Searching for Superconductivity in High Entropy Oxide Ruddlesden-Popper Cuprate Films

In this work, the high entropy oxide A2CuO4 Ruddlesden-Popper (La0.2Pr0.2Nd0.2Sm0.2Eu0.2)2CuO4 is explored by charge doping with Ce+4 and Sr+2 at concentrations known to induce superconductivity in the simple parent compounds, Nd2CuO4 and La2CuO4. Electron doped (La0.185Pr0.185Nd0.185Sm0.185Eu0.185Ce0.075)2CuO4 and hole doped (La0.18Pr0.18Nd0.18Sm0.18Eu0.18Sr0.1)2CuO4 are synthesized and shown to be single crystal, epitaxially strained, and highly uniform. Transport measurements demonstrate that all as-grown films are insulating regardless of doping. Annealing studies show that resistivity can be tuned by modifying oxygen stoichiometry and inducing metallicity but without superconductivity. These results in turn are connected to extended x-ray absorption fine structure (EXAFS) results indicating that the lack of superconductivity in the high entropy cuprates likely originates from a large distortion within the Cu-O plane ({\sigma}2>0.015 {\AA}2) due to A-site cation size variance, which drives localization of charge carriers. These findings describe new opportunities for controlling charge- and orbital-mediated functional responses in Ruddlesden-Popper crystal structures, driven by balancing of cation size and charge variances that may be exploited for functionally important behaviors such as superconductivity, antiferromagnetism, and metal-insulator transitions, while opening less understood phase spaces hosting doped Mott insulators, strange metals, quantum criticality, pseudogaps, and ordered charge density waves.


