a-axis YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers with subnanometer rms roughness

Shortly after the discovery of high-temperature superconductivity in YBa₂Cu₃O₇,^1,2 measurements showed that the superconducting proximity length along the a-axis (ξ_a ≈ 1.1 nm)^3,4 of YBa₂Cu₃O_7−x is nearly an order of magnitude longer than along the c-axis (ξ_c ≈ 0.1 nm).^4,5 Note that ξ_c is shorter than the distance between the CuO₂ planes. This difference makes the a-axis direction relevant to forming controlled and reproducible YBa₂Cu₃O_7−x based Josephson junctions (JJs) for superconducting electronics.⁶ Most JJs in YBa₂Cu₃O_7−x have been made using epitaxial YBa₂Cu₃O_7−x films oriented with the c-axis perpendicular to the film surface.⁷ This is because such films, referred to as c-axis oriented films, exhibit the highest superconducting transition temperature (T_c), highest critical current density (J_c), and smoothest surface. JJs in such films are made in the (001) plane to exploit the longer in-plane coherence length, ξ_a. They occur at weak links present at grain boundaries^8–12 or formed by helium ion bombardment.¹³ They are also made by introducing tunnel barriers by a ramp-junction process that involves patterning the c-axis YBa₂Cu₃O_7−x film followed by epitaxial regrowth.^11,14,15

A more direct approach to fabricate high quality JJs—one that involves pristine interfaces formed without breaking vacuum—is through the growth of YBa₂Cu₃O_7−x films oriented with the a-axis perpendicular to the film surface (i.e., a-axis oriented films). This was recognized early on and numerous groups developed methods to grow a-axis oriented films^16,17 as well as JJs based upon them, e.g., a-axis oriented YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers.^6,18 Although JJs were successfully fabricated, the resulting junctions were neither controlled nor reproducible due to the significant roughness of the a-axis oriented YBa₂Cu₃O_7−x films.¹⁸ Note that the low-energy surface of YBa₂Cu₃O_7−x is the (001) plane,¹⁹ explaining the far smoother morphology of c-axis YBa₂Cu₃O_7−x films compared to a-axis YBa₂Cu₃O_7−x films.

To improve the quality of a-axis YBa₂Cu₃O_7−x films and heterostructures, several techniques have been employed when using PrBa₂Cu₃O_7−x as either a buffer layer or a barrier layer.²⁰ These include increasing the substrate temperature, either gradually²¹ or with a step-like ramp after the a-axis buffer layer has nucleated,^6,20,22,23 and even performing this in tandem with ramping down the background oxidant gas pressure.^21,24,25 Nonetheless, the interface roughness has remained a major challenge for samples showing good superconducting transitions [e.g., an rms of ∼10 nm for a-axis YBa₂Cu₃O_7−x grown on (100) LaAlO₃]²¹ as has avoiding the unwanted nucleation of c-axis YBa₂Cu₃O_7−x or PrBa₂Cu₃O_7−x when the temperature is ramped.^22,23 The smoothest a-axis YBa₂Cu₃O_7−x (or DyBa₂Cu₃O_7−x) films reported were grown utilizing ozone-assisted molecular-beam epitaxy (MBE), and rms surface roughnesses as low as 0.4 nm were achieved.^25–27 This promising smoothness motivated the current work to utilize MBE to make a-axis YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers.

Following the initial pioneering studies on a-axis YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers and a recognition of the challenges involved in making a viable JJ technology by this approach, work on this system has all but ceased. Now decades later, we revisit this challenge harnessing the improvements that have been made in the intervening years in thin film growth methods. Using MBE, we grow a-axis YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers paying particular attention to growth conditions that yield smooth surfaces. We study the thickness dependence of the surface roughness as well as the superconducting transition width. Our results, including cross-sectional scanning transmission electron microscopy with electron energy loss spectroscopy (STEM-EELS) to characterize the interfaces with chemical specificity, demonstrate that the interface roughness can be decreased significantly to a level comparable to the thickness of relevant tunneling barrier layers. The substantial improvement in interface smoothness that we observe in a-axis YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers suggests that a-axis YBa₂Cu₃O_7−x-based JJs with requisite smoothness to provide the precise thickness control of the tunnel barrier needed for a JJ technology are achievable.

YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers with 24 nm, 32 nm, 64 nm, and 100 nm thick YBa₂Cu₃O_7−x layers, in which the PrBa₂Cu₃O_7−x layer thickness is kept constant at 8 nm, were grown on 10 × 10 mm² (100)-oriented LaAlO₃ substrates by ozone-assisted MBE [Fig. 1(a)]. Although high quality a-axis YBa₂Cu₃O_7−x films have been grown on (100) LaSrGaO₄ substrates,²⁸ we used (100) LaAlO₃ substrates in this work because our goal is to identify a path that can be scaled to large diameters to enable its translation to a viable technology. 3-in. diameter LaAlO₃ substrates are currently available; in the past, even 4-in. diameter LaAlO₃ substrates were commercially produced.²⁹ 

The YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers were synthesized in a Veeco GEN10 MBE. Yttrium (99.6%), barium (99.99%), praseodymium (99.1%), and copper (99.99%) were evaporated from thermal effusion cells with fluxes of 1.1 × 10¹³ cm⁻² s⁻¹, 2.2 × 10¹³ cm⁻² s⁻¹, and 3.3 × 10¹³ cm⁻² s⁻¹, respectively. Prior to growth, the (100) LaAlO₃ substrates (CrysTec GmbH) were etched in boiling water, annealed at 1300 °C in air for 10 h, and then etched again in boiling water to obtain an AlO₂-terminated surface with a step-and-terrace morphology.³⁰ Following this surface treatment, the backside of the (100) LaAlO₃ substrates were coated with a 10 nm thick titanium adhesion layer followed by 200 nm of platinum, enabling the otherwise transparent substrates to be radiatively heated during MBE growth. The YBa₂Cu₃O_7−x (or PrBa₂Cu₃O_7−x) layers were grown by simultaneously depositing yttrium (or praseodymium), barium, and copper onto the heated substrate under a continuous flux of distilled ozone (∼80% O₃ + 20% O₂) yielding a background pressure of 1 × 10⁻⁶ Torr. After growth, the samples were cooled to under 100 °C in the same pressure of distilled ozone in which they were grown before turning off the ozone molecular beam and removing the samples from vacuum.

Because YBa₂Cu₃O_7−x is a point compound that is unable to accommodate appreciable off-stoichiometry,³¹ flux calibration presents a significant challenge where secondary impurity phases nucleate easily and significantly degrade film quality.³² We tackle this challenge by separately calibrating the flux of each element by growing binary oxides of the constituents, namely, Y₂O₃, PrO₂, BaO, and CuO. From these separate binary flux calibrations, the temperatures of the effusion cells containing yttrium, barium, praseodymium, and copper are adjusted to match the desired 1:2:3 flux ratio among Y(Pr):Ba:Cu. The temperature of the substrate is measured during growth by using a thermocouple (T_Tc) that is positioned close to but not in direct contact with the substrate and an optical pyrometer (T_Pyr) operating at a wavelength of 1550 nm. The growth of the trilayers starts at low-temperature, T_Tc ≈ 420 °C (T_Pyr ≈ 530 °C), resulting in a cubic perovskite (Y,Ba)CuO_3−x phase³³ for the first few layers and ends at T_Tc ≈ 570 °C (T_Pyr ≈ 620 °C) following a temperature-ramping procedure. The details of the flux calibration method (including the characterization of individual binary oxides) are presented in Figs. S1–S5 of the supplementary material. Also shown are the temperature-ramping details and the in situ reflection high-energy electron diffraction (RHEED) characterization of a reference a-axis YBa₂Cu₃O_7−x single-phase film grown as part of the optimization of the growth procedure (Fig. S6).

