Superconductivity-insensitive order at q~1/4 in electron doped cuprates

One of the central questions in the cuprate research is the nature of the"normal state"which develops into high temperature superconductivity (HTSC). In the normal state of hole-doped cuprates, the existence of charge density wave (CDW) is expected to shed light on the mechanism of HTSC. With evidence emerging for CDW order in the electron-doped cuprates, the CDW would be thought to be a universal phenomenon in high-$T_c$ cuprates. However, the CDW phenomena in electron-doped cuprate are quite different than those in hole-doped cuprates. Here we study the nature of the putative CDW in an electron-doped cuprate through direct comparisons between as-grown and post-annealed Nd$_{1.86}$Ce$_{0.14}$CuO$_4$ (NCCO) single crystals using Cu $L_3$-edge resonant soft x-ray scattering (RSXS) and angle resolved photoemission spectroscopy (ARPES). The RSXS result reveals that the non-superconducting NCCO shows the same reflections at the wavevector (~1/4, 0, $l$) as like the reported superconducting NCCO. This superconductivity-insensitive signal is quite different with the characteristics of the CDW reflection in hole-doped cuprates. Moreover, the ARPES result suggests that the fermiology cannot account for such wavevector. These results call into question the universality of CDW phenomenon in the cuprates.

Furthermore, substantial theoretical work has also been carried out 15,26 . These characterizations of CDW order in hole-doped cuprates have shed light on the essential physics underlying HTSC 14,15 .
Meanwhile, RSXS efforts in Nd 2-x Ce x CuO 4 and La 2-x Ce x CuO 4 have recently expanded these studies to the electron-doped cuprates, where they found putative CDW order in both systems 27,28 . This finding is an important step forward for understanding CDW phenomena in the high-T c cuprates. However, at the same time, there are many aspects of the feature (described below) that are distinct from those seen in the hole-doped cuprates 5-8, 16, 17, 27-29 : (1) the doping range of the observed CDW order extends well beyond the superconducting (SC) dome 28 [see Fig. 1(a)]; (2) the CDW onset temperature is much higher than the onset temperature (T * ) 27-28 of the mysterious pseudogap phase 29in general, the onset temperature of the CDW in hole-doped cuprates is lower than T *5-8, 11, 19 or similar with T *9, 22 ; (3) no temperature dependence of the correlation length is observed 27, 28 ; (4) there is no CDW response when SC is suppressed by an external magnetic field up to 6 Tesla 28 . These distinctions from the hole-doped cuprates leave open the question of the nature and origin of the putative CDW order, as well as its universality in high-T c cuprates.
In this work, we carried out comparative RSXS and angle-resolved photoemission spectroscopy (ARPES) studies of as-grown (non-superconducting) and post-annealed (superconducting) Nd 1.86 Ce 0.14 CuO 4 (NCCO) crystals, aiming to address such questions.
As reported in the previous studies 27, 28 , we could observe the putative CDW reflection at Q = (-1/4, 0, l) in the SC NCCO. Interestingly, we also found the same reflection in the non-SC NCCO. Corresponding ARPES results on both NCCO crystals demonstrate that a CDW arises for reasons that have nothing to do with the fermiology. Detailed RSXS studies indicate that this superconductivity-insensitive order in NCCO is in contrast to the hole-doped cuprates, in particular YBa 2 Cu 3 O 6+x (YBCO). These findings and corresponding implications support one of two possible scenarios proposed by da Silva Neto et al. 28 to understand this reflection's origin. These results also imply that the CDW is different in the electron-and hole-doped cuprates.

II. METHODS
Sample preparation -Dried powder Nd 2 O 3 , CeO 2 and CuO with the appropriate molar ratio were mixed and sintered in air at 1050°C for 24 hours with intermediate grindings.
The pre-fired powders were pressed under hydrostatic pressure to obtain cylindrical rods with a diameter of 6 mm and a length of 100 mm. Subsequently, the rod was sintered at 1200°C for 12 hours. A single crystal of Nd 1.86 Ce 0.14 CuO 4 was grown by the travelingsolvent floating-zone method using the sintered rod. A part of the crystal was annealed under Ar gas flow at 900°C which resulted in superconductivity with the transition temperature of ~25 K. The amount of oxygen removed by annealing was determined to be ~ 0.02 from the weight loss of the sample. A change in disorder of NCCO from the annealing-process was characterized by extended x-ray absorption fine structure (EXAFS) and x-ray diffraction measurements 30 . Experimental details of ARPES -ARPES measurements were carried out at beamline 5-2 of the SSRL using SCIENTA D80 electron analyzers with linearly polarized photons with a photon energy (E ph ) = 53 eV. All measurements were done in ultra-high vacuum (UHV) with a base pressure lower than 6 x 10 -11 Torr. The total energy resolution was set to 15 meV and the angular resolution was 0.3 o . All single crystals were cleaved in situ at 25 K for each ARPES measurement.

