Mott gap collapse in lightly hole-doped Sr2−xKxIrO4

The evolution of Sr2IrO4 upon carrier doping has been a subject of intense interest, due to its similarities to the parent cuprates, yet the intrinsic behaviour of Sr2IrO4 upon hole doping remains enigmatic. Here, we synthesize and investigate hole-doped Sr2−xKxIrO4 utilizing a combination of reactive oxide molecular-beam epitaxy, substitutional diffusion and in-situ angle-resolved photoemission spectroscopy. Upon hole doping, we observe the formation of a coherent, two-band Fermi surface, consisting of both hole pockets centred at (π, 0) and electron pockets centred at (π/2, π/2). In particular, the strong similarities between the Fermi surface topology and quasiparticle band structure of hole- and electron-doped Sr2IrO4 are striking given the different internal structure of doped electrons versus holes.

Remarks to the Author: The paper by JN Nelson et al. present very interesting ARPES results of the "genuinely" hole-doped iridate -Sr_{2-x}K_xIrO4. In my opinion, the main finding of the paper is that "upon hole doping, coherent quasiparticles emerge together with the collapse of the Mott gap". This is a novel result, since all previous hole-doped iridate studies (which probably must have introduced also other changes to the undoped iridium oxide structure) did not report a transition to a system which can be regarded as almost noninteracting or at most weakly interacting. That is why I think that such an interesting study should be published in Nature Communications. Nevertheless, before I can fully recommend the manuscript for publication I would like the Authors to address the following three issues: (1) Interpretation of the undoped ARPES data: The Authors denote the dominant features of the ARPES spectrum of Sr2IrO4 as J_eff=1/2 and J_eff=3/2 bands. While such a description is quite common in the iridate literature, in my opinion this is not the correct way of describing this correlated spectrum: in "reality" what happens in the ARPES experiment is that one introduces a d^4 configuration ("d^4 hole") in the Sr2IrO4 plane -and the eigenstates of the latter should be denoted as having J_eff=0, J_eff=1 quantum numbers (these are the 4 lowest lying "spin-orbit coupled" multiplets of the 15 d^4 ion multiplets). Thus, the proper labelling of the various features of the ARPES spectrum of Sr2IrO4 spectrum (of the "bands", although this is also not a fully correct description in the correlated limit) should bear the J_eff=0, J_eff=1, etc. quantum numbers, cf. EM Paerschke et al., Nature Communications 8, 686 (2017) for details.
(2) Presentation of the model results with finite U: I understand that the result shown in Fig. 4(a-c) is obtained using the mean-field calculationsthis should be stated explicitly in the figure caption.
(3) Similarities between the electron and hole doped iridates [this is actually the main point of the report]: While I appreciate that the Authors would like to discuss this very important problem, I think that the discussion might be better organised and a few issues could (or maybe even should) be clarified: (a) Experimental signatures of the similarities between the electron-and hole-doped iridates: In my opinion, the respective ARPES spectra are still quite different: (i) as the Authors mention "there exist subtle differences such as the antinodal pseudogap in Sr1.9La0.1IrO4, which has been studied both experimentally with ARPES [8]"; (ii) also the ARPES studies on the electron-doped iridates reported by  in the paper] suggest clear signatures of the Fermi arcs and the important role played by correlations in the electron-doped iridates.
That is why I would not support the claim that the electron and hole-doped iridates are similar and I would appreciate, if the Authors can revise the relevant discussion of that issue in the paper accordingly (including, but not limited to, the abstract).
(b) Theoretical situation: In my opinion, on the theory side, the physics of the electron-and hole-doped iridates should be entirely different, at least, if we assume that the correlated physics plays any significant role in the system: In the electron-doped case one introduces "genuine" holes into the system (d^6 configuration on iridium ions; as a result of large splitting to the e_g's this can be regarded a J_eff =0 state, i.e. this is just a single "hole" or "electron" as known from the "single-band" cuprate studies). Thus, on the theoeretical side the problem can be modelled by a single-band Hubbard or t-J-like model and in the "underdoped" regime one expects a "typical" "correlated" ARPES spectrum, e.g. showing the pseudogaps. On the other hand, in the hole-doped iridates locally one introduces the d^4 states [see discussion in (1)] with the 15 possible multiplet states per site (which then can "disperse" and form the resulting "bands" in the ARPES spectrum). Of course, it is not clear how these 15 multiplets "conspire" to form the observed almost noninteracting bands, i.e. why in the end of the day it looks as upon doping the whole system can be described as almost noninteracting already at 7% doping, as the Authors report. In my point of view, this the most interesting question that is left "open" from this study -this requires studying a doped multiband Hubbard / t-J like model with large spin-orbit coupling (a very complicated study, of course…).
While I understand that the above discussion might be seen as a bit subjective and rather lengthy, I would think that at least some of it might be instructive to the Readers -especially the one regarding the need for further *multiband* Hubbard / t-J studies with large spin-orbit coupling.
Reviewer #2: Remarks to the Author: The authors report ARPES study of hole-doped Sr2-xKxIrO4 grown by MBE. Sr2IrO4 has received much attention due to its similarity with cuprate superconductors in terms of the electronic evolution as carriers are doped into the parent Mott insulator. For iridates, many studies are focused on the electron-doped side, partly due to the fact that hole doping is usually done by substitution of Ir ions by Rh, a process that generates disorder in the IrO2 plane and thus can involve unwanted side effects. To my knowledge, this is a first high quality ARPES study on a hole doped iridate though substitution of Sr by K, which is more amenable to studying intrinsic electronic evolution with hole doping. The authors have made very high quality samples as judged by the quality of their ARPES data. The data are impressive and I believe that much insight can be gained by studying the doping evolution systematically.
That being said, the manuscript only provides data on one doped sample, which is not enough to draw any important conclusion. The authors study 7% doped sample and find that the Mott gap has collapsed. As the authors note, Fermi liquid phase is reached at a relatively low doping level in iridates compared to cuprates, and so authors might have missed the interesting evolution that takes place at lower doping levels. In fact, in the electron doped side, a metal phase with LDA-like Fermi surface is observed already at ~8% doping. I think this work will have much more impact if the authors can grow one or two more intermediate doping levels samples and provide ARPES data on them. I understand that MBE growth of iridate films is a very difficult task, but as is written now the manuscript provides very limited information and thus is not sufficient for publication in Nature communications.