During growth, the films were monitored by in situ RHEED with KSA-400 software and a Staib electron gun operating at 13 kV and 1.45 A. RHEED images taken during the growth of the 24 nm YBa₂Cu₃O_7−x/8 nm PrBa₂Cu₃O_7−x/24 nm YBa₂Cu₃O_7−x trilayer are shown in Figs. 1(b)–1(g). The structural quality and the a-axis/c-axis ratio of the samples was explored using a PANalytical Empyrean x-ray diffractometer (XRD) at 45 kV and 40 mA with Cu Kα₁ radiation (1.54057 Å). For surface morphological characterization of the films, ex situ atomic force microscopy (AFM) measurements were conducted using an Asylum Cypher ES Environmental AFM system. Resistance as a function of temperature measurements were carried out using a homemade four-point van der Pauw geometry system that slowly dips the samples into a Dewar of liquid helium.

Detailed investigations of the films were conducted using atomic-resolution scanning transmission electron microscopy (STEM). Cross-sectional TEM specimens were prepared by focused ion beam (FIB) lift-out with a Thermo Fisher Helios G4 UX Dual Beam system. The samples were imaged on an aberration-corrected FEI Titan Themis at 300 kV. STEM high-angle annular dark-field (HAADF) imaging was performed with a probe convergence semi-angle of 21.4 mrad and inner and outer collection angles from 68 mrad to 340 mrad. STEM electron energy loss spectroscopy (EELS) measurements were performed on the same Titan system equipped with a 965 GIF Quantum ER and Gatan K2 Summit direct detector operated in the electron counting mode, with a beam current of ∼50 pA and scan times of 2.5 ms or 5 ms per 0.4 Å pixel. A multivariate weighted principal component analysis routine (MSA Plugin in Digital Micrograph) is used to decrease the noise level in STEM data.³⁴ 

The structural quality of the samples is assessed by XRD measurements. In the coupled θ–2θ XRD scans in Fig. 2(a), only h00, 0k0, and 00ℓ reflections of the YBa₂Cu₃O_7−x and PrBa₂Cu₃O_7−x phases are indexed, indicating that the film only contains phases with the desired stoichiometry; they are free of impurity phases associated with off-stoichiometry. With increasing YBa₂Cu₃O_7−x layer thicknesses, 00ℓ reflections emerge showing the nucleation and propagation of c-axis grains in the films. Off-axis ϕ scans of the 102 family of reflections of the orthorhombic YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x at χ ≈ 56.8° and χ ≈ 33.2° are used to measure the a-axis and c-axis content of the orthorhombic grains, respectively. Note that χ = 90° aligns the diffraction vector to be perpendicular to the plane of the substrate.³⁵ In the 102 ϕ scan of the trilayer sample shown in Fig. 2(b), four peaks associated with the a-axis grains are observed corresponding to 90° in-plane rotational twinning: the c-axis of the YBa₂Cu₃O_7−x and PrBa₂Cu₃O_7−x is aligned parallel to the [010] direction of the (100) LaAlO₃ substrate in one set of twin domains and parallel to the [001] direction of the (100) LaAlO₃ substrate in the other set of twin domains.^17,20,36,37 No intensity associated with c-axis grains is observed, indicating that the film contains no c-axis grains within the resolution of our XRD scan. The off-axis ϕ scans of all trilayer samples shown in Fig. S5 indicate that all four trilayers have more than 97% a-axis content in the Y(Pr)Ba₂Cu₃O_7−x orthorhombic phase. In addition to the orthorhombic phases, we also observe a cubic perovskite phase. This phase has been previously reported in the literature as a low-temperature, kinetically stabilized I-centered cubic phase³⁸ or primitive simple-cubic phase.³⁹ The formation of this phase and its role in stabilizing the a-axis YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers are discussed below in tandem with its observation by HAADF-STEM. In the reciprocal space map (RSM) around the LaAlO₃ $1̄03$ reflection (pseudocubic) in Fig. 2(c), we also observe a perovskite-like $1̄03$ reflection [denoted p-(Y,Ba)CuO_3−x] and the orthorhombic phase $303̄/31̄0$ and $033/1̄30$ reflections associated with the a-axis and b-axis YBa₂Cu₃O_7−x grains, respectively.

