Pair suppression caused by mosaic-twist defects in superconducting Sr2RuO4 thin-films prepared using pulsed laser deposition

Sr2RuO4 (SRO214) is a prototypical unconventional superconductor. However, since the discovery of its superconductivity a quarter of a century ago, the symmetry of the bulk and surface superconducting states in single crystal SRO214 remains controversial. Solving this problem is massively impeded by the fact that superconducting SRO214 is extremely challenging to achieve in thin-films as structural defects and impurities sensitively annihilate superconductivity. Here we report a protocol for the reliable growth of superconducting SRO214 thin-films by pulsed laser deposition and identify universal materials properties that are destructive to the superconducting state. We demonstrate that careful control of the starting material is essential in order to achieve superconductivity and use a single crystal target of Sr3Ru2O7 (SRO327). By systematically varying the SRO214 film thickness, we identify mosaic twist as the key in-plane defect that suppresses superconductivity. The results are central to the development of unconventional superconductivity. The pairing symmetry of superconducting Sr2RuO4 is debated, and analysis is complicated by difficulties in preparing high-quality thin films. Here, thin films of Sr2RuO4 are reproducibly grown by pulsed laser deposition with a Sr3Ru2O7 single crystalline target, and the structural defect responsible for the suppression of the superconductivity on thin films has been identified.

T he past decade has seen rapid developments in the understanding of unconventional superconductivity, particularly in proximity-coupled systems involving conventional s-wave superconductors in combination with magnetic materials and interfaces with strong spin-orbit coupling 1 . Highlights include the discovery of odd-frequency (s-wave) spin-triplet pairing at s-wave superconductor/ferromagnet interfaces 2-10 , evidence for electron-composite particle-antiparticles in nanowire devices with spin-orbit coupling and superconductivity 11,12 , and surface superconductivity in Au with Fermi-level tuning via a ferromagnetic dielectric 13 .
Parallel research on intrinsic unconventional superconductivity in superfluid He and in compounds such as Sr 2 RuO 4 (SRO 214 ) 14,15 has also made dramatic advances. Single crystal SRO 214 has a superconducting critical temperature 16 (T c ) of 1.5 K. Although the underlying nature of the superconducting state in SRO 214 crystals remains highly controversial, the consensus from experiments and theory is that the pairing is unconventional and potentially chiral p-wave state with the d-vector perpendicular to the basal plane 17 , which is even-frequency and conceptually different from the odd-frequency spin-triplet pairing induced at s-wave superconductor/ferromagnetic interfaces. Muon spin-relaxation measurements 18,19 on SRO 214 show evidence for time-reversal symmetry breaking below T c while early nuclear magnetic resonance spectroscopy 20,21 and polarized neutron scattering 22 experiments have demonstrated a constant in-plane spin susceptibility (Knight shift) below T c . However, a constant out-of-plane spin susceptibility below T c goes against a chiral p-wave state 17 . Furthermore, recent nuclear magnetic resonance spectroscopy on SRO 214 crystals show that the Knight shift decays in the superconducting state in the "3 K phase" under uniaxial stress as well as in the "1.5 K phase" without stress 23 , consistent with a d-wave or helical p-wave state.
Although there is a lack of experimental consistency in the underlying superconducting symmetry of SRO 214 , unconventional pairing states are expected on the surface due to broken inversion symmetry, which raises the prospect of coupling different superconducting symmetries via proximity effects with swave or even d-wave superconductors. Nevertheless, developing a full understanding of the superconductivity in SRO 214 including proximity-based experiments is fundamentally limited by the fact that thin-film growth of SRO 214 has proven to be extremely challenging. A robust, reliable, growth protocol for SRO 214 thinfilms is therefore required in order to break the deadlock and enable detailed studies of the electron pairing in SRO 214 and the mixing of different superconducting symmetries in hybrid Josephson junctions.
