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# Evidence of nematic order and nodal superconducting gap along [110] direction in RbFe2As2

## Abstract

Unconventional superconductivity often intertwines with various forms of order, such as the nematic order which breaks the rotational symmetry of the lattice. Here we report a scanning tunneling microscopy study on RbFe2As2, a heavily hole-doped Fe-based superconductor (FeSC). We observe significant symmetry breaking in its electronic structure and magnetic vortex which differentiates the (π, π) and (π, -π) directions of the unfolded Brillouin zone. It is thus a novel nematic state, distinct from the nematicity of undoped/lightly-doped FeSCs which breaks the (π, 0)/(0, π) equivalence. Moreover, we observe a clear V-shaped superconducting gap. The gap is suppressed on surface Rb vacancies and step edges, and the suppression is particularly strong at the [110]-oriented edges. This is possibly due to a $${{d}}_{{{x}}^2 - {{y}}^2}$$ like pairing component with nodes along the [110] directions. Our results thus highlight the intimate connection between nematicity and superconducting pairing in iron-based superconductors.

## Introduction

The discovery of FeSCs has opened a new era in the study of unconventional superconductivity1,2,3,4. Most FeSCs are found to be proximate to a magnetically ordered state and a nematic electronic state that shares similarities with the cuprates5,6,7,8,9,10,11,12,13. In most undoped and lightly-doped FeSCs, the Fe ions are close to 3d6 configuration, which favor a stripe-like collinear antiferromagnetic (AFM) order or spin density wave (SDW), with a wave vector Q = (π, 0) or (0, π) (an exception is FeTe, which has an bicollinear AFM state with Q = (π/2, π/2)). A nematic phase, which breaks the equivalence between a and b directions in the Fe-plane, develops at the Neel temperature (TN) or slightly above, and approaches the superconducting dome upon doping5,6,7,8,9,10,11,12,13. There has been increasing evidence showing the nematicity is driven by magnetic fluctuations14,15, nonetheless the orbital-driven scenario is also proposed, especially for FeSe (ref. 16). The magnetic and/or orbital fluctuations between the nested Fermi surfaces with a vector around Q may play an essential role in superconductivity and determine the pairing symmetry3,4,5. Therefore, the relation between nematicity, magnetic order and superconductivity has become one of the central themes in FeSCs.

To provide a unified understanding of FeSCs and even cuprates, it is important to examine such a theme in regimes where the configuration of Fe ions deviates significantly from 3d6, as the magnetic interactions, electron correlations, and Fermi surface topology will alter drastically3,5,17. In theory, strong correlations are expected for the 3d5 case to drive the system into a Mott insulating phase18,19. It has been suggested that electronic nematicity may occur via doping a Mott insulator20, as evidenced in underdoped cuprates21,22. Meanwhile, the pairing symmetry of FeSC is also predicted to vary with doping3,4,17. For the 3d5.5 configuration, the dominant spin fluctuations are predicted to relocate to (π, π)/(π, −π) due to a change in Fermi surface topology, and consequently, d-wave pairing is favored17,23,24. This configuration has been realized in AFe2As2 (A= K, Rb, Cs), the most heavily hole-doped FeSCs25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42. They have large Sommerfeld coefficients (γ)25,26 and mass enhancement28,34,36, indicative of strong correlations. Recently, a coherence–incoherence crossover27 and heavy-fermion like behavior29 were observed in AFe2As2, suggesting an orbital-selective Mott transition. Heat transport30,32, magnetic penetration depth31, NMR42, and ARPES35,37 measurements have suggested gap nodes in AFe2As2 (A= K, Rb); however, whether the nodes are symmetry protected (d-wave pairing)17,23 or accidental (from anisotropic s-wave pairing)43,44 remains hotly contested. In parallel, neutron scattering40,41 and NMR42 studies on KFe2As2 did reveal spin fluctuations that deviated from (π, 0). It is thus critical to look for possible nematicity with distinct behaviors and its relation with superconductivity.