Response to Reviewer #1:
"The paper by JN Nelson et al. present very interesting ARPES results of the "genuinely" holedoped iridate -Sr_{2-x}K_xIrO4. In my opinion, the main finding of the paper is that "upon hole doping, coherent quasiparticles emerge together with the collapse of the Mott gap". This is a novel result, since all previous hole-doped iridate studies (which probably must have introduced also other changes to the undoped iridium oxide structure) did not report a transition to a system which can be regarded as almost noninteracting or at most weakly interacting. That is why I think that such an interesting study should be published in Nature Communications. Nevertheless, before I can fully recommend the manuscript for publication I would like the Authors to address the following three issues:" We thank the reviewer #1 for their comments regarding our work presenting the first spectroscopic study of Sr2-xKxIrO4 and their positive response. We address reviewer #1's comments below:

" (1) Interpretation of the undoped ARPES data:
The Authors denote the dominant features of the ARPES spectrum of Sr2IrO4 as J_eff=1/2 and J_eff=3/2 bands. While such a description is quite common in the iridate literature, in my opinion this is not the correct way of describing this correlated spectrum: in "reality" what happens in the ARPES experiment is that one introduces a d^4 configuration ("d^4 hole") in the Sr2IrO4 plane -and the eigenstates of the latter should be denoted as having J_eff=0, J_eff=1 quantum numbers (these are the 4 lowest lying "spin-orbit coupled" multiplets of the 15 d^4 ion multiplets). Thus, the proper labelling of the various features of the ARPES spectrum of Sr2IrO4 spectrum (of the "bands", although this is also not a fully correct description in the correlated limit) should bear the J_eff=0, J_eff=1, etc. quantum numbers, cf. EM Paerschke et al., Nature Communications 8, 686 (2017)

for details."
We thank Reviewer #1 for bringing up this issue and agree with them that indeed the proper labeling for the undoped and hole doped lowest energy excitations are Jeff = 0 and Jeff = 1. We appreciate their suggestion that using this notation helps to illustrate the important differences between electron and hole doping which are rather unique to Sr2IrO4 and have modified our manuscript as follows : " In reality, when an electron is removed from Sr2IrO4 (e.g. by photoemission or hole doping) 5d 4 holes are introduced in the IrO2 plane, where the low energy excitations are in fact a nonmagnetic singlet Jeff=0 and a magnetic triplet state Jeff =1 (as described by Pärschke et al. 33 [Parschke et al. Nat. Comm. 8, 686 (2017)]). To remain consistent with the existing iridate literature, these bands may be referred to as Jeff =1/2 and Jeff =3/2 bands, following the convention for the undoped 5d 5 configuration. Furthermore, an electron addition 5d 6 state is non magnetic with no degrees of freedom, suggesting that electrons and holes may couple differently to the local magnetic environment." (lines 111-121).