One of the key issues for growing superconducting films of SRO 214 relates to the destructive nature of magnetic or nonmagnetic impurities and structural defects. In thin-films, the concentration of impurities and structural defects tends to be high and superconductivity is suppressed or localized to pristine regions [24][25][26][27] . Currently, there exist only a few reports of superconducting SRO 214 thin-films, but control continues to be severely limited because the underlying materials properties required for superconductivity remain poorly understood. The first successful report of a superconducting thin-film of SRO 214 nearly a decade ago was fabricated by pulsed laser deposition from a stoichiometric (polycrystalline) target of SRO 214 on (0 0 1) (La 0.3 Sr 0.7 )(Al 0.65 Ta 0.35 )O 3 (LSAT) single crystals, and required high-temperature layer-by-layer growth 28 . This work was later reproduced by our group 29 in one sample albeit with an extremely broad (1.6 K) superconducting transition and an elevated T c of 1.9 K. This result indicated inhomogeneous superconductivity due to out-of-plane defects from stacking faults that create local strain, which locally enhances T c . Recently, superconducting films of SRO 214 have been grown by molecular beam epitaxy on LSAT with a T c of 1.1 K using a Ru-rich flux during growth to reduce Ru loss 30 . The T c was further enhanced to 1.9 K by depositing onto single terminated (1 1 0) NdGaO 3 due to the associated misfit strain 31 .
In this article we set out to develop a protocol for the reliable growth of superconducting SRO 214 thin-films by pulsed laser deposition and to establish and control key materials properties that are destructive for superconductivity. This is achieved using careful control of the starting material, which consists of a single crystal target of Sr 3 Ru 2 O 7 (SRO 327 ). We establish that mosaic twist is a universal structural (in-plane) defect that destroys superconductivity in SRO 214 . This is clearly different from the planar defects (out-of-phase boundaries) reported by Krockenberger 28 . By controlling the degree of mosaic twist in the SRO 214 films, and the associated dislocations that form at the SRO 214 /substrate interface, we demonstrate a reliable protocol for depositing superconducting SRO 214 .

Results
Growth optimization of SRO 214 thin films. A single crystal target of SRO 327 provides 33% Ru excess that compensates for Ru loss during the high-temperature growth of SRO 214 which, in conjunction with fine-control of laser fluence 32 (see Supplementary Fig. 1 for results using a polycrystalline target of SRO 214 ), reduces the volume fraction of impurity phases present in the films. The single crystal target of SRO 327 (see compositional analysis in Supplementary Fig. 2a) has a surface area of 3 × 10 mm 2 and is mounted on a polycrystalline SRO 214 holder (Fig. 1a). Laser alignment is optimized by focusing the laser spot (1.5 mm diameter) onto the SRO 214 holder prior to ablating from the SRO 327 target. During film growth, the rotation of the SRO 327 target is fixed and the target carousel is twisted through an angle β to erode the SRO 327 target along a line (Fig. 1b). All SRO 214 films discussed in this paper are deposited onto heated (950°C) LSAT (0 0 1) as described in the Methods section. Most of the films are grown using a laser pulse frequency of 2 Hz with one sample grown at 4 Hz as discussed at the end of the paper. To minimise in-plane epitaxial strain, SRO 214 (in-plane lattice constant = 0.3873 nm) is grown on LSAT (in-plane lattice constant = 0.387 nm) substrates, and a substrate miscut angle of less than 0.05˚is used to reduce the concentration of out-of-plane stacking faults at step edges.
We first discuss the effect of varying oxygen pressure (P O2 ) during growth. SRO 214 films are grown using a fixed number of laser pulses (5000) at 2 Hz and laser fluence of 1.0 J cm −2 to achieve a thickness (t) around 23 nm (depending on P O2 ). Values of t are estimated by fitting thickness fringes to the (0 0 6) diffraction peak of SRO 214 (see Supplementary Note 1 and Supplementary Fig. 3). In Fig. 1c we have plotted X-ray diffraction traces from three representative SRO 214 films grown using 1.0 Pa, 0.35 Pa and 0.09 Pa of oxygen. For the P O2 = 1.0 Pa film, thickness fringes are barely visible on the (0 0 6) 214 peak and an SRO 327 impurity phase is present (highlighted in green). The P O2 = 0.35 Pa film, however, shows no detectable evidence for SRO 327 or other impurity phases and the (0 0 6) 214 peak shows clear fringes, indicating uniform growth. Reducing P O2 further to 0.09 Pa promotes secondary phases in the Ruddlesden-Popper series (indicated by magenta) such as SRO 327 , SRO 4310 or RuO 2 . While thin films deposited above or below P O2 = 0.35 Pa show metallic behavior with no detectable evidence for superconductivity down to 300 mK, the P O2 = 0.35 Pa film shows a downturn in R(T) below 0.5 K, consistent with the onset of incipient superconductivity ( Supplementary Fig. 4a). The corresponding lattice parameters are a = 0.3870(3) nm (from RSM on (2014) plane) and c = 1.2738(17) nm (from a 2θ-ω scan on the (0 0 l) peak positions after applying a correction for sample displacement).