In this article, we present a milliKelvin scanning tunneling microscopy (STM) study on RbFe2As2 single crystals. Compared to its sister compound KFe2As2, RbFe2As2 has an even larger γ value (~127 mJ/molK2 (ref. 26)) but a lower Tc (~2.5 K). Remarkably, we observe significant two-fold symmetry in the quasi-particle interference (QPI) and magnetic vortex cores, while the surface atomic lattice remains four-fold symmetric within the experimental resolution. Particularly, this C4–C2 symmetry breaking is along the diagonal direction, 45° off from the Fe–Fe bond or the (π, π) direction in the unfolded BZ. This suggests that a new type of electronic nematicity and associated fluctuations developed in RbFe2As2, and such diagonal nematicity was found to persist above Tc. Moreover, high-energy-resolved tunneling spectra revealed a clear V-shaped superconducting gap, which can be well fitted by a nodal gap function. The gap is suppressed by both surface Rb vacancies (non-magnetic impurities) and near atomic step edges, suggestive of sign-change pairing. Particularly, the spatial extension of the suppressed-gap region on [110] oriented edges is found to be much wider than the [100] oriented edges, which is likely due to gap nodes in the [110] directions. Finally, we perform surface K dosing on RbFe2As2 and demonstrate that the (π, π) nematic state can be suppressed by electron doping, while the superconductivity is subsequently enhanced. The possible origin of the diagonal nematicity and its relation to superconducting pairing is discussed.

## Results

### Surface atomic structure and superconducting gap of RbFe2As2

The experiment is mostly conducted in a millikelvin STM working at T= 20 mK (the surface K dosing was conducted in a 4.5 K STM system). The effective electron temperature (Teff) of the former system is calibrated to be 310 mK (see Supplementary Note 1). Sample preparation and more experimental details are described in Methods. RbFe2As2 is stoichiometric with the ThCr2Si2-type structure (see Supplementary Fig. 1a). It is expected to cleave between FeAs layers and results Rb covered surfaces. Figure 1a shows the typical topography of a commonly observed surface (referred as type A surface). It is atomically flat with some basin-like defects. In the defect-free areas, a square lattice with an inter-atomic spacing of 5.4 Å is observed (Fig. 1a inset). This spacing is $$\sqrt 2$$ times the in-plane lattice constant of RbFe2As2 (a0= 3.86 Å). Besides type A surface, we occasionally observed another type of surface region (type B surface), as shown in Fig. 1b. The topography of type B surface is actually similar to type A, and a 5.4-Å square lattice is also observed in its defect-free areas (Fig. 1b inset). However it displays much stronger anisotropy in the electronic states, as we will show below.

To determine the surface atomic structure, higher-resolution STM imaging near the basin defect is shown in Fig. 1c. We find that there is another square lattice inside the basin defect, with a lattice constant equal to a0 (as marked by black dots). The outside lattice (marked by circles) is rotated 45° and forms a $$\sqrt 2 \times \sqrt 2$$ reconstruction with respect to the inside lattice (see Supplementary Note 2 for more details). The surface structure that best explains these observations is sketched in Fig.1d: the surface is Rb terminated with 50% coverage, and the basin areas are Rb vacancies with an exposed FeAs layer. Surface Rb atoms are surrounded by four As atoms underneath, and formed a $$\sqrt 2 \times \sqrt 2$$ lattice with the same orientation as the Fe lattice (as denoted by a, b hereafter). We note in this model the Rb lattice will have two equivalent occupation site that shifted by 1/2 lattice spacing (see Supplementary Fig. 3e). We indeed observe domain structures formed by these two occupations on low-temperature cleaved sample (see Supplementary Fig. 4), and the orientation of the surface Rb lattice is further confirmed by Laue diffraction combined with STM imaging (Supplementary Fig. 5). Moreover, such a surface structure retains four-fold rotational symmetry, at least within the spatial resolution of STM, and is non-polar due to the 50% Rb coverage, which allows STM to access the intrinsic electronic states of RbFe2As2. A similar surface structure was also observed on cleaved KFe2As2 (ref. 39).

Figure 1e shows typical tunneling spectra on defect-free areas of type A and B surfaces, within a relatively large energy scale (±200 mV). On both regions a pronounced conductance peak is observed slightly below EF (at about from −2 to −3 meV). The peak is asymmetric with a higher-intensity shoulder at negative energy. This is likely due to a hole-like band with a top just below EF, as evidenced in the QPI measurements below. The enhanced density of states (DOS) near EF may underlie the large γ value of RbFe2As2. A similar conductance peak near EF was also observed in KFe2As2 (ref. 39).