The surface morphologies of the same as-grown YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers were established by ex situ AFM using tapping mode. With increasing YBa₂Cu₃O_7−x layer thickness, the elongated YBa₂Cu₃O_7−x grains as well as the in-plane 90° rotational twinning of these rectangular-shaped features become visible in the 2 × 2 µm² topography scans presented in Figs. 3(a)–3(d). This morphology arises from the much slower growth rate of YBa₂Cu₃O_7−x grains along [001] than in the (001) plane.⁴⁰ The root-mean-square (rms) roughness also increases with increasing YBa₂Cu₃O_7−x layer thickness from 0.62 nm in the thinnest 24 nm/8 nm/24 nm trilayer to 2.3 nm in the thickest 100 nm/8 nm/100 nm trilayer. Surface roughness is an important metric affecting the yield and electrical performance of YBa₂Cu₃O_7−x-based JJs involving extrinsic interfaces, i.e., tunnel barriers. The 0.62 nm rms roughness we observe is the smoothest reported in the literature and a significant reduction from the 11.3 nm measured previously on a-axis YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x bilayers with 270 nm thick YBa₂Cu₃O_7−x layers grown on (100) LaAlO₃ substrates.²¹ 

The resistance as a function of temperature (R–T) was measured on the same YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers; the results are presented in Fig. 4. As is evident from the R–T plots in Fig. 4(a), all trilayers superconduct. The normal state resistance decreases and the onset temperature of the superconducting transition (T_onset) increases with increasing YBa₂Cu₃O_7−x layer thickness—from 85 K for the 24 nm/8 nm/24 nm trilayer to 90 K for the 100 nm/8 nm/100 nm trilayer, as shown in Fig. 4(b). We define T_onset as the temperature at which the resistance falls below a linear extrapolation of the R vs T behavior from its slope in the 200 K–300 K regime. The superconducting transition width (ΔT_c), here defined as the temperature difference between T_onset and the temperature at which the resistance is zero (within the noise of our measurement), ΔT_c, decreases with increasing YBa₂Cu₃O_7−x layer thickness from 29 K for the 24 nm/8 nm/24 nm trilayer to 10 K for the 100 nm/8 nm/100 nm trilayer, as seen in Fig. 4(c). Compared to c-axis YBa₂Cu₃O_7−x films, however, these transition widths are still relatively broad.⁴¹ Such behavior is ubiquitous in twinned a-axis YBa₂Cu₃O_7−x films,^17,20,21,24 especially when the thickness of the a-axis YBa₂Cu₃O_7−x is under 100 nm.^18,42 A portion of the broad transitions observed might be intrinsic, as is the case for interface superconductivity at La_2−xSr_xCuO₄—La₂CuO₄ interfaces.⁴³ In the present case, an intrinsic contributor could be the generation and flow of Josephson vortices in the vicinity of T_c.^44,45 Extrinsic contributions to the broadening likely arise from local disorder and inhomogeneities in the samples, insufficient oxidation, and the degradation of the samples over time.⁴⁶ 

To reveal the microstructure and interface abruptness of the samples, we studied two trilayer samples with cross-sectional high-resolution STEM. A low-magnification HAADF-STEM image of the 24 nm/8 nm/24 nm YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayer shown in Fig. 5(a) is representative of the complete sample. Individual layers are distinguished as darker and brighter regions due to the atomic number (Z) contrast⁴⁷ of HAADF imaging. The PrBa₂Cu₃O_7−x layer gives brighter contrast compared to the YBa₂Cu₃O_7−x layer because praseodymium (Z_Pr = 59) is heavier than yttrium (Z_Y = 39). The LaAlO₃ substrate also shows relatively bright contrast for the same reason (Z_La = 57). A higher magnification image [Fig. 5(b)] focusing on a representative interface region reveals that the interfaces in the YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayer are coherent. Neither in low-magnification nor in high-magnification scans were c-axis grains observed in our STEM images, consistent with the high volume fraction of a-axis growth measured by XRD. Nevertheless, structural coherence does not prove chemical abruptness at interfaces involving cuprate high-temperature superconductors.^48,49

