Introduction

The spin–orbit-coupled Mott insulator Sr2IrO4 exhibits a fascinating interplay between numerous competing energy scales, including spin–orbit coupling (SOC), Coulomb repulsion (U), Hund’s coupling (JH), and has thus been subject of much recent interest1,2,3,4,5. Close similarities between Sr2IrO4 and the parent cuprate La2CuO4 have also led to theoretical proposals that hole- and electron-doped Sr2IrO4 could likewise exhibit unconventional superconductivity2,6,7. To date, the majority of work has focused on the electron-doped side of the phase diagram with reports of a momentum-dependent pseudogap in Sr2−xLaxIrO48 and a d-wave-like gap in surface K-doped Sr2IrO44,5. These are both features associated with cuprates, although no direct signature of superconductivity has been conclusively identified. On the other hand, the behaviour of Sr2IrO4 upon hole doping is less clear, as the vast majority of studies have examined Sr2Ir1−xRhxO49,10,11,12,13 and Rh substitution introduces a number of complexities beyond the doping of holes. As Rh is introduced into the IrO2 planes, it removes a local Jeff = 1/2 moment, leading to pairs of Rh3+ and Ir5+ non-magnetic impurities14, which is analogous to Zn or Ni substitution for Cu in cuprates15,16. In cuprate superconductors, the preferred doping sites are those that are not part of the CuO2 planes, e.g., the A-site of cuprates with formula A2CuO4 (A = Sr or Ba). The A-sites are preferred because of the lower disorder potential that they evoke compared with sites within the CuO2 planes; by analogy with Sr2IrO4, it is likely similarly advantageous to minimize disorder by doping the Sr-site with an appropriate dopant rather than to dope the Ir-site with Rh. Furthermore, Rh substitution should also change the average strength of the SOC11, a key ingredient in the formation of the low-energy electronic structure.

To reveal the intrinsic behaviour of Sr2IrO4 upon hole doping, it is thus desirable to investigate a system without the intertwined complexity caused by Rh substitution. In principle, substitution of a monovalent alkali (e.g., Na+ or K+) on the A-site for divalent Sr2+ should result in hole doping without the additional complexities introduced by Rh substitution, similar to the hole doping of the cuprate Ca2−xNaxCuO2Cl2 by Na substitution17,18,19. This has been demonstrated in A2−xKxIrO4 (A = Sr, Ba) to preserve the long-range magnetic order at moderate amount of doping (up to x = 0.055)20,21,22. At present, however, no detailed spectroscopic measurements of any kind have been reported for A2−xKxIrO4 presumably due to the difficulty in synthesizing high-quality bulk single crystals. To overcome this challenge, we employ a combination of reactive oxide molecular-beam epitaxy (MBE) to synthesize initially undoped Sr2IrO4(001) thin films, followed by a substitutional diffusion process23,24, which allows us to substitute K for Sr. This approach circumvents the extremely high vapour pressure of KO2 at typical growth temperatures (≈10−2 torr at 850 °C)25, which would otherwise prevent the direct incorporation of K into the thin film; additional details about this process can be found in the Methods section. Afterwards, in-situ angle-resolved photoemission spectroscopy (ARPES) measurements of Sr1.93K0.07IrO4 thin films allow us to disentangle, for the first time, the effects of hole doping from changes in the SOC, magnetic landscape, and strong disorder scattering in the layered iridates. In doing so, we reveal that upon hole doping, coherent quasiparticles emerge together with the collapse of the Mott gap, in contrast to what has previously been reported with Rh substitution.

Results

Chemical potential shift with doping

In principle, the addition of K into Sr2IrO4 can result in either hole or electron doping. If K does not replace Sr, either when adsorbed on the surface4,5,26 or intercalated, this should result in electron doping. On the other hand, if K+ substitutes for Sr2+, this should result in hole doping. To conclusively demonstrate hole doping, we measured the shift in chemical potential Δμ between undoped, K surface-doped, and K-substituted samples. In Fig. 1a, we show representative energy distribution curves (EDCs) of the valence band from a single Sr2IrO4 sample when it is (i) initially undoped (black), (ii) following surface K-deposition (green), and finally (iii) after substitutional diffusion of K for Sr (purple). K surface deposition in step (ii) causes a shift of the spectra by Δμ = +0.5 ± 0.1 eV, consistent with electron doping as previously reported by Kim et al.4,5. In contrast, following substitutional diffusion in step (iii), all features are shifted to lower binding energy by Δμ = −0.4 ± 0.1 eV, in the direction consistent with hole doping as established by Louat et al.12 via Rh substitution. This process also results in a clear change in the K 3p core levels (Fig. 1b), as K is oxidized and substituted into the SrO layer. We excluded the possibility of hole doping via Sr vacancies27, interstitial oxygen, or oxygen vacancies28, by verifying that the post-growth annealing steps had no observable effect when the K-deposition step was omitted (see Supplementary Note 2).