To explore the superconducting state, low-energy tunneling spectra (±1.6 mV) are measured at zero magnetic field. As shown in Fig. 1f, a well-defined V-shaped superconducting gap is observed on type A surface (blue dots), which is the commonly observed case; for type B surface the gap is noticeably broader (green dots). The hump-like structure at negative bias is due to the aforementioned strong DOS peak. The gap on both surfaces are spatially uniform (see Supplementary Fig. 6). We find that the superconducting gap of type A surface can be well fitted with a nodal gap function. The red curve in Fig. 1f is a d-wave fit by using the Dynes formula45 for the superconducting DOS:

$$N(E)_k = |{\mathrm{Re}}[(E - {\mathrm{i}}\varGamma )/\sqrt {\left( {E - {\mathrm{i}}\varGamma } \right)^2 - \Delta _k^2} ]|,\;{\mathrm{and}}\,\Delta _k = \Delta _0{\mathrm{cos}}(2\theta _k).$$

(Note that the gap function Δk = Δ0cos(4θk) which corresponds to nodal s-wave pairing43 will result in exactly the same DOS). The tunneling conductance is given by $${\mathrm{d}}I/{\mathrm{d}}V \propto \mathop {\smallint }\nolimits N\left( E \right)_kf^\prime \left( {E + eV} \right){\mathrm{d}}k{\mathrm{d}}E$$, where f(E) is the Fermi–Dirac function at Teff = 310 mK. The fitting yields Δ0 = 0.47 meV and a small Γ of 0.03 meV that accounts for additional non-thermal broadening (e.g. impurity scattering). The ratio 2Δ0/kBTc is 4.36. For comparison, anisotropic s-wave gap fit is also plotted in Fig. 1f (dashed curve). It does not match the tunneling spectrum, especially around the gap bottom. On type B surface, the nodal fit with a similar gap size of Δ0 = 0.46 meV can match the gap bottom but deviates near the coherence peaks (black curve). The fitting yields a larger Γ of 0.09 meV, which may indicate a detrimental effect to superconductivity on type B surface.

### C4 symmetry breaking in QPI and magnet vortex mapping

Next we turn to examine the electronic structure of RbFe2As2 by performing dI/dV mapping. Figure 2a, b are two representative dI/dV maps taken on the type A surface in Fig. 1a (at T= 20 mK, Teff = 310 mK), where clear interference patterns can be observed. Figure 2e, f display the raw and symmetrized fast-Fourier transform (FFT) maps at different energies, respectively, which give the q-space scattering patterns (see Supplementary Fig. 7 for a complete set of QPI data and raw FFTs). The FFTs display a ring-like structure at relatively high energies (E> 7 meV). However, it becomes diamond-shaped and obviously two-fold symmetric as approaching EF. To identify the orientation of the scattering pattern, in Fig. 2i we plot the FFT map at E= 2.2 meV together with the unfolded BZ (derived from atomic resolved topography and the lattice structure shown in Fig. 1d). It is seen that the two-fold-symmetric axes are along the (π, π) or (π, −π) directions (the diagonal of the Fe plaquette). Such C4 symmetry breaking between (π, π) and (π, −π) in QPI has never been reported for other iron pnictides. Another notable feature is the elongated direction of the scattering pattern rotates 90° as the energy is lowered below EF (e.g., compare the FFTs of E = 2.2 meV and −2.7 meV in Fig. 2f, and see also Supplementary Fig. 7). Despite such a complicated evolution, the overall anisotropic scattering patterns changes with energy (see also Supplementary Fig. 7), indicating that they originate from QPI of anisotropic band(s). To demonstrate the evolvement of such band(s), in Fig. 2j we summarize the FFT profile near (π, 0) direction (where strong scattering weight distributed around) at various energy. An overall hole-like dispersion can be seen, and a parabolic fit yields a band top (Eb) = 27 meV and Fermi crossing at qF = 0.21 Å−1. More specific interpretation to such QPI will require detailed knowledge on the origin of anisotropic band structure.

