Exploration of two surfaces observed in Weyl semimetal BaMnSb₂

Abstract

Single crystalline BaMnSb₂ is considered as a 3D Weyl semimetal with the 2D electronic structure containing Dirac cones from the Sb sheet. We report experimental investigation of low-temperature cleaved BaMnSb₂ surfaces using scanning tunneling microscopy/spectroscopy and low energy electron diffraction. By natural cleavage, we find two terminations: one is Ba (above the orthorhombically distorted Sb sheet) and another Sb2 (at the surface of the Sb/Mn/Sb sandwich layer). Both terminations show the 2 × 1 surface reconstructions, with drastically different morphologies and electronic properties, however. The reconstructed structures, defect types and nature of the electronic structures of the two terminations are extensively studied. The quasiparticle interference (QPI) analysis is conducted at the energy range between −2 V and 2 V, although no interesting states are observed near the Fermi level, the surface-projected electronic band structures strongly depend on the surface termination above 1.6 V. The existence of defects can greatly modify the local density of states to create electronic phase separations on the surface in the order of tens of nm scale. Our observation on the atomic structures of the terminations and the corresponding electronic structures provides critical information towards an understanding of topological properties of BaMnSb₂.

Introduction

Layered materials with a chemical formula AMnX₂ have an advantage of enabling interesting quantum phenomena such as the quantum Hall effect and chiral current¹ (A: alkaline-earth and rare-earth ions, X: Bi and Sb). The crystal structure of AMnX₂ consists of an alternating stack of a 2D conduction layer (X sheet) and a Mott insulating block (A²⁺-Mn²⁺-X³⁻). The magnetic moment of Mn in such a system is typically antiferromagnetically ordered near room temperature^2,3, thus breaking time-reversal symmetry (TRS). The interplay between magnetism, crystal structure, and topological properties hosted by the X sheet has been heavily debated. For example, first-principles calculations predict the existence of Dirac crossings near the Fermi level of BaMnSb₂, assuming X (=Sb) square lattice⁴. Such crossings should not exist in the presence of spin-orbit coupling (SOC), TRS, and inversion symmetry⁵. On the other hand, by considering both SOC and the canted antiferromagnetic ordering of Mn, Dirac crossings remain in a centrosymmetric I4/mmm structure scenario (i.e., assuming X square lattice)⁶. However, recent single crystal x-ray diffraction, scanning transmission electron microscopy and neutron scattering studies revealed that BaMnSb₂ actually forms an orthorhombic structure (Imm2), which is noncentrosymmetric^1,7,8. With the Imm2 structure, Dirac cones are gapped without⁷ or with the consideration of the magnetism (assuming the G-type magnetic ordering in ref. ⁸). Apparently, existing calculations for BaMnSb₂ do not represent the system with both broken inversion symmetry (Imm2, in which X sheet consists of zig-zag chains) and TRS (canted AFM). Experimental investigations, on the other hand, demonstrate that electrons at the Fermi level are nearly zero effective mass with high mobility and the nontrivial Berry phase^6,9, spin-valley locking^1,7, and linear band dispersion⁸, as expected from a Weyl semimetal. With the settlement of both the crystal and magnetic structures determined by experiment^1,2,7,8, it is important to elucidate the relationship between crystal symmetry, magnetic configuration, and electronic structures. For example, while the linear band dispersion has been observed by angle-resolved photoemission spectroscopy (ARPES)⁸, there is no evidence for the formation of a Fermi arc connecting two Weyl nodes, which is expected in a Weyl semimetal¹⁰. When applying surface sensitive techniques such as ARPES and scanning tunneling microscopy/spectroscopy (STM/S), key to understanding experimental data is the determination of the surface structure. The only feasible approach is to combine both STM/S and low energy electron diffraction (LEED) techniques for both the surface electronic and crystal structure determination. It is particularly crucial for layered materials, as there are possibly multiple surface terminations. Techniques such as ARPES cannot correlate the measured band structure with specific surface/layer. By measuring physical properties from the specific surface/layer, we are capable not only to directly compare experimental observations with the calculated band structure but also to guide new materials design for desired properties such as square net versus zig-zag chain arrangement in the X sheet of AMnX₂.

In this paper, low-temperature cleaved BaMnSb₂ single crystal surfaces were studied using the low-temperature STM/S for surface electronic properties measurements and LEED for surface structure determination. Two natural cleavage terminations are found with the Ba termination (T1) and Sb2 termination (T2). The former is above the Sb (Sb1) sheet, while the latter locates at the Sb2/Mn/Sb2 sandwich layer. Although both terminations show 2 × 1 surface reconstructions, their morphologies and electronic properties are drastically different, including the crystal structure, electronic structure, and defect types. The quasiparticle interference (QPI) analysis reveals that the surface-projected electronic structure strongly depends on the surface termination. Especially, defects can greatly modify the local density of state (LDOS) to create electronic phase separation in the order of tens of the nm scale. Our observation on the atomic structures of each termination with reconstruction as well as their well-defined electronic structures provide key information towards an understanding of topological properties in the AMnX₂ system.