Fig. 1: Photoemission measurements showing change in chemical potential and core level spectra upon doping Sr2IrO4.
figure 1

a Measurement of the chemical potential shift, Δμ, for a pristine undoped sample (top), after K surface deposition (middle), and after substitutional diffusion (bottom) with hν = 21.2 eV at kx,ky = (0,0). b Corresponding core level spectra measured with He II photons (hν = 40.8 eV). K peak locations are consistent with reference spectra for elemental29 and oxidized K30.

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Evolution of low-energy electronic structure

To investigate the effects of K substitution, in Fig. 2 we compare an isoenergy map of an undoped Sr2IrO4 film at 0.3 eV binding energy (sample exhibited no weight at EF) with a Fermi surface map of the same sample following K substitution. The isoenergy map of undoped Sr2IrO4 in Fig. 2a closely resembles those reported for undoped bulk crystals of Sr2IrO431. In reality, when an electron is removed from Sr2IrO4 (e.g., by photoemission or hole doping) 5d4 holes are introduced in the IrO2 plane, where the low-energy excitations are in fact a non-magnetic singlet Jeff = 0 and a magnetic triplet state Jeff = 1 (as described by Pärschke et al.32). 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 5d5 configuration. Furthermore, an electron addition 5d6 state is non-magnetic with no degrees of freedom, suggesting that electrons and holes may couple differently to the local magnetic environment. The top of the occupied Jeff = 1/2 band is at (π, 0) and (0, π), and the top of the Jeff = 3/2 band lies at (0,0) and (π, π), using the notation assuming an idealized, undistorted IrO2 square lattice, as has been customary in the literature. Upon hole doping, the Fermi surface of Sr2−xKxIrO4 is now clearly composed of small, elliptical electron pockets closed about (π/2, π/2) and larger square hole pockets centred around (π, 0) and (0, π). A measurement of the Luttinger volumes of these pockets indicates a hole doping of x = 0.07 ± 0.02, consistent with the observed shift in chemical potential, conclusively demonstrating hole doping via K substitution.

Fig. 2: Constant energy maps measured with hν = 21.2 eV and simulated using tight-binding model.
figure 2

a Energy isosurface at EB = 0.3 eV for undoped Sr2IrO4 (left) together with a broadened tight binding + spin–orbit coupling + U calculation, with U = 2 eV (right). All data are shown in a tetragonal Brillouin zone (1 Ir per unit cell), which ignores back-folding due to the in-plane octahedral rotations, which causes a \(\sqrt{2}\times \sqrt{2}\,R4{5}^{\circ }\) reconstruction. b Fermi surface of Sr1.93K0.07IrO4 showing ARPES data (left, averaged ± 20 meV around EF) together with a tight binding and spin–orbit coupling simulation (right) with U = 0 eV; hole and electron pockets are shaded orange and green, respectively. Experimentally extracted kFs are shown as white dots on the tight-binding model simulation.

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In Fig. 3a-d, we compare spectra from undoped Sr2IrO4 and Sr2−xKxIrO4 along both the (0,0)-(0,π) and (π/2,0)-(π/2,π) momentum cuts. For undoped Sr2IrO4, the broad but distinct Jeff = 1/2 band reaches its maximum at (0,-π) as reported previously in bulk single crystals, whereas for Sr1.93K0.07IrO4 samples, this band evolves into a sharp, well-defined quasiparticle band. Comparisons of the individual EDCs at k = (0, 1.2π) from the doped and undoped samples are shown in Fig. 3e), showing that the broad Jeff = 1/2 excitations in Sr2IrO4 evolve into a well-defined quasiparticle peak for Sr1.93K0.07IrO4. In Fig. 3b, d, we compare spectra from Sr2IrO4 and Sr1.93K0.07IrO4 around (π/2, π/2), which in the doped compound intersects the small, elliptical electron pockets as is clear from the momentum distribution curve (MDC) at EF (Fig. 3d). Corresponding EDCs from Sr2IrO4 and Sr1.93K0.07IrO4 taken at k = (π/2, 0.6π) are shown in Fig. 3e. The lack of a large, uniform pseudogap (we observe a leading edge midpoint of less than 5 meV—see Supplementary Note 3—which is substantially less than the 30 meV shift reported in the Rh-doped samples12,13), and the presence of quasiparticle peaks, which are absent in Sr2Ir1−xRhxO4, are both consistent with lower disorder scattering, in the absence of substitutional disorder directly in the IrO2 plane.