Besides commonly observed type A surfaces, on the occasionally observed type B surfaces we find even greater anisotropy. Figure 2c, d g–h show representative dI/dV maps and FFTs taken on a 50 × 50 nm2 area marked in Fig. 1b (a complete set of QPI data is shown in Supplementary Fig. 8). Highly anisotropic interference patterns can be seen in the vicinity of surface defects, which are more pronounced along one of diagonal direction of the Fe lattice. The corresponding FFTs now display two arc-like features, which are also along the (π, π) in the unfolded BZ, manifesting a strong C4 symmetry breaking. Such arc-like features exist in a relatively wide energy range from –10 to 20 meV (see Supplementary Fig. 8) and disperse with energy as well. In Fig. 2k we show the FFT profile of type B surfaces around the (π, π) direction. A hole-like dispersion is observed with Eb = 30 meV and qF = 0.22 Å−1, which are close to the values for type A surface. Thus the basic band structure of type B surface is likely similar to that of type A surface; however, it is driven to be more anisotropic for some reason as discussed later. Despite the anisotropy, the hole-like dispersion in QPI appears to be consistent with a recent ARPES study on RbFe2As238, in which a single hole pocket is observed at Γ. We note that ARPES studies on the sister compound KFe2As2 found three hole pockets at Γ, which is reproduced in DFT calculations on its paramagnetic state34,35,36. As discussed in ref. 38, this difference could be due to the larger spacing between FeAs layers in RbFe2As2, which enhances the two-dimensionality of the system.

Another notable feature in Fig. 2j is that besides the main hole-like dispersion, there is likely a second band with the top very close to EF (tracked by black dashed line). Such feature is more clearly seen in the FFT profiles of type B surface along the (π, −π) direction, as shown in Fig. 2l. However, it is totally absent in the (π, π) direction (Fig. 2k), which also reflects the C4–C2 symmetry breaking. This band may closely relate to the DOS peak observed in dI/dV (Fig. 1e), as there could be van-Hove singularity near the band top39. Its exact origin is unclear at this stage.

To further investigate this novel C4 symmetry breaking and its effect on the superconductivity, we studied magnetic vortices induced by an external field. Figure 3a shows a zero-bias conductance (ZBC) mapping taken on a 150 × 150 nm2 area of type A surface, under a perpendicular field of B= 0.5 T. A vortex lattice is reflected by the high conductance regions. One sees that the vortex cores display anisotropic shape. To show this more clearly, a spatially averaged core (of 6 vortices) is shown in the Fig. 3c inset. It is slightly elongated along the diagonal of the Fe lattice, consistent with the two-fold symmetry of QPI. At the core center, a zero-bias peak is observed in dI/dV (Fig. 3b), and the peak “splits” on moving away from the center. This is typical behavior of vortex core states for a clean superconductor46. The core states decay spatially on approximately the scale of the superconducting coherence length (ξ). Exponential fits to the profile along the long and short axes of the vortex core yield ξAL = 15.0(±0.35) nm and ξAS = 12.5(±0.2) nm (Fig. 3c), respectively. For type B surface, ZBC map of a 225 × 225 nm2 area under B = 0.5 T is shown in Fig. 3d. The vortex cores are clearly more anisotropic (a zoom-in of single core is shown in Fig. 3f); while a zero-bias peak is also observed in the core center (Fig. 3e). The coherence lengths for the long and short axes are found to be ξBL = 26.7(±0.7) nm and ξBS = 16.3(±0.5) nm, respectively. As expected, the ratio ξLS of type B surface (1.63) is larger than that of type A surface (1.2), reflecting stronger anisotropy in the former. Since the spatial shape of the vortex core is intimately related to the underlying band structure47, the elongated vortex cores provide further evidence for C4 symmetry breaking in the electron states. To see the orientation of the anisotropic core with respect to the k-space band structure, we superpose FFT maps (taken near EF) onto the vortex maps as insets in Figs. 3a, d. On type B surface, the vortex is elongated along the direction where the FFT displays a (dispersive) arc-like feature. This is apparently consistent with the BCS expectation that ξ is longer in the direction with larger Fermi velocity (ξ ~ hvF/πΔ). On type A surface, a similar tendency is observed, despite weaker anisotropy in the vortex core and QPI. We note the k-space structure of Δ and the possible nematic order as discussed below should also related to the anisotropy of vortex core48,49.