Results and discussion

Existence of two cleavage terminations

Figure 1a shows the ball and stick model of the Imm2 crystal structure of bulk BaMnSb₂ with lattice parameters a = 4.45 Å, b = 24.22 Å and c = 4.51 Ź. There are two nonequivalent Sb sites: Sb1 forming a sheet and Sb2 forming a (Sb2)/Mn/(Sb2) slab. Compared to a bonding length between Ba and Sb1 atoms (3.519 Å), the bonding between Ba and Sb2 is longer (3.585 Å)¹. One would thus expect the bond between Sb2 and Ba is broken when cleaving. As a result, the cleavage creates two terminations: Sb2 and Ba (the two sides cut along the blue dashed line in Fig. 1a). Top view of the truncated Ba and Sb2 surface layers are shown in the Fig. 1b, c, respectively. The neighbor atoms surround Ba and Sb2 are clearly revealed. Figure 1d is the LEED pattern collected at 77 K on an in situ low-temperature cleaved single crystal, revealing two-domain 2 × 1 reconstruction with weak fractional spots on a white background. Although the domain size is sufficiently large to reveal 2 × 1 reconstruction, strong background results from imperfections including defects, domain boundaries, and step edges on the surface.

Fig. 1: Crystal structure of BaMnSb₂.

a Schematic ball and stick model showing the crystal structure of BaMnSb₂ with the Imm2 space group. Ba, Sb1, Sb2 and Mn layers are indicated. b, c Schematic drawing of the two cleavage terminations Ba and Sb2 which correspond to the blue dotted layers in (a), respectively. d LEED pattern from a surface showing 2 × 1 reconstruction with domains, collected at 77 K with the energy of 60 eV. The integer spots are marked with black circles.

To understand the origin of the 2 × 1 surface structure observed in LEED, we have cleaved several crystals at low temperatures for STM investigation. By surveying many areas of cleaved surfaces, we find that the surface morphologies can be categorized into two types: termination 1 (T1) and 2 (T2). Figure 2a and d show the typical STM images of T1 and T2, respectively. The corresponding fast Fourier transformation (FFT) in the inset reveals that, for both T1 and T2, there are both integer spots (black circles) and 2 × 1 spots (red circles). Although both T1 and T2 have 2 × 1 reconstructions, those reconstructions are morphologically and electronically different.

Fig. 2: Surface morphology of BaMnSb₂ showing two terminations: T1 (a–c) and T2 (d-f).

a, d Large area STM images of T1 and T2. 2D-FFTs are shown in the insets with integer spots indicated by black circles, 2 × 1 spots in red circles. The scale bars represent 10 nm. b, e Atomically resolved images from T1 and T2. Two types of defects are circled in red and green circles. Black arrows in (b) point to moving defects generated by tip disturbance. Line profiles along the blue and green lines are shown in (g and h), A and B in (h) mark the positions of the two types of defects along the green line, respectively. A yellow line in (d) shows the reconstruction domain boundary. The scale bars represent 3 nm. c, f Defect maps of T1 and T2 created by removing 2 × 1 reconstructions. The scale bars represent 3 nm. Scan conditions: (a), −1 V, 100 pA, (b), −1 V, 100 pA, (d), −1.5 V, 30 pA, and (e), −0.6 V, 100 pA.

To observe features in the atomic resolution, the STM images are enlarged and shown in Fig. 2b, e, respectively. Note that (1) the 2 × 1 reconstruction on T1 and T2 and (2) the domain size on the T2 surface is much smaller than that on T1. For example, there is only one domain in the 65 nm × 65 nm image on T1 as shown in Fig. 2a. There are meandering domain boundaries across the whole image as marked by a yellow line in the T2 image (Fig. 2d). These domains are normal to each other (i.e., 90 degrees), forming 2 × 1 or 1 × 2 stripes. As a result, the FFT of the T2 surface shows two sets of ½ spots (red circles in the inset of Fig. 2d), while FFT from T1 has only one pair of ½ spots (red circles in the inset of Fig. 2a). The existence of large amount of reconstruction domains in the T2 surface implies that the 2 × 1 reconstruction in the T2 surface requires higher energy than that in the T1 surface. The creation of a large amount of domains is to compensate the energy cost.