The chemical abruptness of the YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x interfaces was assessed by atomic-resolution elemental mapping via STEM-EELS. Figures 5(c)–5(e) show the elemental maps obtained using Pr–M_5,4 (red), Y–L_3,2 (green), and Ba–M_5,4 (blue) edges in the region outlined by the tan rectangle in Fig. 5(a). A red, green, blue (RGB) overlay of the elemental maps from this region is shown in Fig. 5(f), while Fig. 5(g) shows the simultaneously acquired ADF-STEM image of the same region. Atomic-resolution EELS maps reveal abrupt interface profiles, corroborating the STEM-HAADF images. Both interfaces show minimal Y–Pr intermixing, although some asymmetry of the interface profiles is seen. The lower YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x interface shows a nearly perfect interface profile free of Y–Pr intermixing; the upper interface (PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x) presents a slightly rougher local profile with a roughness limited to 1–2 monolayers.

The roughness of the interfaces revealed by HAADF-STEM and STEM-EELS in Fig. 5 is consistent with the qualitative observations made during growth by in situ RHEED [Figs. 1(b)–1(g)] of this same YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayer. The arrowed streaks of a-axis oriented YBa₂Cu₃O_7−x in Fig. 1(b) promptly disappear in transitioning from the lower YBa₂Cu₃O_7−x layer to the PrBa₂Cu₃O_7−x barrier layer in Fig. 1(c), indicating that the PrBa₂Cu₃O_7−x barrier layer uniformly covers the lower YBa₂Cu₃O_7−x layer. At the upper interface, however, it takes noticeably longer for the arrowed streaks of the upper YBa₂Cu₃O_7−x layer to reappear [Figs. 1(f) and 1(g)]. Furthermore, the time that it takes for the arrowed streaks of a-axis oriented YBa₂Cu₃O_7−x to reappear in going from the PrBa₂Cu₃O_7−x barrier to the YBa₂Cu₃O_7−x upper layer takes progressively longer for the thicker trilayers. This is consistent with the increased surface roughness seen by AFM in Fig. 3 as the thickness of the YBa₂Cu₃O_7−x layers increases.

In addition to the coherent and chemically sharp interfaces, some defects were observed by STEM. For example, intergrowths of an extra Cu–O layer intercalated into the YBa₂Cu₃O_7−x structure to locally form YBa₂Cu₄O_8−x (Fig. S7) are seen. Such intergrown layers are well-known and common in YBa₂Cu₃O_7−x—in bulk, thin-films, and heterostructures.^50–52 

The cross-sectional HAADF-STEM imaging also unveils the location of the cubic perovskite (Y,Ba)CuO_3−x phase detected in the XRD measurements. The thickness of the cubic (Y,Ba)CuO_3−x layer is found to be ∼10 nm, and it is located under the bottom YBa₂Cu₃O_7−x layer [Fig. S7(a)]. This cubic (Y,Ba)CuO_3−x layer forms at the start of growth when the substrate is coldest and surface diffusion is most constrained. Yttrium and barium are unable to diffuse sufficiently far to establish the Y–Ba–Ba–… ordered arrangement found in the unit cell of YBa₂Cu₃O_7−x; instead, yttrium and barium share the A-site of the resulting perovskite structure, with copper on the B-site.⁵³ 

As the temperature of the substrate is ramped, the diffusion lengths increase, and in-plane structural order emerges. The resulting a-axis YBa₂Cu₃O_7−x grains grow epitaxially in one of two symmetry equivalent orientations: with the c-axis parallel to either [010] or [001] of the cubic (Y,Ba)CuO_3−x layer on which they nucleate on the (100) LaAlO₃ substrate. One set of such domains is clearly seen in Fig. S7: the set with the c-axis along the horizontal direction of the image. The other set, with the c-axis oriented into the plane of the image, is more difficult to establish because the spacing of these domains along the horizontal direction is the same perovskite spacing as the cubic (Y,Ba)CuO_3−x layer on which these domains nucleated.