So far, the C4 symmetry breaking between (π, π)/(π, −π) has been clearly evidenced in QPI and vortex measurements. The emergence of significant symmetry breaking in such heavily hole-doped region is surprising. It cannot be a surface effect since the surface atomic structure remains four-fold symmetric (Fig. 1d), and there is no bulk structural transition reported for AFe2As2 (A = Rb, K, Cs). Furthermore, the surface Rb vacancies are point-like without noticeable uniaxial anisotropy that may introduce anisotropic QPI, and the shape of the vortex core is also unrelated to surface defects. Thus, the observed symmetry breaking is reminiscent of a nematic-like electron state. Previously, anisotropic QPI, which breaks the symmetry between (π, 0) and (0, π), was observed in undoped and lightly-doped iron pnictides, such as Ca(Fe1–xCox)2As27, NaFeAs12, and LaOFeAs9. It was commonly considered to be a signature of electronic nematicity with an origin closely related to spin and/or orbital degrees of freedom. Theoretical works have shown that the (π, 0) stripe AFM (SDW) order tends to open a partial gap along the antiferromagnetic direction, which distorts the Fermi surface and thus the QPI to be two-fold symmetric50,51. Such symmetry breaking may even persist above TN due to short-range spin fluctuations52. Here, it is the first time to visualize a C4 symmetry breaking in heavily hole-doped FeSC, and in a 45° rotated direction, this may suggest RbFe2As2 is likely proximate to a stripe-type AFM order or SDW with a Q along (π, π) direction, which breaks the (π, π)/(π, −π) equivalence. We note that two-fold anisotropic QPI along (π, π) has been reported in FeTe films, which exhibit a bicollinear AFM with Q = (π/2, π/2)53. While direct measurements of spin fluctuations in RbFe2As2 are still lacking, spin fluctuations that deviated from (π, 0) has been observed in KFe2As240,41,42. However, whether these fluctuations can drive the C4 symmetry-breaking needs further study. On the other hand, orbital order can also drive nematicity, as proposed for FeSe16, which will result in an anisotropic Fermi surface and QPI8. A similar orbital order was also observed in FeSexTe1-x54. No matter which mechanism may apply, details of the anisotropic band structure will depend on material parameters such as Hund’s coupling and on-site Coulomb interaction50,51, which require further investigations.

Assuming the symmetry breaking is from electronic nematicity, there remains a question as to why type B surface shows stronger anisotropy than type A surface, despite their seemingly identical surface lattice structure. We note that for undoped iron pnictides, the (π, 0)/(0, π) nematicity (and the stripe AFM order) can be enhanced by applying uniaxial pressure55. Thus we speculate that type B surface may have local strain (e.g. due to different shrinkage of the sample and its glue upon cooling), which enhances the nematic state in these regions, while even type A surface may also have strain but is likely weaker than type B surface. Nevertheless, even if the strain plays a role here, our observations still imply that RbFe2As2 has a strong tendency or “susceptibility” to form nematic states along (π, π)/(π, −π) rather than (π, 0)/(0, π). Furthermore, it is clear that the superconducting gap features observed on type B surface are significantly broader than on type A surface (Fig. 1f). This reflects a competition between superconductivity and the degree of anisotropy, resembling the anti-correlation between superconductivity and the (π, 0)/(0, π) nematicity observed in NaFe1-xCoxAs13 and FeSexTe1-x54. More evidence on such anti-correlation behavior is shown in the surface K dosing measurement below.