Using P O2 = 0.35 Pa, we now discuss the effect of laser fluence on the structural and electrical properties of SRO 214 . In Fig. 1d we have plotted X-ray diffraction traces from three films grown using laser fluences of 0.75 J cm −2 , 1.0 J m −2 and 1.4 J cm −2 , with a fixed number of laser pulses (5000). The traces show sharper peaks with decreasing laser fluence, indicating improved structural properties (vertical microstrain). The in-plane resistance versus temperature R(T) for the 1.4 J cm −2 film saturates to a constant minimum below 10 K with no evidence for superconductivity down to 300 mK. In contrast to the 1 J cm −2 film, the 0.75 J cm −2 film shows sharper diffraction peaks, but a downturn in R(T) is not observed, even down to 300 mK ( Supplementary Fig. 4b). This is likely due to the lower laser fluence reducing Ru ablation from the SRO 327 target 32 and hence, the SRO 214 film is deficient in Ru, which prevents superconducting behaviour 29,30 .
Characterization of superconducting properties. We now discuss electrical transport of SRO 214 films versus t in the 15 nm to 166 nm range using optimized growth parameters (oxygen pressure of 0.35 Pa and fluence of 1.0 J cm −2 ). For each film we investigate R(T) and for those that show a superconducting transition, we define T c as the temperature halfway through the resistive transition. In Fig. 2a we have plotted T c (t) where the vertical error bars represent the temperature width of the superconducting transition (See Supplementary Fig. 5). These data show a critical thickness for superconductivity of approximately 50 nm with T c rising to 1.05 K for t = 166 nm (Fig. 2a). Although the largest T c is lower than the T c of bulk SRO 214 single crystals (1.5 K 16 ), T c values are higher than previous reports for SRO 214 films grown by pulsed laser deposition ( Supplementary  Fig. 6a).
In Fig. 2b we have plotted the t-dependence of the residual resistivity ratio (RRR), defined at the resistance at room temperature divided by the saturated minimum in resistance at low temperature before the onset of superconductivity. RRR(t) broadly divides into two regimes: for t < 50 nm, RRR is low (<30) with metallic transport down to 300 mK (highlighted in red); for t > 50 nm, RRR rapidly increases with increasing t with superconducting transport at low temperature (highlighted in blue). The low RRR(t) values in the metallic regime cannot be simply explained on the basis of a thin-film effect or t approaching the out-of-plane superconducting coherence length of SRO 214 which we estimate to be ξ c~3 -8 nm (see Fig. 2c and Supplementary Note 2). The metallic regime indicates a large density of defects due to impurity phases in conjunction with structural defects (e.g. mosaic tilt or mosaic twist), consistent with the high (low) values of residual resistivity (ρ 0 ) for the films with a low (high) RRR as shown in Fig. 2d. In the superconducting regime, RRR reaches 110 for t = 100 nm, which is high relative to equivalently-thick SRO 214 films reported elsewhere ( Supplementary Fig. 6b).
Analysis of the microstructure. To identify the underlying mechanisms which suppress superconducting behavior in SRO 214 films, we have systematically investigated the potential presence of structural defects that may affect long-range crystal order. We first discuss scanning transmission electron microscopy (STEM), high resolution scanning transmission electron microscopy (HR-STEM) and energy-dispersive X-ray (EDX) maps acquired on a SRO 214 superconducting film (Fig. 3a-f) and a metallic film (Fig. 3g-l) (see Methods). We compare STEM (Fig. 3a, g) and HR-STEM micrographs which demonstrate coherent c-axis growth (Fig. 3b, l). For those films that show a full superconducting transition, the micrographs reveal inclusions near the SRO 214 /LSAT interface (Fig. 3a). These crystalline (Fig. 3f) inclusions are elemental Ru (Fig. 3c-e) or Ru oxide (Supplementary Fig. 7) and spaced over distances larger than ξ ab and so should not directly affect T c .