In addition to domain size difference, we also observe the difference in defect types on T1 and T2. To better show the defects and their correlations, both FFT and reverse FFT methods are used to obtain defect maps by removing the 2 × 1 stripes from morphological images. The defect maps from T1 and T2 are shown in Fig. 2c, f, respectively. Note that most of defects are regular voids as marked by green circles (type-A) in Fig. 2b, c, e, and f. Another type of defects (type-B) is only observed on T1 as indicated by the red circles in Fig. 2b, c. These type-B defects have a protrusion in the middle of the 2 × 1 stripes. To reveal the details of the two types of defects, we plot the line profiles in Fig. 2g, h along the blue and green lines in Fig. 2b. Figure 2g shows the height profile across the 2 × 1 rows without defects (i.e., along the blue line in Fig. 2b), thus showing smooth height oscillation with the amplitude of ~50 pm (i.e., 0.5 Å). Along the green line in Fig. 2b (i.e., along a 2 × 1 row), the height profile reveals height difference between type-A and type-B defects as shown in the right panel of Fig. 2g.

A closer look of the two types of defects are shown in Fig. 3a, b, respectively, marked by a green (type-A defect) and a red (type-B defect) circle. The type-B defect is easily mobile during STM scans. Figure 2b shows two type-B defects marked by the black arrows, which jump between two neighbor scan lines. On the contrary, the type-A defect is very stable in both surfaces. To statistically verify the stability of these defects, we continuously take images and spectra at the same location. Figure 3c, d show two images collected in 12 hours separation, respectively. To make the comparison easier, we circled all type-A defects (63) in green circles and type-B defects in red circles (14) in Fig. 3c. Then all the circles are copied and pasted without any position adjustment to Fig. 3d. In Fig. 3d, all the green circles have a defect (type-A) in it, but there is no defect in the majority of the red circles (11), with three exceptions (red circles with X); and there exists an un-circled defect nearby most of the red circles. This means that in-between Fig. 3c, d, 11 out of the 14 type-B defects are moved at least on atom position along the 2 × 1 stripes. In contrast, none of the 63 type-A defects is moved. Counted from STM images, there are about 5% type-A and 0.7 % type-B defects (per 1 × 1 surface unit cell). Shown in Fig. 3e is the local barrier height (LBH) image from the same area, the slight contrast difference between type-A and type-B defects suggests there exists some chemical composition difference surround these defects. Figure 4a displays the gradual change of the conductance (dI/dV) spectra across two type-A defects (green spectra) and one type-B defect (red spectra) as indicated in the corresponding morphology image (right of Fig. 4a). Note that the electronic influence of these defects is extensive as discussed below. Compared with the black spectra with their peak positions guided by a dotted line, the green spectra obviously show peak splitting, while the red spectra show peak shift to higher energies in the occupied state.

Fig. 3: Defects in BaMnSn₂.

a, b, STM and current images (set point: −2 V, 50 pA) of an area show both type-A defect (green circle) and type-B (red circle) defects. A 2 × 1 unit cell is marked in a black rectangle. The scale bars represent 4 nm. c, d Two sequential STM images collected at the same location with 12 hours separation (set point: −1 V, 100 pA). All defects are marked by green (type-A) and red (type-B) circles, there are three of the red circles marked with blue crosses. See text for details. The scale bars represent 3.5 nm. e Local barrier height image from the same area as (c and d). f, g 2 × 1 reconstruction models (black rectangles) for T1 and T2 with both type-A (green circle) and type-B (red circle) defects. To differentiate from the truncated surface, the reconstructed atoms are draw in blue (R-Ba) and yellow (R-Sb2), respectively.

Fig. 4: Average electronic behavior of two terminations.

a STS spectra across two type-A defects (green spectra), one type-B defect (red spectra), and surrounding defect-free area (black spectra). The corresponding morphology image with the defects positions and spectra positions is included on the right (set point: −1 V, 100 pA, the scale bars represent 1 nm). b Average dI/dV spectra normalized to same set point (2 V, 100 pA) for T1 and T2. Inset: data replotted in a semi-logarithmic scale. c LDOS calculated as dI/dV/I/V from (a). Inset: zoom-in data near V = 0.