### Effect of Rb vacancy and atomic step edges on superconductivity

The (π, π)/(π, −π) symmetry breaking may have a more profound relation to the superconductivity in RbFe2As2—the interactions and fluctuations of the nematic state could also underlie the electron pairing. Investigating the pairing symmetry of the system can provide further insight on this. In Fig. 1f, the well-defined V-shaped superconducting gap has suggested a nodal pairing, to further investigate the pairing symmetry, we studied the impurity effect that was induced by surface Rb vacancies and atomic step edges. Figure 4a shows an STM image around a Rb vacancy (VRb) on type A surface, while Fig. 4b displays the tunneling spectra taken near it. The superconducting gap has an increased DOS near EF at the VRb site, which evidences a local suppression of superconductivity. This gap suppression quickly disappears on moving away from VRb (the Fig. 4b inset details the gap bottom). An exponential fit to the ZBC value as a function of distance yields a decay length of 1.41 nm (Fig. 4c). Similar gap suppression was also observed near the VRb on type B surfaces, as shown in Fig. 4d–f. Since Rb vacancies are expected to be non-magnetic, this suppression of the superconductivity suggests a sign-changing pairing56. However, we note both d-wave and extended s-wave pairing with accidental nodes may have a sign-change, as recently suggested in the sister compound KFe2As2 (refs. 35,43,44,). A further way to gain k-space information on the gap is to detect its response to sample boundaries. It was predicated that for a nodal pairing with a sign-change, Andreev bound states at zero energy will be formed at boundaries perpendicular to the nodal direction, due to the phase change in the quasi-particles’ reflection, and decay into the bulk on the scale of coherence length57. However, no bound states will form on boundaries perpendicular to the anti-nodal direction (in the ideal case). Experimentally, atomic step edges on the surface can be treated as (weak) 1D boundaries since they carry line scattering potential, and evidence of Andreev bound state has indeed been observed near [110]-oriented step edges in Bi2Sr2CaCu2O8-δ58.

On type A surfaces we have found [110]- and [100]-oriented step edges formed during cleavage. Topographic images around these steps are shown in Fig. 5a, c. The orientations of the edges are confirmed by imaging the atomic lattice nearby (e.g. see Fig. 5b), and they are all verified to be single steps with height equal to half of the c-axis lattice constant of RbFe2As2 (Fig. 5d). Figure 5e, g shows tunneling spectra taken along lines perpendicular to the [100] and [110] edges, respectively. To clearly see the variation of the spectra with distance to the edge, we subtract from them a spectrum taken far away from the step edge and show the difference in Fig. 5f, h. The superconducting gap is suppressed in the immediate vicinity (d= 0) of both edges, as indicated by the in-gap peaks in the difference spectra. However, on moving away from the step edge, the decay of the in-gap peaks along [110] is much slower than along the [100] direction. In Fig. 5i, we plot the ZBC values as function of distance from the step edge. The exponential fit yields a decay length of 6.28 nm for the [110] step edge and 1.46 nm for [100]. Such a large (over three times) difference cannot be solely explained by the anisotropic coherence length as reflected in vortex mapping (Fig. 4), since the anisotropic ratio ξLS of type A surface is only 1.2 (the orientation of the vortex core relative to the step edge is indicated in Fig. 5a, c). It is more likely due to the presence of gap nodes in the {[110]} directions. As shown in Fig. 5j, for $$d_{x^2 - y^2}$$ like pairing, a [110] boundary can give rise to bound states as it is perpendicular to the nodal direction, and these will decay into the bulk on the scale of ξ, while the [100] boundary cannot induce such a state. For the extended s-wave pairing suggested in35,43 (Fig. 5k), neither [110] nor [100] boundaries can induce bound states because both are perpendicular to anti-nodal directions. The relatively long decay length for the [110] step edge evidences the formation of bound states (although it is still shorter than the 15 nm ξ for this direction, as discussed below). Gap suppression is not expected for an ideal [100]-oriented edge under $$d_{x^2 - y^2}$$ pairing. However, we notice that the decay length on [100] edge (1.46 nm) is very close to the decay length of gap suppression near VRb (1.41 nm, see Fig. 4c), which is measured roughly along [100] direction. Thus the gap suppression on [100] edge could be induced by random disorders near the edge (local disorders always exist on step edges, particularly for the energy-disfavored [100] edge here). We note that the point-like defect induced in-gap states are usually localized within several lattice constant to the defect site59,60, as theoretically their intensity varies as 1/d2e-d/ξ, gives a decay scale much shorter than ξ 59,61.

The above observations are consistent with the $$d_{x^2 - y^2}$$ -like pairing suggested by several theoretical works on heavily hole-doped FeSC17,23. We also note some recent theoretical work has suggested that electronic nematicity is compatible with a mixing of s + d (or s + id) pairing62,63, which may also be applicable for RbFe2As2. In the mixed state, signatures of d-wave pairing should still exist, such as the nodal gap in dI/dV and different response at the [110] and [100] edges. However, these signatures could be blurred by the s-wave component, e.g., it weakens the intensity of bound states at [110] edges and gives shorter decay length. How these theories would be modified by the (π, π) diagonal nematicity observed here requires further study.