Our hypothesis is that the ∼10 nm thick cubic (Y,Ba)CuO_3−x layer only lies under the a-axis oriented YBa₂Cu₃O_7−x layer and that the regions in which this perovskite structure appears to extend further, i.e., through and all the way to the surface of the trilayer, are actually the set of a-axis domains oriented with the c-axis running into the plane of the image. This hypothesis is consistent with the grain size of the a-domains seen in the AFM images [Figs. 3(a)–3(d)] as well as published by others for a-axis YBa₂Cu₃O_7−x grown on (100) LaAlO₃.^{17,20,36,37,53,54} We know from the XRD ϕ-scans [Figs. 2(b) and S5] that there is an equal volume fraction of both 90° in-plane rotation twin variants, and although the volume sampled in our STEM investigation is small, this hypothesis is also consistent with our STEM observations. Once the substrate temperature is sufficiently high that the a-axis YBa₂Cu₃O_7−x grains nucleate, both twin variants continue through the entire YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayer.

Finally, in order to gain insights into the effect of c-axis grains in the trilayers, we perform additional cross-sectional STEM investigations on a less-ideal 32 nm/8 nm/32 nm sample. XRD shows the sample chosen to contain a higher volume fraction (16%) of c-axis oriented YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x (Fig. S8) and to have a higher rms roughness (> 1 nm) than the 32 nm/8 nm/32 nm trilayer characterized in Figs. 2–4. HAADF-STEM imaging (Fig. S9) of this less-ideal 32 nm/8 nm/32 nm trilayer confirms the presence of c-axis oriented grains in the structure and also demonstrates the rougher interfaces. Although the interfaces are rougher, STEM-EELS (Fig. S10) shows that they remain chemically abrupt. These results, when evaluated together, explain the rougher surfaces of the thicker samples. The formation of c-axis grains in the bottom YBa₂Cu₃O_7−x layer not only disturbs the PrBa₂Cu₃O_7−x layer (and interface) profiles, but also directly influences the top surface roughness by changing the local structural homogeneity in the first layers of the growth. The strong correlation between surface roughness and the volume fraction of c-axis grains in a-axis YBa₂Cu₃O_7−x films has been previously noted.⁴² To avoid c-axis oriented YBa₂Cu₃O_7−x, we initiate growth at a substrate temperature where only cubic (Y,Ba)CuO_3−x can nucleate.

In conclusion, we revisited the growth of a-axis YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers and were able to improve their structural quality. By leveraging a temperature-ramping procedure that begins with a cubic (Y,Ba)CuO_3−x buffer layer, we have grown high-quality a-axis trilayers as confirmed by ex situ XRD measurements. AFM investigations revealed an improved surface quality with an rms roughness that is less than ξ_a for the thinnest YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers. STEM analyses unveil the interrelation between c-axis oriented regions and surface roughness. Resistivity vs temperature measurements exhibit an onset of the superconducting transition at T_onset ∼ 85 K and also the widening of the superconducting transition width with decreasing YBa₂Cu₃O_7−x film thickness. Sharp and coherent interfaces with limited elemental intermixing are evidenced by atomic-resolution HAADF-STEM and STEM-EELS. Our findings suggest that with precise control of the growth conditions, the sharp interfaces and smooth surfaces required in a-axis-based YBa₂Cu₃O_7−x heterostructures for high-performance Josephson junctions and other oxide electronics are within reach.

See the supplementary material for details on the flux calibration method conducted immediately prior to the growth of the YBa₂Cu₃O_7−x/PrBa₂Cu₃O_7−x/YBa₂Cu₃O_7−x trilayers as well as additional characterization of the trilayers by RHEED, XRD, HAADF-STEM, and STEM-EELS.