For the SRO 214 films that do not show a full superconducting transition, STEM maps consistently reveal a 1-2-nm-thick region above LSAT (indicated with an arrow) that has mixed stoichiometry (Fig. 3g). STEM-EDX confirms that this region has the correct Sr atomic concentration for SRO 214 , but is deficient in Ru and rich in O (Fig. 3i-k). This is further confirmed by HR-STEM on different areas of the film (Fig. 3h,l), which show atomic layers of decreased concentration of heavy atoms, and stoichiometric SRO 214 layers above and below this region (Fig. 3g)  33 ). This depleted region most likely forms due to a separation of the Ruddlesden-Popper phase of SRO 214 into layers of SRO 113 or SRO 327 34 (ferromagnetic and paramagnetic, respectively, with a perovskite structure), and SrO (rock salt unit cell). In the oxidizing atmosphere used during growth, SrO can stabilize into SrO 2 leading to O-rich and Rudeficient regions matching the results extracted from EDX at the interface.
We note that SRO 113 and SRO 327 impurities are an issue for SRO 214 single crystals since the ferromagnetic exchange field of these phases can suppress superconductivity 26 . To investigate the presence of SRO 113 as well as SRO 327, we have measured the temperature dependence of the magnetic moment m(T) of the non-superconducting SRO 214 films (Supplementary Fig. 8). We compare these data to a control sample of bare LSAT that has been exposed to matching conditions as SRO 214 /LSAT films during growth but without SRO 214 deposited on the LSAT. m(T) shows no evidence for SRO 113 since no ferromagnetic transition 35 is observed at or below the expected Curie temperature of 160 K or a maximum at 16 K due to SRO 327 (Supplementary Fig. 8a). We also investigated magnetization hysteresis loops m(H) at a range of temperatures (20-300 K) with the applied field (H) directed normal to the LSAT substrate. For all T investigated, m is constant and matches the moment of bare LSAT within an error of 1 μemu (Supplementary Fig. 8a inset and 8b). This rules out the presence of ferromagnetic SRO 113 and would explain the XRD peak marked as "*" in Fig. 1c corresponding to SRO 327 . Nevertheless the SRO 327 is not consistently observed and its presence/absence does not correlate with superconductivity. The possible SRO 327 phase would be concentrated at the SRO 214 /LSAT interface in the initial growth, considering the thickness dependence of our superconducting films. Such intergrowth could be controlled later by changing the dynamic nature of PLD. Further studies are highly desirable. Additionally, since STEM-EDX confirms stoichiometric Ru content 36 on the SRO 214 thin films (see example in Supplementary Fig. 2b), our study focuses on the analysis of structural defects that could alter the superconducting transition.
Degree of tilt and twist. Another potential source of crystallographic defects that may suppress superconductivity relate to misoriented crystalline regions. This can be visualized with the mosaic crystal model, in which the film is described as the combination of smaller crystallites (blocks), misoriented with respect to each other and the substrate. A rotation of these blocks about an axis parallel to the surface is known as mosaic tilt, and a rotation about an axis perpendicular to the surface is known as mosaic twist. Tilted and twisted blocks are separated by low-angle grain boundaries consisting of dislocations, which can be edge-or screw-like, with a Burgers vector (b) perpendicular or parallel to the dislocation line vector (u), respectively (see Supplementary  Fig. 9), and cause local variations of interplanar distance (microstrain) at grain boundaries. Tilt can be measured from the full width half maximum in omega (FWHM ω ) of the (0 0 l) diffracting planes by X-ray diffraction in a symmetric (coplanar) geometry. Values of tilt extracted from SRO 214 films with different t show that all films (superconducting or non-superconducting), with the exception of one, have similar values of tilt. Tilt does not therefore affect the electrical properties SRO 214 films (see Supplementary Fig. 10a-c). . Filled squares correspond to films grown with a laser frequency of 2 Hz and the hollow square at 4 Hz. c Superconducting coherence length in-plane ξ ab (orange squares) and out-of-plane ξ c (green squares) for multiple films versus t, determined from resistivity versus temperature measurements with a magnetic field applied along the ab-plane or the c-axis directions, respectively. d T c versus residual resistivity ρ 0 for superconducting and metallic films marked as in (a) and (b). In all plots, background shading indicates a full superconducting transition (blue) or metallic (red) behaviour at low temperatures with or without incipient superconductivity.