### Effect of surface potassium (K) dosing on RbFe2As2

To gain more insights on how the (π, π) nematic state and superconductivity interplay, we hereby explore how they evolve with doping. We thus performed in situ surface K dosing on RbFe2As2 in an STM system working at T = 4.5 K (see Methods for details). Dosing K atoms will lower the hole-doping of the (top) FeAs layer via introducing electrons. Figure 6a–c shows typical topographic images with various K coverages (Kc = 0.012–0.17 ML, and one monolayer (ML) is defined as the areal density of Fe atoms in a FeAs layer, which is ~13.4 nm-2). Without K dosing (Kc = 0), anisotropic QPI patterns that breaks (π, π)/(π, −π) equivalence were also observed at T = 4.5 K, as shown in Fig. 6f, g (see Supplementary Fig. 9 for additional data), indicating that the (π, π) nematicity persists above Tc. Upon K dosing, as shown in Fig. 6d, the broad DOS peak below EF is gradually suppressed as Kc increases, while a gap of Δ ~3.5 meV is opened at EF at Kc = 0.17 ML, which is spatially uniform (Fig. 6e). The QPI patterns at Kc = 0.17 ML are shown in Fig. 6h, i, which remarkably became rather four-fold symmetric (see Supplementary Fig. 9 for raw FFTs). This indicates that the nematicity is greatly suppressed in the less-hole-doped regime, compatible with the current understanding of the phase diagram. We further checked the temperature dependence of the tunneling gap at Kc = 0.17 ML and found it closes at T ~12 K (Supplementary Fig. 10). Note that for Kc = 0.17 ML, the doping of the top FeAs layer is expected to be 0.33 holes/Fe atom (assuming each K atom can dope one electron, which could be less). Then it will be comparable to Ba1-xKxFe2As2 with x ≥ 0.66 in the hole over-doped region. Thus the observed 3.5 meV gap is most likely a superconducting gap with a Tc of ~12 K (which gives 2Δ/kBTc = 6.8). Therefore, the above results directly evidence that the (π, π) nematicity is suppressed at reduced hole-doping, while the superconductivity is simultaneously enhanced.

The scattering weight in Fig. 6i (Kc = 0.17 ML) are particularly strong near the (π, 0)/(0, π) directions (dashed lines), suggesting they are from intra-band scattering of a square-shaped pocket. In Fig. 6j, k we plot FFT profiles taken around (π, 0) directions for Kc = 0 and 0.17 ML, respectively, with parabolic fitting applied. The overall dispersion for Kc = 0 has a qF = 0.19 Å−1 and Eb = 25 meV, which is similar to Fig. 2j that measured at T = 20 mK (Teff = 310 mK) on type A surface. For Kc = 0.17 ML, the dispersion is also hole-like but has a significantly larger qF = 0.34 Å−1 and Eb = 50 meV (Assuming qF= 2kF for intra-band scattering, the resulting kF = 0.17 Å−1 is comparable with that of ARPES observed α pocket of Ba0.3K0.7Fe2As2 (kF ~ 0.21 Å−1, ref. 37)). However, a reduced qF at Kc = 0 is apparently unexpected, as it has a higher hole concentration than the K-dosed case. It would then imply certain band reconstructions happened in the presence of (π, π) nematicity at Kc = 0.

