High-temperature superconductivity in cuprates emerges out of a highly enigmatic ‘pseudogap’ metal phase. The mechanism of high-temperature superconductivity is probably encrypted in the elusive relationship between the two phases, which spectroscopically is manifested as Fermi arcs—disconnected segments of zero-energy states—collapsing into d-wave point nodes upon entering the superconducting phase. Here, we reproduce this distinct cuprate phenomenology in the 5d transition-metal oxide Sr2IrO4. Using angle-resolved photoemission, we show that the clean, low-temperature phase of 6–8% electron-doped Sr2IrO4 has gapless excitations only at four isolated points in the Brillouin zone, with a predominant d-wave symmetry of the gap. Our work thus establishes a connection between the low-temperature d-wave instability and the previously reported high-temperature Fermi arcs in electron-doped Sr2IrO4 (ref. 1). Although the physical origin of the d-wave gap remains to be understood, Sr2IrO4 is the first non-cuprate material to spectroscopically reproduce the complete phenomenology of the cuprates, thus offering a new material platform to investigate the relationship between the pseudogap and the d-wave gap.
Sr2IrO4 is a single-electron-band magnetic insulator with pseudospin-1/2 moments2,3 on a square lattice4. Despite very strong spin–orbit coupling inherent to 5d transition-metal elements, magnetic interactions between iridium pseudospins are predominantly of Heisenberg type5, with a large energy scale6,7 as reflected in their magnon bandwidth of ∼200 meV. This one-to-one correspondence between Sr2IrO4 and high-temperature superconducting (HTSC) cuprates in their lattice, electronic and magnetic structures allows us to present, in Fig. 1a, b, angle-resolved photoemission (ARPES) intensity maps of approximately 7% electron-doped Sr2IrO4 recorded at the Fermi level following the standard notations used in the cuprate literature. A sign difference between the two systems in one of the tight-binding parameters8 characterizing the hopping of an electron in a quasi-two-dimensional (2D) square lattice renders Fermi surfaces shifted by (π, π) with respect to each other in their non-interacting electron descriptions. This sign of the next-nearest hopping can be reversed by electron–hole conjugation, which means that our results on electron-doped Sr2IrO4 can be directly compared to those of hole-doped cuprates9.
At T = 10 K, the map shows a locus of finite intensities, which is largely concentrated at a point near (π/2, π/2). Upon inspection of the energy distribution curves (EDCs) along this locus, plotted in Fig. 1c after symmetrization with respect to the Fermi level following standard procedures10, it is clearly seen that the spectra are gapped everywhere except at a single momentum (k) point in a quadrant of the Brillouin zone. This ‘nodal’ Fermi surface is completely unexpected from the single-electron band structure, which implies that a highly non-trivial, correlated electronic phase develops upon electron doping of Sr2IrO4.
Density-functional calculations of Sr2IrO4 predict a circular electron Fermi surface centred at the Γ point whose enclosed area is half of the 2D Brillouin zone2. Indeed, such a ‘large’ Fermi surface is observed at a sufficiently high doping and/or temperature1, implying that the nodal Fermi surface arises in close proximity to the Mott insulating, (π, π) antiferromagetic ground state of the parent Sr2IrO4 (ref. 3). Thus, the previously reported high-temperature Fermi arcs interpolate between these two contrasting electronic phases: the node evolves to a Fermi arc of a finite length at high temperature (Fig. 1b) as the gap closes along this arc (Fig. 1c). This establishes a non-trivial origin the Fermi arcs, which was indicated by the strong temperature and doping dependence of the arc length, and its position displaced from the large Fermi surface1. These features distinguish the Fermi arcs in electron-doped Sr2IrO4 from other Fermi-arc-like features in manganites11 or nickelates12, which merely show anisotropic suppression of spectral weights at the Fermi level, but otherwise are consistent with their density-functional descriptions. To further investigate the connection between the Fermi arcs and the nodal Fermi surface, we follow in Fig. 2a the temperature evolution at a k point on the Fermi arc, 17° away from the node. With decreasing temperature, a finite gap (2Δ) is resolved below T = 30 K, reaching a maximum of approximately 22 meV at T = 10 K (Fig. 2d). The temperature evolution of the spectra at the node (Fig. 2b) and the antinode (Fig. 2c) is insensitive to the near-nodal gap opening, indicating that the near-nodal gap is a defining feature that differentiates between the low-temperature nodal metal phase and the high-temperature Fermi arc phase. This k-dependent temperature evolution of the spectra is strikingly reminiscent of that observed in the cuprates10,13.
