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

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{d}}_{{{x}}^2 - {{y}}^2}$$\end{document}dx2-y2 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.

pre-aligned to X scan and Y scan directions (Vb = 8 mV, I = 1 nA, scale bar: 2 nm)). The lattice constant is measured to be 5.4 Å, and the lattice is rotated 45° with respect to a0, b0. (d) Laue diffraction pattern of a FeSe single crystal. (e) Simulated Laue pattern of FeSe with a0, b0 along X and Y directions. The Miller indices (hkl) of the plane corresponding to the diffraction points near center are also marked. (f) STM image of cleaved FeSe crystal with a0, b0 pre-aligned to X scan and Y scan directions (Vb = 100 mV, I = 100 pA, scale bar: 2 nm). The lattice constant is measured to be 3.75 Å, and the lattice has the same orientation with a0, b0. Note: The spots marked by red and blue circles in panels a, d are corresponding to the spots marked by the same colored indices in the simulated pattern (in panels b, e). They originated from {10X} and {11X} plane families, respectively.  Fig. 1b of the main text. Each dI/dV maps are taken at a Vb equal to the mapping energy (labeled on the map) and I = 100 pA; the lock-in modulation (ΔV) for each map has an amplitude of 5% Vb. Details about the FFT symmetrization is described in Supplementary Note 3. Every dI/dV map has 256 × 256 pixels. Scale bar in the dI/dV image is 20 nm, and that in FFTs are 0.5 Å -1 .

Supplementary Figure 8 | A full set of dI/dV maps taken on type B surface and their FFTs.
The topography of the mapping area is shown in Fig. 1c of the main text. Each dI/dV maps are taken at a Vb equal to the mapping energy (labeled on the map) and I = 100 pA; the lock-in modulation (ΔV) for each map has an amplitude of 5% Vb. Every map has 256 × 256 pixels. Scale bar in the dI/dV image is 20 nm, and that in FFTs are 0.5 Å -1 .

Supplementary Note 1: Calibration of the effective electron temperature of the STM system
Due to the electrical noise and RF radiations, the effective electron temperature (Teff) of a low-T STM is usually higher than the thermometer reading. The Teff of the dilution refrigerator STM used in this work is calibrated by measuring the superconducting gap of an Al film grown Si(111). Supplementary Fig. 2a shows a typical STM image of the Al/Si(111) film, with a thickness of ~ 20 monolayer (ML), and Supplementary Fig. 2b shows its superconducting gap spectrum. A standard BCS fit (red curve) yields Δ = 0.19 meV and Teff = 310 mK. Here we note that in order to make a conservative estimation of Teff, Dynes broadening term is not used in the fitting (Γ = 0). In the presence of finite Γ or other broadening factors, the actual Teff could be slightly lower than the fitted value.

Supplementary Note 2: Determining the surface atomic structure of cleaved RbFe2As2
The surface structure of cleaved RbFe2As2 is revealed by resolving the atomic lattice of the defect-free area and that inside of the Rb vacancies. Supplementary Fig. 3a is a typical image of type B surface with multiple Rb vacancies. Supplementary Fig. 3b shows the region marked in Supplementary Fig. 3a in greater detail (shown with a linear color scale). A square lattice inside of the Rb vacancies can be seen and has a lattice constant of ~3.8 Å, matching a0, which is mostly likely from the underlying FeAs layer. The lattice of the defect-free area is hard to see in Supplementary Fig. 3b due to its much smaller corrugation. To enhance the contrast, a nonlinear color mapping is used in Supplementary Fig. 3c, in which both the surface Rb lattice and lattice inside the vacancy can be seen. By comparing the atomic sites of these two lattices (as marked in Supplementary Fig. 3d), the surface lattice model is derived and shown in Supplementary Fig. 3e. The surface Rb forms a √2×√2 (R45°) lattice with respect to the As lattice.
For the lattice model in Supplementary Fig. 3e, the surface Rb atoms will have another set of occupation sites, as illustrated by the dashed circles. These two equivalent occupation sites are shifted by 1/2 unit cell with respect to each other (along both a and b directions), which should result in domain structures when both are present. We indeed observed such domain structures on samples cleaved at a lower temperature (~30K), as shown in Supplementary Fig.  4a. There are domain boundaries running through the surface (marked by red arrows). Supplementary Fig. 4b is an atomically resolved image near a domain boundary. One can see aside of the boundary, the surface still displays a √2×√2 lattice. However, the lattice of the upper domain is shifted by 1/2 unit cell along a and b with respect to the lower domain. To illustrate this, we draw a lattice of white spots which matches the atomic lattice of the lower domain, however it mismatches the upper domain by the above offset. The existence of different domains gives further support to the surface lattice model in Supplementary Fig. 3e.
The assignment of surface atomic structure above is based on STM imaging. To further confirm the orientation of surface √2×√2 lattice with respect to the bulk FeAs lattice, we performed Laue diffraction measurement to accompany STM imaging. The results are summarized in Supplementary Fig. 5. We first determined the orientation of a0 and b0 (the inplane basic vectors of 2Fe unit cell) of RbFe2As2 single crystal by comparing its measured Laue pattern with a simulated pattern. As shown in the simulation in Supplementary Fig. 5b, the four diffraction spots that closest to the center, labelled by red colored Miller indices, are originated from {10X} plane family (defined by 2Fe unit cell, so they are along the a0 or b0 directions); while the spots with blue colored Miller indices are from {11X} plane family. In the measured Laue pattern, only the spots close to the center show up with significant weight ( Supplementary Fig. 5a), so the crystal orientation can be determined by comparing it to Supplementary Fig. 5b. Then the crystal was glued on STM sample holder with a0 and b0 aligned to X and Y scan directions, respectively. The STM image of cleaved surface ( Supplementary Fig. 5c) then directly shows the surface √2×√2 lattice is rotated 45° with respect to a0 and b0. We also repeated the same procedure on a pure FeSe single crystal, the results are shown in Supplementary Figs. 5d-f. The FeSe has a Laue pattern in analogous to RbFe2As2, and its a0, b0 directions are determined in a similar way. The STM image in Supplementary Fig. 5f show that its surface lattice has a constant of 3.75 Å, with the direction the same as a0 and b0. This is well expected for a Se terminated surface of FeSe. Therefore, combined Laue and STM measurement directly indicates the surface √2×√2 lattice of RbFe2As2 is rotated 45° with respect to a0, b0.