"(2) Presentation of the model results with finite U:
I understand that the result shown in Fig. 4(a-c) is obtained using the mean-field calculationsthis should be stated explicitly in the figure caption." We thank Reviewer #1 for this comment and have amended the figure caption, for additional clarity we also state in lines 168-170 "The Coulomb repulsion U is implemented as an additional self-consistent mean-field term, which is proportional to the average electron density of each band." "(3) Similarities between the electron and hole doped iridates [this is actually the main point of the report]. While I appreciate that the Authors would like to discuss this very important problem, I think that the discussion might be better organised and a few issues could (or maybe even should) be clarified:

(a) Experimental signatures of the similarities between the electron-and hole-doped iridates:
In my opinion, the respective ARPES spectra are still quite different: (i) as the Authors mention "there exist subtle differences such as the antinodal pseudogap in Sr1.9La0.1IrO4, which has been studied both experimentally with ARPES [8]"; (ii) also the ARPES studies on the electrondoped iridates reported by

in the paper] suggest clear signatures of the Fermi arcs and the important role played by correlations in the electron-doped iridates. That is why I would not support the claim that the electron and hole-doped iridates are similar and I would appreciate, if the Authors can revise the relevant discussion of that issue in the paper accordingly (including, but not limited to, the abstract). (b) Theoretical situation:
In my opinion, on the theory side, the physics of the electron-and hole-doped iridates should be entirely different, at least, if we assume that the correlated physics plays any significant role in the system: In the electron-doped case one introduces "genuine" holes into the system (d^6 configuration on iridium ions; as a result of large splitting to the e_g's this can be regarded a J_eff =0 state, i.e.

this is just a single "hole" or "electron" as known from the "single-band" cuprate studies). Thus, on the theoeretical side the problem can be modelled by a single-band Hubbard or t-J-like model and in the "underdoped" regime one expects a "typical" "correlated" ARPES spectrum, e.g. showing the pseudogaps. Indeed, this is what the experiments on the electron-doped iridates suggest [see point (2)(a)].
On the other hand, in the hole-doped iridates locally one introduces the d^4 states [see discussion in (1)] with the 15 possible multiplet states per site (which then can "disperse" and form the resulting "bands" in the ARPES spectrum). Of course, it is not clear how these 15 multiplets "conspire" to form the observed almost noninteracting bands, i.e. why in the end of the day it looks as upon doping the whole system can be described as almost noninteracting already at 7% doping, as the Authors report.

While I understand that the above discussion might be seen as a bit subjective and rather lengthy, I would think that at least some of it might be instructive to the Readers -especially the one regarding the need for further *multiband* Hubbard / t-J studies with large spin-orbit coupling."
We thank Reviewer #1 for these insightful comments and agree that there remain important differences between electron and hole doped iridates which could be more effectively highlighted in our paper. We also agree that a multiband Hubbard or t-J study would greatly help in understanding this system and hope that our work prompts future theoretical studies. We have made numerous changes to the manuscript to address these concerns, including : Modifying the abstract: "In particular, the strong similarities between the Fermi surface topology and quasiparticle band structure of hole-and electron-doped Sr2IrO4 are striking given the different internal structure of doped electrons versus holes." (lines 11-13).

Modifying the main text:
"This striking similarity between electron-doped Sr2-xLaxIrO4 and hole-doped Sr2-xKxIrO4 in the global quasiparticle band structure and Fermi surface topology, apart from a shift in the chemical potential, is unexpected given the differences in the internal structure of the doped electrons (Ir 5d 6 in a simple Jeff = 0 state) versus doped holes (Ir 5d 4 with a complex spin-orbit coupled multiplet structure). This surprising apparent symmetry between electron and hole doping should motivate future many-body calculations (e.g. Hubbard, t-J model, or dynamical mean field theory calculations) which explicitly consider the complex multiplet structure of hole doped Sr2IrO4." (lines 207-218).
"Despite the apparent symmetry of the global electronic structure upon both electron and hole doping, there remain important distinctions between the two systems at the lowest energy scales. Whereas the electron doped iridates (surface K or La substitution) in a similar doping range exhibit a large (~ 20 meV), d-wave-like pseudogap at EF, we do not experimentally resolve a pseudogap to within 5 meV." (lines 219-225).

