaporated by electron guns and the flux of each element is monitored and controlled by EIES. The system is equipped with a RF oxygen source as well as an ozone injector.

FIG. 2.

Evaporation rate profiles of Pr, Cu, and Ce prior and during the synthesis of Pr_2−x Ce _x CuO_4+δ.

FIG. 3.

Crystal structure (a, b) and HAADF-STEM images (c, d, e) of Pr_2−x Ce _x CuO_4+δ thin films grown by reactive molecular beam epitaxy onto SrTiO₃ substrates. Simulated images are inset in (d, e). The superconducting transition T _c ≈ 20.0 K.

FIG. 4.

(a) EDS map of Cu K_α; (b) EDS map of Pr/Ce L_α; (c) EDS map of O K_α; (d) composite color map of Cu K_α (red), O K_α (blue), and Pr/Ce L_α (green). The superconducting transition T _c ≈ 20.0 K.

FIG. 5.

Diamagnetic shielding of Pr_2−x Ce _x CuO_4+δ thin films recorded for various values of $\ell$ . In (a), (b), (c), and (d), $\ell$ is 108.0, 75.8, 24.2, and 21.3 nm, respectively. Note that the external magnetic field (10 Oe) was applied perpendicular to the film surface and perpendicular to the CuO₂ planes of the Pr_2−x Ce _x CuO_4+δ thin films.

FIG. 6.

Temperature dependency of R _H of Pr_2−x Ce _x CuO_4+δ thin films recorded for $\ell$ = 12.6 and 75.8 nm, respectively. The inset shows the corresponding resistivity behaviors of samples A and B.

FIG. 7.

Residual resistivity ratio plotted as a function of the annealing temperature used on Pr_2−x Ce _x CuO_4+δ thin films after the growth. For annealing temperature equal “0”, we skipped the annealing procedure.

FIG. 8.

Normalized magnetoresistance of Pr_2−x Ce _x CuO_4+δ thin films as a function of the magnetic field applied perpendicular to the CuO₂ planes for $\ell$ = 97 nm, and 24 nm, respectively.