Twist can be measured using four different configurations: edge [by measuring the (h k 0) planes from the FWHM ω with an offset in chi (χ offset ) of 90˚ (Fig. 4a)]; glancing angle in-plane; transmission; or skew geometry 37 . For our thin-film geometry we adopt the skew geometry (non-coplanar) configuration because the signal intensity is the strongest, and measure the FWHM ω of the (4 1 3) diffracting planes, which provides a good estimate of twist due to the large χ offset (>70˚) 37,38 . The dependence of twist, FWHM ω extracted from a pseudo-Voigt profile fit after the subtraction of the instrumental contribution (see Supplementary Note 3), on t is shown on Fig. 4a. Since the in-plane crystallite size (L || ) is of the order of micrometres, its contribution to peak broadening is negligible (see Supplementary Fig. 10a). We observe that FWHM ω (Fig. 4b inset), and hence the degree of twist, rapidly rises as t decreases below 50 nm, corresponding to the metallic films that do not show full superconducting transition (Fig. 4b). From Fig. 4c we demonstrate a direct correlation between twist and the suppression of superconductivity by a reduction (increase) of T c (residual resistivity) when the degree of twist increases.
Identification of dislocations. The increase in twist with decreasing t (Fig. 4b) indicates a higher concentration of dislocations with b in-plane at low t for non-superconducting films.
To confirm this and determine the nature of the dislocations, we have performed g Á b TEM analysis, with g being the diffracted beam direction on a superconducting and non-superconducting film. In g Á b TEM analysis, dislocations are in-contrast (visible) when g Á b ≠ 0, but out-of-contrast (invisible) for g Á b = 0 39,40 as illustrated in Fig. 4a. Figure 4d-o shows g Á b bright field TEM analysis performed on three different cross-sectional areas for the superconducting and non-superconducting films using two perpendicular diffraction vectors g 00l and g h00 . The nonsuperconducting films shows a larger concentration of dislocations compared to the superconducting film. Furthermore, for the nonsuperconducting film the dislocations are mostly in-plane and screw-like with both u and b in-plane (horizontal orange arrow), as they can only be resolved when b || g h00 (Fig. 4d-f) and are extinct when b ⊥ g 00l (Fig. 4g-i). These results are consistent with the high degree of twist observed in non-superconducting films and therefore demonstrate that horizontal screw dislocations are a key defect that strongly suppresses superconductivity in SRO 214 . In contrast, the lower density of dislocations present in the superconducting film are in-plane edge-like with u in-plane and b out-of-plane (vertical orange arrow), as they are visible when b || g 00l (Fig. 4j-l) and not visible when b ⊥ g h00 (Fig. 4m-o). In both the superconducting and non-superconducting films, a few threading mixed dislocations, with both edge and screw components (tilted orange arrow) are resolved with both g 00l and g h00 . The presence of threading dislocations with a screw component is also revealed in topographic images acquired using an atomic force microscope (Supplementary Fig. 10d-g). We note that, we cannot confirm that the white contrast in Fig. 3j located in the Ru-deficient layer (confirmed in Fig. 4g-i), is also dislocation related as it might be the result of a combination of features such as Ru-deficiency, interface effect and dislocations.
Finally, we note that the superconductivity in SRO 214 can be further optimized by tuning additional growth parameters (not discussed in this paper) such as deposition frequency. We have tested the effect of doubling the laser pulse frequency to 4 Hz during SRO 214 growth, while keeping the same growth conditions as for the rest of the study (oxygen pressure of 0.35 Pa, fluence of 1.0 J cm −2 , 950°C), which has the effect of reducing the degree of twist (Fig. 4b) and the residual resistivity (Fig. 2d), and increasing T c (Fig. 3a) and RRR (Fig. 3b), compared to equivalent films grown at 2 Hz.

Discussion
In conclusion, we have systematically investigated the structureelectrical-properties relationship of SRO 214 thin-films grown on LSAT by pulsed laser deposition from a single crystal SRO 327 target. The absence of superconductivity in films thinner than 50 nm is correlated with the in-plane misorientation mosaic twist, caused by in-plane screw dislocations, and with the most defective region near the SRO 214 /LSAT interface. The application of single crystal SRO 327 targets offers a robust reliable platform for the creation of superconducting SRO 214 thin-films and will initiate experimental studies involving multilayer structures and devices based on this highly important superconducting oxide.