Response to Reviewer #2:
"The authors report ARPES study of hole-doped Sr2-xKxIrO4 grown by MBE. Sr2IrO4 has received much attention due to its similarity with cuprate superconductors in terms of the electronic evolution as carriers are doped into the parent Mott insulator. For iridates, many studies are focused on the electron-doped side, partly due to the fact that hole doping is usually done by substitution of Ir ions by Rh, a process that generates disorder in the IrO2 plane and thus can involve unwanted side effects. To my knowledge, this is a first high quality ARPES study on a hole doped iridate though substitution of Sr by K, which is more amenable to studying intrinsic electronic evolution with hole doping. The authors have made very high quality samples as judged by the quality of their ARPES data. The data are impressive and I believe that much insight can be gained by studying the doping evolution systematically.
That being said, the manuscript only provides data on one doped sample, which is not enough to draw any important conclusion. The authors study 7% doped sample and find that the Mott gap has collapsed. As the authors note, Fermi liquid phase is reached at a relatively low doping level in iridates compared to cuprates, and so authors might have missed the interesting evolution that takes place at lower doping levels. In fact, in the electron doped side, a metal phase with LDA-like Fermi surface is observed already at ~8% doping. I think this work will have much more impact if the authors can grow one or two more

intermediate doping levels samples and provide ARPES data on them. I understand that MBE growth of iridate films is a very difficult task, but as is written now the manuscript provides very limited information and thus is not sufficient for publication in Nature communications."
We thank Reviewer #2 for their positive comments about our manuscript and agree that substitutionally doped Sr2-xKxIrO4 is an ideal platform for studying the evolution of the electronic structure with hole doping. We absolutely agree that a detailed doping dependence of the electronic structure is an important and natural next step in the study of hole doped iridates. Along these lines, we have indeed attempted to synthesize Sr2-xKxIrO4 with different levels of hole doping, but have been unable to achieve hole doping levels appreciably different from 7% (as will be described below). Nevertheless, we believe that our results provide very important insights into the hole doping evolution of the iridates, particularly when contrasted to Sr2IrO4 doped with similar concentrations of La and Rh, and warrant publication in Nature Communications.
Likewise, we can also make comparisons between Sr1.93K0.07IrO4 and electron-doped Sr2IrO4 with similar electron carrier concentrations. For example, Kim et al. have shown (by surface K dosing), that at a surface electron doping of 6-8%, a d-wave-like gap is observed. Similarly, in bulk electron-doped Sr2-xLaxIrO4, both de la Torre et al. (PRL 115, 2-6 (2015)) and Terashima et al. (PRB 96, 041106(R) (2017)) have reported a momentum-dependent pseudogap of approximately 20 meV in the range of 5-10% electron doping, in clear contrast to our observations. To address this point, we have also added new text between lines 207 and 225.
We agree with Reviewer #2 that investigating a sequence of different doping levels would certainly be desirable. We have invested significant efforts into synthesizing samples with varying degrees of K substitution, but have been unable to appreciably change the hole concentration. In total, we have synthesized eleven Sr2-xKxIrO4 thin films for this study. Of these eleven samples, the post-growth K substitutional diffusion conditions have been varied significantly, including (1) the amount of K deposited on the surface has been varied by a factor of 40; (2) the concentration of ozone used in the annealing step (both 10% and 80%); (3) and the amount of time during the vacuum annealing (24 to 40 minutes) and ozone annealing (20 to 55 minutes). Despite varying all these conditions, we have found that of the seven samples that yielded high quality ARPES spectra which can be reliably analyzed, all seven samples give the same extracted hole doping concentration of 7± 2% (from Luttinger volume) and a chemical potential shift of Δμ =-0.4 ± 0.1 eV. We believe that a 7% doping may be energetically favored in the substitutional diffusion process, or that this represents the solubility limit of K in Sr2IrO4. We are continuing to investigate this substitutional diffusion technique, but controlling the doping level is far more challenging than by conventional co-doping or bulk chemical substitution.
To address this issue, we have added a short note in the Methods section on line 294, stating that : "Multiple doped samples synthesized and investigated in this study showed highly consistent values in the chemical potential shift, near-EF electronic structure, and extracted hole concentrations, despite significant variations in the amounts of K deposited, annealing times, or ozone concentration." We have also added additional detail in the Supplemental Information (lines 31-40) detailing the number of samples synthesized, investigated by ARPES, and the variation in the range of K deposited and annealing conditions. Despite the fact that we have not been able to appreciably change the hole doping level, we believe that this work represents an important advance in our understanding of doped iridates worthy of publication in Nature Communications. In particular, by making direct comparisons to both Rh-doped and La-doped iridates with similar electron / hole concentrations, we are able to point out important differences between these cases (namely, the collapse of the Mott gap and the absence of a large pseudogap), distinctions which we highlight in this revised manuscript. We believe that these surprising observations will ignite new experimental and theoretical efforts into understanding the physics of electron-and hole-doped iridates.