It is unclear on the basis of our data whether or not the gap opening is associated with a phase transition. In superconducting cuprates, the near-nodal gap follows a canonical temperature dependence of a Bardeen–Cooper–Schrieffer order parameter13. In non-superconducting cuprates, such as the stripe compound La2−xBaxCuO4 with one-eighth doping14 and a highly underdoped Bi2Sr2CaCu2O8+δ (ref. 15), the Fermi arcs continuously shrink to d-wave nodes without encountering a phase transition. In either case, nodal fermions arise from d-wave pairing correlations, which regardless of the presence of phase-coherent superconductivity results in a d-wave gap in the single-particle excitation spectra16. However, it is also plausible that some other phase distinct from superconductivity leads to a similar gap structure. For example, d-density waves, predicted long ago to compete with d-wave superconductivity, may be consistent with our data17,18. Although we are not able to discriminate among such possible scenarios, the symmetry of the gap structure places a stringent constraint on the possible underlying electronic phases. Figure 3a documents the gap extracted from fitting to the Dynes formula as a function of the d-wave form factor |cos(kxa) − cos(kya)|/2. We have repeated the measurements on two samples with the same nominal doping of approximately 7%, and two other samples with slightly lower (Fig. 3b) and slightly higher doping levels (Fig. 3c). In all four measured samples, we find a good agreement with the d-wave form factor near the node, but a prominent deviation from it in the antinodal region. A linear extrapolation of the near-node gaps returns a d-wave gap maximum in the range 16 ≤ 2Δ0 ≤ 30 meV, which is smaller by roughly a factor of two than the actual gaps 2Δ∗ measured at the antinode. We note that this particular gap profile deviating from a simple d-wave form is observed across many different families of underdoped cuprates, suggesting that the near-nodal gap and the antinodal gap have two different origins19,20. This in turn connects to the elusive relationship between the superconducting and the pseudogap phase, which is one of the outstanding issues in the field of HTSC widely believed to be important for unravelling its mechanism. Although the nature of the d-wave instability in electron-doped Sr2IrO4 remains to be understood, the striking parallel between the two microscopically disparate systems points to a common origin of the pseudogap that arises in close proximity to a d-wave instability.
Some remarks are in order regarding the origin of the d-wave gap in Sr2IrO4. We believe that it is most probably associated with HTSC. The temperature at which the d-wave gap appears (∼30 K) is comparable to the highest critical temperature for La2CuO4 (∼40 K). In fact, to the best of our knowledge, all observations of d-wave gaps so far involve pairing of electrons. d-wave superconductivity is also expected from theoretical studies9,21,22 of electron-doped Sr2IrO4. On the other hand, it is well known that doping a spin-1/2 antiferromagnetic Mott insulator generates a plethora of electronic orders23,24, such as spin/charge density waves, electron liquid crystals, and loop current orders25,26; and therefore it cannot be ruled out that the d-wave gap in Sr2IrO4 represents an entirely new quantum state of matter that competes with d-wave superconductivity. For guidance to future identification of the precise nature of the d-wave nodal metal, we note that well-defined quasiparticles, sharper at higher doping, are observed along the entire k-trajectory from the node to the antinode, which implies that the d-wave nodal metal phase supports a coherent charge excitation without a significant momentum anisotropy. We note that the antinode quasiparticle intensity in cuprates has been shown to correlate with the superfluid density27. We now turn to describing our unique experimental approach that allowed ARPES measurements of the clean, low-temperature phase of electron-doped Sr2IrO4. Unlike cuprates, chemical doping of Sr2IrO4 turns out to be challenging; we are not aware of any ARPES data measured on a chemically doped sample28,29,30 that show sharp quasiparticles, which is a measure of a coherent charge transport, let alone a d-wave gap. The in situ doping method provides an alternative to conventional chemical doping, and has been successfully applied across many different systems31,32,33, including HTSC cuprates32.