I. INTRODUCTION
Since the discovery of high Tc superconductivity in 1986 1 , the underlying mechanism for Cooper pair formation in the cuprates has continued to baffle researchers.
Both electron and hole doping from the antiferromagnetic Mott insulating ground state of the parent compounds leads to a rich phase diagram where pseudogaps, density waves and strange metals surround a superconducting dome 2 . Based on competing experimental evidence from a variety of techniques, two prominent schools of thought for the formation of the pairing glue have emerged. Inelastic neutron scattering 3,4 and Resonant Inelastic Xray Scattering 5 (RIXS) have revealed an interplay between antiferromagnetic spin fluctuations and superconducting pairs with exchange energy scales sufficient for forming a superconducting condensate, suggestive of a spin mediated pairing mechanism [6][7][8] . On the other hand, "kinks" in the electronic dispersion revealed by Angle-Resolved Photoemission Spectroscopy 9 (ARPES) as well as the isotope effect in both ARPES 10 and Scanning Tunnelling Spectroscopy 11 (STS) measurements provide evidence for strong electron phonon coupling as the origins of the Cooper pairing glue 2,12 . Similar debates appear regarding the origins of the pseudogap phase in hole doped compounds and whether it is due to preformed Cooper pairs without phase coherence 13 or density wave phenomena competing with superconductivity 14,15 . Differences in the pseudogap phase are also observed with the electron doped compounds where AFM order is more robust 2 . Despite the array of conflicting information, the physical arrangement of the atomic layers is simplistic in that it can be viewed as alternating layers of ionic metal-oxygen charge reservoir layers interleaved with active doped CuO2 layers where superconductivity is believed to reside. A key to unraveling the mysteries of high Tc cuprate superconductors is finding new ways to disentangle the contributions of electrons, lattice, and spins in the electronic structure. In this study, we create a metal-oxide charge reservoir with high entropy, while leaving the doped CuO2 layers intact. The random distribution of cations in the charge reservoir layer should provide a control parameter on the phononic and magnetic degrees of freedom in the system.
The extraordinary compositional and structural tunability of the high entropy oxides (HEOs) make them outstanding candidates to provide never before possible accessibility to the nearly degenerate spin, charge, orbital, and lattice energies that drive emergent correlated behaviors. HEOs are an emerging class of materials in which one or more cation sublattices host 5 or more different cations connected by an oxygen anion sublattice [16][17][18] . An important distinction of HEOs from more traditional metal-metal bonded high entropy alloys is the fact that the bonding network of the HEOs are built upon covalent and ionic bonds which permit structural motifs and electron interactions not accessible in metal-metal bonded high entropy alloys [19][20][21][22] . When comparing to less compositionally complex oxides, the presence of the many different cations in the HEOs act to facilitate uniform mixing on cation sublattices 16,[23][24][25] . This allows for chemical doping design well beyond what is conventionally accessible, since materials of lower complexity are more strongly dominated by enthalpic energies during synthesis which leads to chemical segregation and formation of impurity phases 26 . Entropy stabilization has led to the synthesis of a broad array of functionally relevant crystal structures including spinel [27][28][29] , rocksalt 30-32 , Ruddlesden-Popper (RP) 33,34 , and perovskite 26,[35][36][37] . In the ideal case, the microstructure of HEOs can be viewed as the solid state of an ideal solution, which can bring about unique functionalities compared to conventional oxides. For example, HEOs have exhibited remarkable thermal [38][39][40] , optical 19,41 , and dielectric properties 42,43 with potential applications in thermal barrier coatings 38,39 , Li-ion batteries 44,45 , and catalysis 21 . Importantly, studies have shown that HEOs possess unexpected thermal transport behaviors, which point to the ability to manipulate phononic degree of freedom through cation selection 36,38 . Functionalities in strongly correlated HEO systems are still in their infancy, however recent works related to magnetism and the development of synthesis approaches that enable single crystal HEO films suggest that this area is likely to produce many exciting and unexpected behaviors, which are not accessible in low complexity systems. 20,27,28,30 In this work, we investigate electron and hole doping of (La0.2Pr0.2Nd0.2Sm0.2Eu0.2)2CuO4 (5ACuO)allowing both the exploration of the effects on cation size variance and electronic doping on the electronic state. Both n-type (via Sr) and p-type (via Ce) dopings are shown to be single-phase and epitaxial. Regardless of doping type, the as-grown films are insulating at all measured temperatures. Owing to the known sensitivity to oxygen mobility and tunability in Cu-O plane morphology 46,47 , annealing studies are carried out on all samples. X-ray diffraction (XRD) measurements confirm characteristics of changing oxygen vacancy density that result in changes to resistivity. In the electron doped sample, a high temperature metallic state is achieved, but no evidence of superconductivity is observed. Extended x-ray absorption fine structure (EXAFS) measurements show buckling in the Cu-O plane which is suspected as the primary driver in preventing the onset of superconductivity. As oxygen vacancies form, buckling in the Cu-O plane decreases, which relieves local strain from different cation sizes and is the likely mechanism that induces the observed drop in resistivity after annealing in reducing environments. These results provide insight into the evolution of electronic phase in high entropy cuprates, where strain, oxygen vacancy density, and A-site cation size variance are all found to play a role in functionality.

A. Sample Growth
All films are synthesized at 720 °C using pulsed laser deposition (PLD) with a 248 nm KrF excimer laser at a fluence of 0.7 J/cm 2 and frequency of 5 Hz with a steady oxygen pressure of 1 mTorr throughout growth and cooling to room temperature at a rate of 25 C/min. Targets are prepared using the conventional solid-state method with a stoichiometric ratio of cation elements 34

B. Structural Characterization
The thickness and microstructure of the as-deposited films are characterized via xray diffraction (XRD) using a PANalytical X'Pert PRO, X'Pert 3 MRD equipped with Cu Kα1. In-situ high temperature XRD measurements are conducted in air using a heating stage. Small background peaks observed in these scans result from the Inconel heating stage, the polymer dome/heat shield, and the silver epoxy used in mounting the sample.

C. Electronic Characterization
Van der Pauw configuration is utilized for transport measurements in a Physical Property Measurement System (PPMS, Quantum Design). During transport measurements, the samples are zero-field cooled from 300 K to 10 K with a cooling rate of 5 K/min.