## Discussions

Our measurement evidences a novel (π, π) diagonal nematicity that coexists with a nodal $$d_{x^2 - y^2}$$ like pairing component in the strongly hole-doped RbFe2As2 (with a 3d5.5 configuration). The diagonal nematicity persists into the normal state above Tc, which implies that the superconductivity emerges in the nematic phase, and nematic fluctuations may play a role. Furthermore, the surface electron doping clearly demonstrated an anti-correlation between such a nematicity and superconductivity. In Fig. 7 we summarize above results in a sketch of global phase diagram of 122 type iron pnictides. These results give important clues on the origin of nematicity, and highlight the intimate relation between nematicity and superconducting pairing. As shown in Fig. 7, the stripe AFM and (π, 0) nematicity of the parent material weakened through hole-doping, and disappear near the “optimal” doping with highest Tc (refs. 1,2,15). The pairing at optimal doping is widely believed to be s± wave and mediated by (π, 0) spin fluctuations3,4. Here in the over-hole-doped regime, the re-emergence of a new type of diagonal nematic state and change in the pairing symmetry with suppressed Tc imply the system approaches a new regime with different fluctuations. Since an AFM Mott insulting state resembling the parent compound of cuprates was predicted for 3d5 configuration18,19, the related spin/nematic fluctuations are likely the candidate. It may give rise to or mediate both the diagonal nematicity and the d-wave pairing component, although the microscopic details require further theoretical refinement. Therefore, our results would lay the groundwork for a unified understanding of the cuprates and FeSCs.

While preparing this paper, we became aware of an NMR study on CsFe2As2, which also suggests a nematic state along the (π, π) direction64. It thus provided complementary evidences for the re-emergence of electronic nematicity in heavily hole-doped FeSCs. We also noticed that another NMR study65 has revealed strong spin fluctuations in RbFe2As2 and CsFe2As2.

## Methods

### Sample growth and transport measurements

The RbFe2As2 singles crystals were grown in alumina crucibles by a self-flux method, as described in ref. 28. Zero resistance is observed below Tc ~ 2.5 K (Supplementary Fig. 1c). By fitting the resistance data with R = R0+kT2 for T 50 K (Supplementary Fig. 1b), the residual resistivity ratio (RRR = R(T = 300 K)/R0) is calculated to be 533. Such a large RRR value has been reported for AFe2As2 (A= K, Rb, Cs), which was attributed to a strong correlation induced coherence–incoherence crossover at high temperatures27.

### STM measurements and surface K dosing

Low-temperature STM experiment (except the surface K dosing effect) was conducted in a commercial 3He/4He dilution refrigerator STM (Unisoku) at the base temperature of ~20 mK. The effective electron temperature (Teff) of this system was checked to be ≤310 mK by measuring the superconducting gap of Al films (see Supplementary Note 1). RbFe2As2 samples were cleaved in ultrahigh vacuum at ~80 K (liquid nitrogen temperature) and immediately transferred to the STM module. Pt tips were used after careful treatment on Au (111) sample. The tunneling spectroscopy (dI/dV) was performed using a standard lock-in technique with modulation frequency f = 787 Hz, and the modulation amplitudes (ΔV) are specified in the figure captions.

The surface K dosing on RbFe2As2 was conducted in another cryogenic STM at T = 4.5 K. RbFe2As2 sample was cleaved at ~30 K and Pt tips were also used after treatment on Au (111). K atoms were evaporated from standard SAES alkali metal dispensers, and the sample was kept at 80 K during deposition. The deposition rate was carefully calibrated by directly counting surface K atoms at low coverage. The tunneling spectra were obtained by using lock-in technique with modulation frequency f = 915 Hz and amplitude ΔV = 1 mV.

## Data availability

All the original data related to this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank Professor P. Adelmann for the help on sample growth, and thank Professors T. Wu, J. P. Hu, D. H. Lee and Dr. D. Peets for helpful discussions. This work is supported by the National Natural Science Foundation of China, National Key R&D Program of the MOST of China (Grant No. 2016YFA0300200 and 2017YFA0303004), National Basic Research Program of China (973 Program) under grant No. 2015CB921700, and Science Challenge Project (grant no. TZ2016004).

## Author information

Authors

### Contributions

The growth of RbFe2As2 singles crystals was performed by T.W. The STM measurements and data analysis were performed by X.L., R.T., M.R., W.C., Q.Y., Y.Y. and T.Z.. T.Z. and D.L. Feng coordinated the project and wrote the manuscript. All authors have discussed the results and the interpretation.

### Corresponding authors

Correspondence to Tong Zhang or Donglai Feng.

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### Competing interests

The authors declare no competing interests.

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Liu, X., Tao, R., Ren, M. et al. Evidence of nematic order and nodal superconducting gap along [110] direction in RbFe2As2. Nat Commun 10, 1039 (2019). https://doi.org/10.1038/s41467-019-08962-z

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