Anomalous High-Energy Waterfall-Like Electronic Structure in 5 d Transition Metal Oxide Sr2IrO4 with a Strong Spin-Orbit Coupling

The low energy electronic structure of Sr2IrO4 has been well studied and understood in terms of an effective Jeff = 1/2 Mott insulator model. However, little work has been done in studying its high energy electronic behaviors. Here we report a new observation of the anomalous high energy electronic structure in Sr2IrO4. By taking high-resolution angle-resolved photoemission measurements on Sr2IrO4 over a wide energy range, we have revealed for the first time that the high energy electronic structures show unusual nearly-vertical bands that extend over a large energy range. Such anomalous high energy behaviors resemble the high energy waterfall features observed in the cuprate superconductors. While strong electron correlation plays an important role in producing high energy waterfall features in the cuprate superconductors, the revelation of the high energy anomalies in Sr2IrO4, which exhibits strong spin-orbit coupling and a moderate electron correlation, points to an unknown and novel route in generating exotic electronic excitations.

that has been reached is Sr 2 IrO 4 being a typical system where the Mott-and slater-type behaviors coexist. In addition, Sr 2 IrO 4 has attracted much attention because it exhibits a number of similarities to the parent compound La 2 CuO 4 of high temperature cuprate superconductors in the crystal structure, electronic structure, magnetic structure, and even possible high temperature superconductivity that is predicted in doped Sr 2 IrO 4 23,24 .
Angle-resolved photoemission spectroscopy (ARPES) is a powerful tool to directly probe the low energy electronic structures of solid materials 25 . While the ARPES results on Sr 2 IrO 4 and related compounds within a relatively narrow energy window agree with the J eff = 1/2 Mott insulator model 7,[13][14][15]18 , little work has been done in studying its high energy electronic behaviors. In this paper, we report the observation of unusual high energy bands in Sr 2 IrO 4 . Our comprehensive angle-resolved photoemission study over a wide energy window reveals for the first time nearly-vertical bands in Sr 2 IrO 4 . Such exotic bands cannot be understood in terms of the band structure calculations; they cannot be understood within the J eff = 1/2 Mott insulator model either. The observed high energy anomaly resemble the unusual high energy waterfall bands discovered in the high temperature cuprate superconductors [26][27][28][29][30][31][32][33][34][35] . These observations point to the significant role of the strong spin-orbit coupling, together with a moderate electron correlation, in giving rise to new high energy excitations in the 5d transition metal oxides. Figure 1 shows the constant energy contours of Sr 2 IrO 4 at different binding energies. No spectral weight is present at the Fermi level (not shown in Fig. 1), consistent with the insulating nature of Sr 2 IrO 4 [5][6][7] . At a binding energy of 0.2 eV, the spectral weight appears first as a circular spot around the X(π, 0) and its equivalent locations (Fig. 1a). Further increase of the binding energy to 0.4 eV results in the enlargement of the spot into a square-shape and the emergence of spectral weight near the Γ (0, 0) point (Fig. 1b). When the binding energy increases to 0.8 eV, the strong spectral weight near X points vanishes with a formation of a few disconnected patches around X, while the spectral weight near Γ exhibits a petal-like shape with four leaves (Fig. 1c). The measured constant energy contours at low binding energy (0 ~ 0.4 eV) are consistent with those reported before 7,14 . The constant energy contours at an intermediate binding energy (e.g., 0.4 eV) are also consistent with the band structure calculations (Fig. 1d) that include both the on-site Coulomb repulsion U and the spin-orbit coupling 7 . In terms of the spin-orbit-coupling-driven Mott insulator model 7 , the unoccupied states are mainly the J eff = 1/2 state, while the occupied states are a mixture of the J eff = 1/2 and 3/2 states. Due to the strong spin-orbit coupling, the topmost low energy valence state at X is more with J eff = 1/2 character (β sheet near X in Fig. 1d), while the topmost low energy valence state at Γ is more with J eff = 3/2 character (α sheet near Γ in Fig. 1d) 7 . The consistency of the low energy electronic structure with the previous reports and the band structure calculations lays a foundation for our following investigation of high binding energy electronic structure in Sr 2 IrO 4 .