III. RESULTS AND DISCUSSION
We first investigate the annealed NCCO crystal using RSXS at the Cu L 3 -edge (931.0 eV) using similar measurements as the earlier work 27,28 . As shown in Fig. 1(b), we clearly observe the reflection, as reported previously 27,28 at the same in-plane wavevector (-0.26, 0). Next, we repeat the same measurements on the as-grown NCCO. Note that there is no SC phase in the as-grown sample [ Fig. 1(c)]. Nonetheless, we observe the same reflection at the same in-plane wave vector [ Fig. 1(d)]. Note that the as-grown (i.e. non-SC) NCCO, as well as the SC NCCO, was followed up a technically similar approach in the previous work 27, 28 , aiming to directly compare the putative CDW between the SC and non-SC samples.
To understand why the same reflection is present for both as-grown and annealed NCCO, we examine the correlation length and the intensity of the reflection as a function of temperature. Figure 2(a) shows data of as-grown NCCO at T = 30, 240, 300, and 380 K.
The background (black solid line) is the fit to the RSXS data at T = 380 K (see Methods).
However, even at room temperature, which is already much higher than T * (~ 80 K in annealed NCCO 33, 34 ), there is still a bump around (-0.26, 0, l) as presented in the annealed case 27,28 . Figure 2(b) summarizes the temperature dependence of the peak intensity (upper) and its width (lower) along with the results from the annealed NCCO.
Interestingly, the temperature behaviors in the both as-grown and annealed NCCO are indistinguishable. The peak intensity shows the same gradual development from 380 K, while the peak width is constant as a function of temperature [lower panel in Fig. 2 The estimated correlation length from a Lorentzian fitting function is 2/FWHM × (a/2π) ~ 15 Å, while the lattice constant of NCCO, a, is 3.95 Å. The estimated correlation length is just comparable to 1 period of the real space length (15.8 Å) of the proposed CDW with a q-vector ~ ¼. Even at T = 17 K, which is lower than the T c of the annealed NCCO, no change in the width is seen, indicating no interaction with its SC. This is also consistent with the implication from the reported scattering result with 6 Tesla 28 .
However, this field independence 28 in NCCO is in contrast to the strong enhancement of the CDW strength found in vortex cores of Bi-based cuprates 2 , which have a similar correlation length as NCCO. Furthermore, we performed 2θ-dependences of the peak in as-grown NCCO 30 , showing a strange behavior, which the in-plane h-vector shifts with varying 2θ-angle (i.e. at different l-vectors). These properties strongly contrast with the CDW order character observed in the hole-doped cuprates, in particular Y/La-based In Ref. [28], the authors proposed two possible scenarios for interpreting the scattering feature in annealed NCCO. First, a disorder-pinned scattering intensity could come from a CDW. The second scenario is that the reflection is a signature of fluctuations in the inelastic excitations. Considering that the annealing process removes oxygen from the crystal and generates secondary phases, superconducting NCCO should have more defects and disorder 35-38 . However, the scattering results in the as-grown and annealed NCCO crystals are nearly identical, despite the difference of the disorder -which was monitored by EXAFS and x-ray diffraction 30 . In the absence of quenched disorder (i.e., the very clean limit), a CDW phase has spontaneously broken symmetry. It appears below a sharply defined thermodynamic phase transition temperature, resulting in CDW order with zero width (infinite correlation length). In this limit, the scattering feature results from a strictly elastic (static) scattering structure factor. On the other hand, in the presence of disorder, this correlation length becomes finite. However, despite the difference in the strength of disorder between the as-grown and annealed NCCO, the estimated correlation length is identical. Therefore, changes in disorder from annealing are unlikely related to this reflection, conflicting with the first scenario in Ref. [28].
Moreover, a correlation between the fermiology and the CDW has been discussed in both hole-doped 9, 10 and electron-doped 27, 28 cuprates, and the possible importance (and some problems) of the Fermi surface (arc) instabilities for the CDW has been discussed 9, 10, 27, 28, 39 . Note that the superlattice peak in Bi-based cuprates is not relevant to this discussion. and as-grown [ Fig. 3(b)]. The distance between the parallel segments at k x ~ π, are estimated and summarized in Fig. 3(c). We find (h, k) ~ (0.283±0.002, 0) and (0.270±0.002, 0) for the annealed and as-grown NCCO, respectively. As expected, because of stronger AFM and the excess oxygen 35-38 , the distance in the as-grown sample is smaller than in the annealed sample. This observation is in good agreement with previous work reporting the annealing dependence of the Fermi surface [40][41][42] . Both in the annealed and as-grown samples, the wave vectors connecting the two Fermi surfaces at k x ~ π are larger than the in-plane wavevector of the scattering reflection [the vertical lines in Fig. 3(c)]. Apparently, the wavevectors connecting the hot spots due to either the Fermi arc formation by the pseudogap or (fluctuating) antiferromagnetism are even larger.
Furthermore, the annealing dependence on the nesting wave vector is in sharp contrast with the annealing independence of the reflection. Our direct comparison of the RSXS and ARPES data on the same set of samples makes it possible to conclude that the Fermi surface (arc), i.e. fermiology, is not directly relevant to the CDW. This conclusion is supported by recent numeric work 39 , which argues that Fermi surface nesting is unlikely to cause CDW formation in the high-T c cuprates.
Based on our findings which show the difference with the CDW features found in the hole-doped cuprates 5-11, 16, 17 , including the directly compared fermiology, the appreciation of the universality of CDW feature in cuprates still seems in early stage.
Concurrently, one raises the critical question -where does this reflection come from? In order to gain additional insight into this critical question, we study the energy dependence (i.e., resonant profile) of the reflections in both as-grown and annealed NCCO. while the feature at h ~ -0.26 is shifted to -0.27. Note that this shifting feature is more pronounced when a fluorescence background is eliminated 30 and the shifting value is much larger than the change in the real part of the atomic form factor (i.e. refractive index) as a function of the x-ray photon energy 44 . These facts, as well as its temperature dependence, contradict the idea that the CDW features from the hole-doped cuprates, in particular YBCO. To determine whether an elastic contribution coexists or not, it is worth doing that the high-resolution RIXS studies should be carried out in future work.