Methods
Substrate preparation and growth. SRO 214 films are grown by pulsed laser deposition onto 5 × 5 × 0.5 mm 3 single crystal (0 0 1) (LaAlO 3 ) 0.3 -(Sr 2 AlTaO 6 ) 0.7 (LSAT) with miscut angles of less than 0.05°. Prior to loading into the pulsed laser deposition chamber, the LSAT substrates are ultrasonicated for 10 min in acetone followed by 10 min in isopropyl, and subsequently dried using nitrogen gas. The LSAT substrates are attached to a SiC crystal (10 × 10 mm 2 ) with Pt paste (Tanaka Kikinzoku Kogyo K.K.) and secured with clips onto the substrate holder. The LSAT substrates are pre-baked for 30 min at 250°C in vacuum in the load-lock chamber. In the main chamber, the LSAT is annealed in ultra-high vacuum (7.5e-6 Pa) for 30 min at 950°C to promote terrace formation, with a warming ramp rate of 50°C min− 1 . The SRO 214 films are grown in different oxygen pressures and KrF excimer laser (LPXpro 210 F Coherent Inc. 248 nm) energies as discussed in the main paper with the LSAT substrate temperature maintained at 950°C using an infrared diode laser heater. The SRO 214 films are deposited by ablating from a single crystal target of SRO 327 at a repetition rate of 2 Hz for the majority of the samples prepared in this work (or 4 Hz for one film) and a substrate to target distance of 5 cm. Following film growth, the sample is cooled in oxygen at a rate of 50°C min −1 .
Target preparation. Single crystal targets of SRO 327 are prepared by floating zone method as discussed in refs. 41,42 . These are cleaved in isopropyl and ultrasonicated for 10 min in acetone and then 10 min in isopropanol and subsequently dried using nitrogen gas. The cleaved crystals have a volume of approximately 3 × 10 × 0.5 mm 3 . The surfaces of the crystals are examined by optical microscopy with polarized light to confirm a low concentration of Ru and SRO 113 surface impurities. The SRO 327 target is attached to a holder (polycrystalline SRO 214 ) using Epoxy-Ag paste and cured for 30 min at 150°C. Prior to loading it into the pulsed laser deposition main chamber, the SRO 327 target is baked for 30 min at 250°C in vacuum in the load-lock.
Transport and magnetic measurements. Electrical transport measurements are performed in a pulsed tube cryogen free physical property measurement system. Electrical resistance is measured using a current-bias four-point electrical setup with Au contact pads evaporated onto the SRO 214 surface.
X-ray diffraction. X-ray diffraction data were acquired using a Panalytical Empyrean X-ray diffractometer, with a Cu Kα1 X-ray source and a hybrid two bounce primary monochromator.
Transmission electron microscopy. Samples for transmission electron microscopy are prepared using focused ion beam milling. Bright field transmission electron microscopy imaging for g Á b analysis is performed using an FEI Tecnai Osiris at 200 kV. Compositional mapping is carried out using scanning transmission electron microscopy (STEM)energy dispersed X-ray spectroscopy (EDX) in the same instrument, employing a Super-X detector with a total collection solid angle of 0.9 sr. High resolution STEM images are acquired on a probe-corrected FEI Titan operated at 300 kV. Fig. 4 Nature of dislocations and their effect on superconductivity in Sr 2 RuO 4 films. a An illustration of an edge dislocation with an out-of-plane line vector u (grey arrow) and Burgers vector b in-plane (orange arrow) on the (h 0 0) planes of SRO 214 . The diagram also shows the X-ray diffraction setup in edge geometry (Tilt angle of the sample stage χ offset = 90˚) to measure the in-plane misorientation, twist, from the peak broadening in ω (angle between the X-ray incident beam and the diffracted planes) due to variations in the scattering direction (white and yellow arrows). Transmission electron microscopy TEM g Á b analysis to reveal edge dislocations using bright field imaging with two perpendicular diffraction conditions (g 00l and g h00 ) is also shown. b Degree of twist versus thin-film thickness t, determined from the full width half maximum in ω FWHM ω , measured from χ offset~7 8˚in skew symmetric on the (4 1 3) planes (inset curves are vertically offset for clarity). c, Superconducting critical temperature T c versus and resistivity ρ versus twist (inset). d-o g Á b analysis by bright field TEM showing dislocations on three areas of a lamella from metallic (d-i) and superconducting (j-o) SRO 214 films (marked as three asterisks in b and c). The diffraction vectors g 00l and g h00 are indicated by green arrows and b by orange arrows: for in-plane edge dislocations the arrows are horizontal, for out-of-plane screw dislocations the arrows are vertical, and for mixed dislocation the arrows are tilted. The interface film/substrate interface is marked with a yellow dotted line. Scale bar in d-o, 50 nm.