Fig. 3: Dispersions measured with hν = 21.2 eV.
figure 3

a ARPES spectra along (0,0)−(0, π) and b along (π/2,0)−(π/2,π) in undoped Sr2IrO4; insets show the Brillouin zone with red lines indicating the direction of the dispersion. Blue and red arrows show the momentum of the EDCs shown in e. c, d Corresponding ARPES spectra for Sr1.93K0.07IrO4 intersecting the square hole pocket c and elliptical electron pocket d with MDCs at EF shown at the top. e EDCs at kF in the doped samples (solid lines) and corresponding EDCs at the same k in the undoped samples (dashed lines), indicating a clear shift of spectral weight towards the Fermi level and a quasiparticle peak at (0,1.2π/a).

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Tight-binding model

A key distinction between Sr1.93K0.07IrO4 and earlier studies of Sr2Ir1−xRhxO4 is the clear presence of elliptical electron pockets, shown both in the Fermi surface map in Fig. 2b and in the band dispersion in Fig. 3d, which were not observed in Sr2Ir1−xRhxO4. To better understand the origin of these features, we employ a tight-binding parametrization of the t2g bands following refs. 8,33,34, which has previously shown good agreement with photoemission data8:

$${\mathcal{H}}=\sum_{\langle ij\rangle \alpha \beta \sigma }{t}_{ij}^{\alpha \beta }{c}_{i\alpha \sigma }^{\dagger }{c}_{j\beta \sigma }+\sum_{i,\alpha = {d}_{xy}}{\Delta }_{t}{c}_{i\alpha \sigma }^{\dagger }{c}_{i\alpha \sigma }+\lambda \sum_{i}{\overrightarrow{L}}_{i}\cdot {\overrightarrow{S}}_{i},$$
(1)

where 〈ij〉 are nearest-neighbour pairs of Ir sites, α and β index the t2g orbitals, t0 = 0.35 eV, σ indicates the spin, Δt = 0.15 eV is the tetragonal crystal field splitting and λ = 0.57 eV is the SOC parameter. These are the same values used in ref. 8. 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. Additional details of the calculation can be found in Supplementary Note 4.

In Fig. 4, we show the tight-binding band structure together with extracted experimental dispersions from both Sr2IrO4 and Sr1.93K0.07IrO4. We find good agreement in both the isoenergy maps (Fig. 2a) and extracted band dispersions (Fig. 4a) for the undoped case for a value of U = 2 eV, consistent with earlier studies of undoped Sr2IrO48. Rigidly shifting μ into the top of the Jeff = 1/2 band of this band structure would result in a Fermi surface comprised solely of hole pockets centred at (π, 0) and (0, π), as shown in Fig. 4b. This is reminiscent of the Fermi surface of Sr2Ir1−xRhxO4, where it was argued that the Mott gap is largely preserved up to a hole doping of x = 0.209,10,12,13, but counter to our observations in Sr1.93K0.07IrO4.

Fig. 4: Tight-binding model compared with extracted band dispersions.
figure 4

a Tight-binding model of the band structure with an additional mean-field Coulomb repulsion term U = 2 eV illustrating the behaviour of undoped Sr2IrO4 with extracted experimental dispersions of undoped Sr2IrO4 shown (purple circles), together with a schematic density of states, error bars indicated estimated uncertainty due to broad bands characteristic of insulating Sr2IrO4. Dashed black line indicates the chemical potential with x = 0.07 hole doping in a rigid band shift scenario similar to Rh-doped Sr2IrO4, dashed red line indicates chemical potential with x = 0.07 electron doping. Simulated tight-binding Fermi surfaces in a rigid band shift scenario are shown for b hole and c electron doping. d Tight-binding model with U = 0 eV, where the Mott gap has collapsed with extracted experimental dispersions of Sr1.93K0.07IrO4 (purple circles) together with a schematic density of states. Simulated tight-binding Fermi surfaces when U = 0 eV shown for hole e and electron doping f.

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A few important distinctions can be made between 7% hole-doped Sr2−xKxIrO4 and Sr2Ir0.93Rh0.07O4 with a comparable hole doping from ref. 12. First, the top of the Jeff = 1/2 band at (π,0) differs by approximately 0.1 eV (approximately +0.04 eV above EF for Rh-doped, approximately +0.15 above EF for K-doped). This demonstrates that Sr2Ir0.93Rh0.07O4 is consistent with the rigid band shift scenario in Fig. 4a. Although Sr2Ir0.93Rh0.07O4 only shows appreciable spectral weight near EF around (π,0), albeit without sharp spectral features, Sr1.93K0.07IrO4 possesses a two-sheet Fermi surface comprised of sharp, well-defined quasiparticle bands. In particular, the two-pocket fermiology observed in Sr1.93K0.07IrO4 strongly suggests a scenario where the Mott gap has collapsed when U becomes sufficiently small (Fig. 4d-f), as the elliptical electron pocket originates from the upper Hubbard band itself. Although our data stands in clear contrast to studies of Sr2Ir1−xRhxO4, it bears qualitative resemblance to the case of electron doping in Sr2−xLaxIrO4, where both hole and electron pockets have likewise been reported8. Nevertheless, electron vs. hole doping can be clearly distinguished from the relative sizes of the hole and electron pockets, as shown in Fig. 4e, f.