IV. CONCLUSION
In summary, we investigated the recently observed putative CDW scattering in the electron-doped superconducting NCCO using RSXS and ARPES measurements. We

S1: Disorder in NCCO before and after annealing
The superconductivity in NCCO emerges only after proper annealing process [1,2]. It is well known that this annealing process changes oxygen contents and forms secondary phases [2,3], although exact mechanism of the annealing is still under debate [4]. In this context, we performed the extended x-ray absorption fine structure (EXAFS) and x-ray diffraction measurements, aiming to monitor a change in disorder before and after annealing in our NCCO crystals. Figure S1 found that the annealed sample shows a larger anomaly at the low-temperature, which corresponds to static disorder [5]. This means that the annealing process creates more local disorder. In addition, using the lattice Bragg peaks (0 0 2) on both samples [see Fig.   S1(b)], we show that the annealed sample's peak becomes broader, consistent with the statement that the annealed sample has more defects (i.e. disorder). Therefore, these findings indicate the change of defects (i.e. disorder) in NCCO is caused by the post annealing-process.

S2: Angular (2θ) dependence in RSXS
Generally, the charge density wave (CDW) in hole-doped cuprates shows a quasi 2dimentioanl (2D) feature [6,7]. In other words, there is no (or weak) l-dependence in hk (or kl) reciprocal spaceAs shown in the YBCO case [ Fig. S2(left)], there is no shift of inplane k vector while the l-value is varying (i.e. a change in detector angles, 2θ). Note that all data are obtained by sample angle (θ) scans with fixed 2θ and the YBCO sample was the same ortho-VIII single crystal which was studied in Ref [8,9]. Strangely, in contrast to the hole-doped case, in NCCO case the in-plane h-value is shifted while the l-value is varying [ Fig. S2(right)]. Note that the peak position is larger than -0.26 r.l.u., because the detection angles are lower than 176 o which was used at the main text We note that this angular dependence was only measured in as-grown sample and this strange behavior may be shown only in as-grown sample. However, it is unlikely because other propertiestemperature dependence and energy dependence -are all similar in both samples. and as-grown NCCO (right). Black ticks indicate the fitted peak center.

S3: Energy dependence in RSXS
In NCCO case, it is very difficult to see a change of the peak (the putative CDW) when we change the photon energy. This is because the signal to background ratio is just less than 2 %. Furthermore, there is a huge background (e.g. 'fluorescence background') caused by the resonant process as a function of the photon energy. Thereby, in order to see such the small change during the change in photon energy, we need to plot the RSXS intensity after a proper background subtraction. Unfortunately, the detectors, such as photodiode, channeltron and CCD, in the general RSXS setups don't have an energy resolution (note: our RSXS setup is same). Therefore it is impossible to properly subtract the fluorescence background. However, we would alternately subtract a simple fluorescence background spectrum measured by the fluorescence yield (FY). After this subtraction, we plot Energy-Q map [ Fig. S3]. To confirm this simple subtraction's reliability, first we tested the map in YBCO which is generated by the subtraction process