III. RESULTS AND DISCUSSION
The structure of the as-deposited films is first examined by XRD. Fig. 1(a) shows the specular diffraction patterns of the undoped, Ce-5ACuO and Sr-5ACuO films grown on STO (001) substrates. XRD demonstrates that the films are of single crystal RP structure with preferred (00l) growth direction and no secondary phases 33 Fig. 1(b), where the film is shown to be epitaxially strained to the substrate. The electronic character of each of the films are characterized using transport measurements. As seen in 1(c) all of the as-grown films are insulating in nature, with the Sr-doped film being immeasurable in its virgin state. After characterizing the as-grown state of the films, annealing studies are conducted on all films to better understand how insertion and removal of oxygen influences structure and behavior. This is important, since modifying oxygen vacancy density is known to influence electronic character in the parent cuprate systems 47 . The resulting in-situ high temperature XRD of a Ce-5ACuO film is shown in Fig. 2(a). Here the sample was heated from 300 °C to 850 C in air where remarkably little change is observed. The film shows high thermal stability even at temperatures higher than its deposition temperature of 720 C, where the (004) and (006) film diffraction peaks show no significant change in intensity and no extraneous peaks appear. A small expansion is observed with increasing temperature, which is consistent with thermal expansion of the film.
Establishing that little to no change occurs upon annealing in air, additional experiments annealing in ozone (10% O3/90% O2) and H2 (forming gas, 5% H2/95% N2) were done to further promote the insertion/removal of oxygen respectively. Fig. 2(b) shows the resulting XRD of the film (004) for a Ce-5ACuO film after annealing at different temperatures in H2. A small expansion in the out-of-plane lattice parameter is observed with increased annealing temperature up to 600 C; a change which is consistent with loss of oxygen. Despite the increased temperature, the film's crystal structure is well maintained with clear RP phase and no impurity peak formation or shifts to in-plane registry (Fig.   2(c)). At higher temperatures of 800 °C, a dramatic peak shift is observed, which indicates that the film undergoes a phase transition. This is accompanied by a color change of the sample, where the film is converted from dark to transparent and is commensurate with the formation of mobile oxygen vacancies, as discussed in more detail below. Additional XRD from O3 annealed Ce-5ACuO and the Sr-5ACuO films (after annealing in H2 and O3) can be found in the supplementary materials (Fig. S1) 54 .
Transport properties of doped 5ACuO films are investigated as a function of annealing. Fig. 3(a) shows the resistivity vs. temperature curves of a Ce-5ACuO film after annealing at various temperatures in H2. After 200 C annealing in H2, the film's resistivity is relatively unchanged, as the thermal threshold for oxygen migration has not been met.
As annealing temperature increases, the resistivity of the film decreases over the entire temperature range. The film resistivity at room temperature is decreased by about 20% after annealing at 400 C and further decreased by 50% after the 600 C anneal.
Importantly, a high temperature metallic phase appears (Fig. 3(b)) after forming gas annealing at 400 C, which demonstrates that not only resistivity, but also electronic phase transitions can be controlled through oxygen stoichiometry. After annealing the sample at 800 C, the film becomes immeasurably insulating, which coincides with the structural changes observed in XRD. This, considering the notable change in XRD, may be indicative of a critical oxygen vacancy density at which a vacancy ordered phase might emerge, though further microscopy and x-ray diffraction should be done to confirm.
In addition to the H2 annealing process aimed at reducing oxygen content, the Ce-5ACuO films are also annealed in O3 with the intent of increasing oxygen content from the as-grown state. Fig. S1(a)  annealing experiments, these results show that the formation of oxygen vacancies lead directly to improved transport properties. These results are summarized in Fig. 3(c), where all films are also shown to be immeasurable after annealing in ozone. To understand the mechanism of the observed functional changes, it is important to first rule out possible extrinsic effects that could result from the STO substrate becoming more conducting with oxygen vacancies 55 . This effect is confirmed to be intrinsic to the film by growing on DSO substrates, as detailed in the supplementary materials (Fig. S1, S2) 54 . One possible intrinsic explanation for the change in transport is that the shift in oxygen content simply acts to donate electrons to the copper charge carrier concentration.
However, this is unlikely to be the only factor. Changes to Cu-O plane bond distortions driven by cation size variation on the perovskite layer are well known to influence electron conduction in cuprates 56,57 . Furthermore, the cation disorder may enable the local trapping of charge which is then mediated by the rearrangement of oxygen vacancies which help redistribute charge resulting in a drop in resistivity. This concept regarding the polaronic tendencies of these materials can be further investigated by, for example, ARPES 2 . In the present study, we investigate Cu-O plane distortions which would influence inherent stable oxygen coordination environments after initial synthesis. This would partially contribute to the large difference in resistivities of the as-grown samples. The changes to resistivity observed in the undoped and Sr doped samples after annealing would then be influenced by the reduction in buckling of the Cu-O plane due to changes to oxygen coordination. To investigate this further, it is important to identify both the Cu coordination and local displacement in the undoped film and doped films.
X-ray absorption near edge structure (XANES) was used to study the electronic and valence state of Cu. Normalized K-edge XANES of the Cu K-edge for 5ACuO, Ce-5ACuO, and Sr-5ACuO are plotted in Fig. 4(a) and compared to a Cu metal foil for reference. The edge was consistently chosen across all spectra to be the first peak in ∂μ/∂E.
The primary feature changing between the three films is a slight shift to lower or higher energy with the introduction of Ce or Sr, respectively. In the case of Ce-5ACuO this suggests a partial change in oxidation state from Cu 2+ to Cu 1+ , however the actual ratio of these states cannot be determined without further measurement. In the Sr-5ACuO this suggests a dominant Cu 2+ state. Further analysis, comparing measured spectra to a reference spectrum from previous studies 33,58 (Fig. 4(b) Fig. 5(a-c) show the best-fit magnitude (|I (R)|) and imaginary part (im(R)) of the k-weighted FT of the EXAFS spectra for 5ACuO, Ce-5ACuO, and Sr-5ACuO respectively. The final fit results and additional details for each composition are provided in the supplementary materials (Table S1) 54 . The half scattering-path length, R, varies appropriately with the unit cell dimensions of each sample composition, and further Debye-Waller, σ 2 ) of the Cu-O plane, regardless of dopant, which has been shown to suppress conductivity in other cuprates 59,60 . This agrees with studies showing that a large variance in cation size negatively impacts the critical temperature of conducting perovskites and cuprates 56,62 The effect of the formation of oxygen vacancies, rather than a simple modification to the electronic structure, is shown to have a minimal impact on conductivity with traditional hole/electron doping in the present work. Therefore, it is believed the primary impact of annealing is on the structural homogeneity of the films. As in the case of strain engineering, oxygen vacancy formation is known to directly affect the Cu-O lattice plane homogeneity. When oxygen vacancies form in doped 5ACuO, we suggest the large RMS roughness is decreased in the Cu-O plane, by vacancies forming selectively near highly distorted regions, which in turn decreases resistivity in this plane.