This method involves evaporating alkali metals on a clean sample surface prepared in an ultrahigh vacuum, and induces electron doping without disrupting the host material, through diffusion of alkali valence electrons into the sample surface. In an earlier study using a combination of in situ doping and ARPES, the single-particle spectral function for the entire doping range from the Mott insulator to a Fermi liquid metal on the electron-doped side has been revealed using a parent insulator Sr2IrO4 (ref. 1). However, a drawback of this method is that doping is limited to few surface layers and the bulk of the sample is left undoped, so that standard bulk-sensitive probes are not applicable. Moreover, because insulators are intrinsically difficult to measure using single-particle probes owing to sample charging, the accessible temperature range is limited as the sample becomes more insulating at lower temperatures. This limits the ARPES measurement temperature to above approximately 70 K for pristine Sr2IrO4, leaving the low-temperature region of the phase diagram unrevealed.
To circumvent the charging problem, we inserted few-layers-thick slabs of Sr2IrO4 into its more conducting sister compound Sr3Ir2O7 (ref. 34), as illustrated in Fig. 4. We found no sign of a change in the physical properties due to interfacing the two members of the Ruddlesden–Popper series (Supplementary Fig. 1). Indeed, we were able to reproduce the previously reported high-temperature Fermi arcs in our ‘engineered’ sample (Supplementary Fig. 2). As demonstrated in Fig. 2, our approach allows ARPES measurement down to the base temperature of T = 10 K. The absence of a gap at the node (Fig. 2b) in the EDCs confirms that there is no charging down to T = 10 K.
Our work shows that when clean electron doping is achieved, Sr2IrO4 exhibits a correlated electron phenomenon expected for a doped (pseudo)spin-1/2 antiferromagnetic Mott insulator, whose material realization has thus far been limited to cuprates. In order for the nature of the d-wave nodal metal to be scrutinized using the full arsenal of condensed matter physics, the observations presented herein must be reproduced in a chemically doped sample. This will also directly verify, or disprove, the superconducting origin of the d-wave gap in electron-doped Sr2IrO4. Either way, our work represents the discovery of a novel quantum state in the emerging family of 5d magnetic insulators. With their diverse spectrum of magnetism beyond the conventional Heisenberg paradigm35,36, they open a new route to investigate the elusive connection between the spin and charge degrees of freedom, long believed to lead to high-temperature superconductivity.
Note added in proof: A scanning tunnelling spectroscopy study of electron-doped Sr2IrO4 (ref. 37), shows results similar to what we report here.
Angle-resolved photoemission spectroscopy.
ARPES measurements were performed at Beamline 4.0.3 at the Advanced Light Source, equipped with a Scienta R8000 electron analyser. We evaporated potassium atoms in situ onto the freshly cleaved surface of the sample using a commercial SAES evaporator to dope electrons into the sample surface. The samples were cleaved and doped at T = 70 K and p ∼ 3 × 10−11 torr, and measured in the temperature range T = 10–70 K with an overall energy resolution of 14 meV at hν = 68 eV. Because of the short lifetime of the sample after in situ doping (∼1 h), data shown in Figs 1–3 were collected on seven different samples. The reproducibility of the surface coverage level was about ±0.05 ML. The surface coverage of potassium (K) was monitored through the K 3p core level and the K overlayer quantum well band, as described in ref. 1.
The samples were grown by the flux method. Sr2CO3, IrO2 and SrCl2 were mixed in a molar ratio of 2:1:7, melted and soaked at T = 1,125 °C, and then slow-cooled down to 880 °C. The degree of intergrowth of the Sr2IrO4 phase was controlled by varying the soaking temperature in the range 1,050 °C–1,300 °C.
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We acknowledge helpful discussions with C. Kim, G. Khaliullin, B. Keimer, M. Le Tacon, G. Jackeli, J. F. Mitchell, M. Norman and J. W. Allen. We thank B. Y. Kim for technical assistance. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under Contract No. DE-AC02-05CH11231. This work was supported by IBS-R009-D1.
The authors declare no competing financial interests.
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Kim, Y., Sung, N., Denlinger, J. et al. Observation of a d-wave gap in electron-doped Sr2IrO4. Nature Phys 12, 37–41 (2016). https://doi.org/10.1038/nphys3503
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