At high binding energies, we find that the electronic structure of Sr 2 IrO 4 is quite unusual. Figure 2 shows band structure along two high-symmetry momentum cuts covering a large energy range till ~6 eV: one cut is across Γ (Fig. 2a-d), the other is across X (Fig. 2e-h) (for more momentum cuts, see Fig. S1, S2 and S3 in Supplementary Materials). Here we show both the original data (Fig. 2a,e), and their corresponding momentum- (Fig. 2b,f) and energy-second-derivative (Fig. 2c,g) images. The second-derivative images help to highlight the band structure more clearly although many features are already clear in the original data. Since momentum-second derivative image may miss the flat horizontal bands while the energy-second derivative image may miss the vertical bands, the energy-and momentum-second-derivative images are complementary to each other to provide a full picture. As seen in Fig. 2, at low binding energy (0 ~ 1 eV), two prominent bands are observed labeled as α 0 and β 0 (Fig. 2c,g) that are consistent with the previous reports 7, 14 . However, at higher binding energy, the electronic structure becomes quite unusual. First, the momentum-second derivative images and energy-second-derivative images give rather different band structures for both the Γ and X momentum cuts. Second, as seen in Fig. 2b, a clear vase-shaped band (labeled as α 1 in Fig. 2b) and a vertical waterfall-like band (labeled as α 2 in Fig. 2b) are observed around the Γ point. The vertical band structure is present even beyond 3 eV up to ~6 eV (Fig. 2b). Note that these features are not due to the artifact of the momentum second-derivative image because they are already clear in the original data (Fig. 2a). Such features can also be identified clearly in the momentum distribution curves (MDCs) where the peaks corresponding to α 1 and α 2 bands are marked (Fig. 2d). Similar behaviors are observed for the momentum cut across the X point ( Fig. 2e) where nearly vertical band structures (labeled as α 3 and β 1 in Fig. 2f) are observed up to 4 eV, and another set of vertical bands are seen even up to 6.5 eV (Fig. 2f). We note that such a high energy band anomaly was not revealed before because the previous ARPES measurements cover a relatively small energy range (0 ~ 2 eV) 7, [13][14][15]18 . In fact, upon careful examination, some indications of the high energy waterfall-like features appear to be present in a recent ARPES study on Sr 2 IrO 4 18 which are consistent with our results. The unusual high energy electronic structure of Sr 2 IrO 4 is present over a large momentum space. Figure 3 shows the detailed momentum evolution of the high energy electronic structure: one is near the Γ region ( Fig. 3a-d) and the other near the X(0, π) region ( Fig. 3e-h). While the energy-second-derivative images (Fig. 3d,h) show normal two bands (α 0 and β 0 ) in the covered energy range as already seen in Fig. 2, nearly vertical bands are observed in the momentum-second-derivative images (Fig. 3c,g) in both cases for different momentum cuts. Furthermore, the constant energy contours exhibit dramatic evolution with the binding energy (Fig. 3a,e). The spectral weight distribution around the Γ point ( Fig. 3a) changes from a pocket centered at Γ at a binding energy of 0.4 eV, to butterfly-shaped at 0.6 eV and 0.8 eV, to big-X-shaped at 1.2 eV and to dumbbell-shaped at 2.0 eV and 2.4 eV. It is interesting to note that the spectral weight distribution shows discrete four strong spots at 0.6 eV and 0.8 eV, other than a continuous contour. From Fig. 3c,d, it becomes clear that the drastic spectral distribution change with the binding energy above 1.0 eV is directly related with the presence of the nearly-vertical α 1 and α 2 bands. It is also clear from Fig. 3b that, moving away from the cut across Γ (cut 1), the vase-shaped band and vertical structure persist for the cuts 2 and 3. The same is true for the X point constant energy contours (Fig. 3e) and the momentum-dependent band structures (Fig. 3f-h). First, the constant energy contours near X also exhibit an obvious evolution with the binding energy (Fig. 3e). Second, the vertical bands are present over a large area of momentum space near X (Fig. 3g).   (Fig. 4a,b). In the calculated band structure (Fig. 4a), the electronic states between the Fermi level and 3 eV binding energy are mainly from the Iridium's t 2g orbitals (white lines in Fig. 4a) while above 3 eV binding energy the contribution is mainly from the oxygen p orbitals (yellow lines in Fig. 4a). In addition, the orbital-resolved density of states (DOS) is also calculated where the peak position of α 0 and β 0 bands are well resolved (Fig. 4b). In the measured band structure, from the energy-second-derivative image (Fig. 4d), two bands are clearly observed that are marked as α 0 and β 0 between E F and ~1 eV binding energy. These two bands show good agreement with the band structure calculations (Fig. 4a) and previous reports 7-14 . Also above 3 eV binding energy, the observed bands in the energy-second-derivative image (Fig. 4d) can find some good correspondence in the calculated band structure (Fig. 4a). The most dramatic difference between the measurements and calculations lies in the binding energy region above 1 eV. As seen in Fig. 4a, a couple of energy bands from Iridium are expected from the band structure calculations within the energy range of 1 ~ 3 eV but are not observed in the measured data (Fig. 4d). Instead, a number of nearly-vertical band features (α 1 , α 2 , α 3 and β 1 bands in Fig. 4e) appear within this energy range that are completely absent in the calculated band structure (Fig. 4a). The same is for the 3 ~ 6 eV binding energy range where some vertical bands are observed (Fig. 4e) but are not present in the calculated band structure at all (Fig. 4a).