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 5d6 in a simple Jeff = 0 state) vs. doped holes (Ir 5d4 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.

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.

Discussion

The differences between Sr2−xKxIrO4 and Sr2Ir1−xRhxO4 allow us to elucidate the intrinsic effects of hole doping vs. the additional effects caused by Rh substitution. The lack of electron pockets in the Rh-doped materials is suggestive of a rigid band shift scenario where the Mott gap is largely preserved, in contrast to Sr2−xKxIrO4, where we find that the Mott gap collapses and coherent quasiparticle excitations are formed. A possible explanation is that structural and magnetic disorder in the IrO2 planes may cause holes to be strongly localized around Rh dopants, inhibiting free carriers from effectively screening the Mott gap, whereas for the K-doped materials, the carriers are more delocalized and are thereby able to more efficiently screen the strong Coulomb interactions. In addition, the existence of coherent quasiparticle peaks and the lack of a large pseudogap in Sr2−xKxIrO4 also suggests that the incoherent metallic and the large pseudogap reported in Sr2Ir1−xRhxO4 are likely induced by substitutional disorder in the IrO2 plane12, rather than an intrinsic property of hole-doped iridates.

Our findings point towards a universal underlying electronic structure upon doping Sr2IrO4, irrespective of the sign of the carriers, and thus a more symmetric doping phase diagram than previously realized. This stands in contrast to the cuprates, which exhibit a fundamental asymmetry between electron and hole doping35. Whereas the evolution of the Fermi surface contours in electron-doped cuprates can be qualitatively modelled by introducing a (π, π) spin–density wave via a conventional weak coupling phenomenology36, explaining the disconnected Fermi arcs of the hole-doped cuprates remains an outstanding challenge for sophisticated many-body approaches, which necessarily include strong local interactions37. Furthermore, the Mott gap in the cuprates appears far more robust upon doping, where spectral weight is gradually transferred from the Hubbard to low-energy quasiparticle bands38,39, whereas the gap in both hole- and electron-doped iridates appears to collapse far more rapidly. These differences may arise from the fundamentally weaker on-site Coulomb repulsion in the Ir 5d orbitals vs. the Cu 3d orbitals. Another distinction is that the cuprates are charge-transfer insulators where the hole- and electron-doped states have stronger O 2p vs. Cu 3d character, respectively, whereas the iridates are better described as Mott insulators where both the hole- and electron-doped states are of primarily Ir 5d orbital character, although they have very different internal magnetic structure32. Future work including detailed doping dependence of the electronic structure and magnetism, and a study of the electronic structure with advanced many-body techniques such as dynamical mean-field theory used in electron-doped Sr2IrO440,41, will be necessary to fully explain the collapse of the Mott gap in hole-doped Sr2−xKxIrO4 and the symmetric, universal electronic structure upon both hole and electron doping.

Methods

Film growth

Epitaxial Sr2IrO4(001) thin films were grown on single-crystalline (LaAlO3)0.3 (SrAl1/2Ta1/2O3)0.7 substrates by MBE at a substrate temperature of 850 °C as measured by an optical pyrometer with a measurement wavelength of 980 nm, in a background partial pressure of 1 × 10−6 torr of distilled ozone (80% O3 + 20% O2). A 7 nm buffer layer of SrIrO3 was initially deposited, followed by 20 nm of Sr2IrO4; the conducting SrIrO3 layer facilitated measurements below 100 K. Additional details about the growth may be found in refs. 42,43 and in Supplementary Note 1.

Substitutional diffusion

K substitution was achieved through a substitutional diffusion process23,24 where K was deposited on an undoped Sr2IrO4 film using a SAES evaporator at temperatures below 70 K and then annealed at a temperature of 300 °C in vacuum, followed by exposure to 1 × 10−6 torr of ozone at 300 °C for 20 min (both 10% and 80% O3 were used). 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. This method was used because of the extremely high vapour pressure of KO2 (≈1 × 10−2 torr at 850 °C), which prevents the direct incorporation of K into a Sr2−xKxIrO4 film at its growth temperature of 850 °C.

ARPES measurements

Following growth, the samples were transferred for ARPES measurements using He Iα (hν = 21.2 eV) photons with an energy resolution of ΔE = 11 meV at a temperature of 15 K. All stages described occurred within a single ultrahigh vacuum manifold, i.e., the samples were never exposed to air.