IV. SUMMARY AND CONCLUSIONS
The effects of hole (Sr) and electron (Ce) doping on the high entropy cuprate 5ACuO were investigated via x-ray scattering and transport experiments. XRD demonstrates the PLD grown films are single phase and epitaxially strained to the substrate.
From in-situ XRD it is found that the films exhibit excellent thermal stability, showing no structural change when annealing to 850 C in air and 600 C in H2. Each of the films, regardless of doping, are found to be insulating at all measured temperatures. However, the resistivity of the films could be effectively tuned by annealing in a reducing (forming gas) or oxidizing (ozone) environment. Increased oxygen vacancy density in the films was shown to effectively decrease the resistivity of films for all A-site doping, with a MIT emerging for the Ce-5ACuO film. While doping shows limited change to transport properties, XANES confirms Cu valence changes with doping in the expected manner.
From EXAFS, we gain insight into the mechanism preventing a metallic or superconducting phase in the as-grown state as a large distortion of the Cu-O plane is observed. This distortion has been connected to lowering critical temperatures in cuprates and observed in systems where A-site cation size variance is attributed to decreases in Tc.
In connection to transport results, the EXAFS suggests the primary role of oxygen vacancy formation in increasing conductivity may be in lowering the distortion or buckling of the Cu-O plane. These results shed light into a possible mechanism towards finding superconductivity in entropy stabilized cuprates, where a delicate balance of cation size variance, oxygen vacancy density, and strain must be considered as they relate to the uniformity of the conducting Cu-O plane. While superconductivity was not observed in any films presented in this work, it appears that superconductivity is not out of reach in these materials with tuning of size variances to reduce distortion in the Cu-O plane.

DATA AVAILABILITY
Data contained in this work made available upon reasonable request by contacting the corresponding author.