Further inspection of the measured band structure indicates that the new nearly-vertical high energy bands appear to have a close connection with the lower energy α 0 and β 0 bands, as shown in Fig. 4c which summarizes all the observed bands on top of the original measured data. One can see that the three vertical bands α 1 , α 2 and α 3 merge into the α 0 band at lower binding energy while the other vertical band β 1 also merges into the lower binding energy β 0 band. The low-energy electronic structure of Sr 2 IrO 4 are mainly composed of t 2g bands that are split into two branches with the effective J eff = 1/2 and J eff = 3/2 because of the strong spin-orbit coupling 7 . It has been shown that the β 0 band is predominantly with the J eff = 1/2 character while the α 0 band is mainly with the J eff = 3/2 character (Fig. 4a,b) 7 . It is interesting to note that one vertical band (β 1 ) emerges from the J eff = 1/2 β 0 band while three vertical bands (α 1 , α 2 and α 3 ) emerge from the J eff = 3/2 α 0 band (Fig. 4c), consistent with the orbital degeneracy of both the J eff = 1/2 and 3/2 bands. These observations indicate the multi-orbital nature of the low energy electronic states in Sr 2 IrO 4 . In both the J eff = 1/2 and 3/2 bands, we have observed such waterfall-like features splitting out of the original bands, this means that the high energy anomaly in Sr 2 IrO 4 is a general feature appearing for all orbitals over a rather high energy scale.
To the best of our knowledge, such unusual high energy waterfall-like electronic structures are observed for the first time in Sr 2 IrO 4 . The appearance of nearly-vertical bands is quite unusual because it implies nearly infinite electron velocity if interpreted literally in the conventional band structure picture. This is reminiscent to the high energy waterfall feature observed in the high temperature cuprate superconductors [26][27][28][29][30][31][32][33][34][35] . The high energy behaviors are similar between the cuprates and Sr 2 IrO 4 in a couple of aspects. First, the energy-and momentum-second-derivative images give different band structure 27,33 . For a conventional metal, the energy-and momentum-second-derivative images are supposed to produce similar band structure. The dichotomy between them already points to an exotic behavior and the effect of strong correlation. Second, nearly vertical bands are observed in the momentum-second-derivative images. The behavior in Sr 2 IrO 4 is even more dramatic in that several bands show such waterfall-like high energy features (Fig. 4e) while only one band in cuprates shows such a behavior [26][27][28][29][30][31][32][33][34][35] . Moreover, the high energy features in Sr 2 IrO 4 extend over a much larger energy range (1 ~ 3 eV for Ir states) (Fig. 4) while it is in the scale of 0.4 ~ 1 eV in cuprates [26][27][28][29][30][31][32][33][34][35] . The high energy behavior in Sr 2 IrO 4 is even more complicated, such as the observation of a vase-like shape near the Γ point ( α 1 band Fig. 2a,b).
The revelation of the high energy waterfall-like bands in Sr 2 IrO 4 provides another system that can be used to compare and contrast with the cuprates in order to understand the origin of the high energy anomaly. In the cuprate superconductors, the high energy anomalous band has attracted extensive experimental [26][27][28][29][30][31][32][33][34][35] and theoretical interest [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] although there has been no consensus reached on its origin. The prime candidate for the anomalous high energy behavior can be simply an intrinsic property of a strong electron correlation system or Mott physics 30,36,38,[44][45][46]48,49,51,52 . The second possibility is due to quasiparticle scattering with some electronic or bosonic excitations, such as phonons 28 , plasmons 39 , paramagnons 29,40,42,49 , and other spin and charge excitations 53 . It can also be due to other novel effects such as the spin-charge separation 27 , spin polarons 37 , photoemission matrix element effect 32 , charge modulations 41 , quantum critical fluctuation 43 , in-gap band-tails 47 and so on. Compared with the cuprates where there is a strong electron correlation (5-7 eV) 2,19,54 , the electron correlation in 5d transition metal oxide Sr 2 IrO 4 is much weaker (1 ~ 3 eV) owing to the much extended 5d orbitals 7,19 . On the other hand, due to heavier atomic mass, the spin-orbit coupling becomes an order of magnitude stronger(~0.4 eV) 4,7,19,55,56 in the 5d transition metal oxides than that in their 3d counterparts (~20 meV), reaching a comparable energy scale with the on-site Coulomb repulsion U and the bandwidth W 7,55 . This indicates that the spin-orbit coupling provides a novel tuning parameter in dictating the ground state and physical properties of the 5d transition metal oxides. While the strong electron correlation plays an important role in producing high energy anomaly in the cuprate superconductors, the observation of the high energy anomaly in Sr 2 IrO 4 provides a new scenario where the high energy anomaly can be observed in a system with a moderate or weak electron correlation and strong spin-orbit coupling.
One further question comes to whether the moderate electron correlation or the strong spin-orbit coupling alone can produce such a high energy anomaly in Sr 2 IrO 4 or it is a combined effect. It would be surprising if a moderate electron correlation alone in Sr 2 IrO 4 can cause the high energy anomaly over much larger energy scale than that in cuprates which has much stronger electron correlation although the possibility cannot be fully ruled out. There is no observation of high energy anomaly reported in systems with dominant spin-orbit coupling like simple metal Bi 57 or topological insulators 58,59 . The anomalous high energy features can be most likely a combined effect of both the electron correlation and the spin-orbit coupling. This is consistent with the proposition that, in order to understand the insulating behavior of Sr 2 IrO 4 , both the on-site Coulomb interaction and strong spin-orbit coupling are necessary 7 . It is also consistent with the recent observation of a high energy anomaly in UCoGa 5 that exhibits a moderate electron correlation and strong spin-orbital coupling 60 . Exotic quasiparticles like a composite particle has been reported lately in Sr 2 IrO 4 61 . How the combination of the moderate electron correlation and the strong spin-orbit coupling can lead to such anomalous high energy excitations in Sr 2 IrO 4 needs further theoretical and experimental investigations.
Interestingly, Sr 2 IrO 4 exhibits a number of features that are similar to those of the high temperature cuprate superconductors. First, its crystal structure 5 is similar to that of a parent compound La 2 CuO 4 2 with a slight distortion. Second, its insulating nature can be described by a J eff = 1/2 Mott insulator model 7 that is similar to the Mott insulator model for the parent compounds of the cuprate superconductors 2 . Third, the electron-doped Sr 2 IrO 4 shows a single hole-like Fermi surface and Fermi arc 62 that are quite reminiscent to that found in doped cuprate superconductors 25 . It is suggested that the half-filled doublet J eff = 1/2 band would be mainly responsible for the low energy insulating physics in Sr 2 IrO 4 as the role of the half-filled d x2−y2 band in cuprate parent compounds. The structural, electronic and magnetic similarities between Sr 2 IrO 4 and the cuprate parent compound La 2 CuO 4 23 imply potential realization of superconductivity in doped Sr 2 IrO 4 24 . Our present observation of anomalous high energy waterfall-like feature in Sr 2 IrO 4 adds one more prominent similarity to that in the cuprate superconductors.
In summary, our ARPES measurements over a wide energy window have revealed for the first time a new phenomenon of the high energy anomalous bands in Sr 2 IrO 4 . It resembles the high energy waterfall feature observed in high temperature cuprate superconductors. While the low energy electron excitations in Sr 2 IrO 4 can be described properly by considering both the on-site Coulomb repulsion and the strong spin-orbit coupling 7 , the high energy anomalous bands cannot be understood in the framework of the existing band structure calculations. Different from the cuprate superconductors where strong electron correlation plays an important role in producing high energy anomalies, the present results in Sr 2 IrO 4 provides a new scenario that high energy anomaly can occur in a system with moderate or weak electron correlation and strong spin-orbit coupling. We hope these experimental observations can stimulate further theoretical work in understanding the anomalous electronic behaviors in Sr 2 IrO 4 in particular, and the high energy anomaly in other materials in general.

Methods
The Sr 2 IrO 4 single crystals were synthesized by flux method 6 . High-resolution angle-resolved photoemission measurements were carried out on our lab system equipped with a Scienta R4000 electron energy analyzer 63 . We use helium discharge lamp as the light source that can provide photon energy of hυ = 21.218 eV (helium I). The overall energy resolution was set at 20 meV. The angular resolution is ~0.3 degree. The Fermi level is referenced by measuring on a clean polycrystalline gold that is electrically connected to the sample. The sample was cleaved in situ and measured at ~20 K in ultra-high vacuum with a base pressure better than 5 × 10 −11 Torr. The measurements were carried out on different samples for several times and the results are reproducible.