Identification of the two terminations

Given drastically different morphology and defect types, we believe that the nature of T1 and T2 is chemically different. STM images (Fig. 2a, b) clearly show that the 2 × 1 stripe consists of dimers, implying that both cleavage terminations keep all the top layer atoms. This is in contrast to the 2 × 1 reconstructed cleavage surfaces of BaFe₂As₂, where half of the Ba or As atoms at the cleavage surfaces are removed¹¹. The surface energy can be lowered by dimerizing the top layer atoms at cleaving, in the format similar to the Si (001) surface at annealing. The surface atoms of BaMnSb₂ form Ba-Ba or Sb2-Sb2 dimers, revealing a 2 × 1 structure on Ba and Sb2 surfaces, respectively. To distinguish T1 and T2, we further analyze the domain size and defect types observed by STM. It can be clearly seen that, from Fig. 1c, Sb2-Sb2 dimerizing in the a or c direction is equivalent. Energetically, it is reasonable to form 2 × 1 domains that are normal to each other on the Sb2 surface. However, the broken inversion symmetry by the zig-zag Sb1 chains under the Ba termination in Fig. 1b makes Ba-Ba dimerizing inequivalent in the a and c directions. The zig-zag Sb1 chain helps create large reconstructed 2 × 1 domains along the chain direction (the a direction). Although the zig-zag structured Sb1 sheet consists of normal to each other domains according to ref. ⁷, these domains are much larger (in the μm range) than our STM scanning area. As a result, we expect to observe much larger 2 × 1 domains on the Ba termination than that in the Sb2 termination. Our STM indicates that the 2 × 1 reconstruction in T1 is always in the same direction in a large area (Fig. 2a). In contrast, there exists many small domains that are normal to each other in the T2 termination (Fig. 2d). Thus, we consider that T1 is the Ba termination with the beneath Sb1 layer and T2 is the Sb2 termination with the beneath Mn layer. The structure models of the reconstructed T1 (R-Ba) and T2 (R-Sb2) are shown in Fig. 3f, g, where Ba (blue in Fig. 3f) and Sb2 (yellow in Fig. 3g) atoms dimer up to form 2 × 1 stripes.

The defects models are also proposed in Fig. 3f, g. The defects A and B are all unpaired monomers, but the difference between type-A and type-B defects is that the sublayer atom under the monomer is missing or not. As already shown in Figs. 2 and 3, both terminations prefer to form a dimer structure to lower the surface energy. In other words, the unpaired monomers are unstable, unless the local environment around the monomers is changed, for example, missing surrounding atoms (type-A) or local deformation by the zig-zag chain (type-B). As shown in Fig. 3f, for the type-A defect on T1, the Sb1 atom under the Ba monomer is missing. On the contrary, for the type-B defect, the underlayer zig-zag Sb1 atom is still in position. The Ba monomer in the type-A defect sinks down because of the missing Sb1 atom, which becomes relative stable compared to the type-B defect. The type-B defects only appear in T1 because of the existence of the deformed zig-zag Sb1. For T2, the symmetrized Mn layer makes the monomer totally unstable. The proposed model also explains why the type-B defect moves around but leaving no trace in its prior position: because the sublayer atoms are all in position, the STM tip rearranges the Ba dimers by breaking one dimmer and re-dimmer monomers.

Electronic property of the two terminations

Electronically, band calculations suggest that the Sb1 sheet is conductive and hosts Weyl fermions, while the (Sb2)/Mn/(Sb2) slab is insulating^1,4. Fig. 4b, c show the bias dependence of the average dI/dV and local density of states (LDOS, calculated from (dI/dV)/(I/V), by definition equals unity at V = 0) from large area spectra maps of T1 and T2, respectively. From the zero-bias dI/dV value in the inset of Fig. 4b, T1 is more conductive than T2, consistent with theoretical calculations^1,4. For T2, one can find that the gap is around 0.5 eV, indicating its non-metallic nature of the Sb2 layer^4,6. For T1, the local minimum of LDOS is shifted into the empty state around 0.35 eV, corresponding to hole doping. This is consistent with Hall effect measurements⁶. While the empty states for T1 and T2 are similar, their filled states are quite different. The highest LDOS below the Fermi level for 2 × 1 reconstructed T1 and T2 are 1.7 eV and 1.0 eV, respectively. Compared to theoretical calculations for bulk⁴, the LDOS for the reconstructed T1 and T2 surfaces is modified, especially in the occupied states.

The electronic structure of BaMnSb₂ is modified drastically by defects. Figure 5 shows spectra maps from T1 (a–e) and T2 (f–j). Figure 5b, g present cluster maps obtained from the continuous imaging tunneling spectroscopy (CITS) maps shown in Fig. 5a, f, respectively. A cluster map differentiates electronic structure in colors: areas with the similar electronic structure are represented by one color¹². Fig. 5e, j are the average dI/dV spectra of those clusters for T1 (in the filled states) and T2 (in the empty states), respectively. For both terminations, the main feature in the cluster maps is the percolated same color patches around defects, i.e., brown & blue areas in Fig. 5b (spectra 4&1 in Fig. 5e) for T1 and blue & cyan areas in Fig. 5g (spectra 1&2 in Fig. 5j) for T2. Only small areas far away from the defects are not influenced by defects, i.e., cyan and yellow areas in Fig. 5b (spectra 2&3 in Fig. 5e) for T1 and yellow area in Fig. 5g (spectra 3 in Fig. 5j) for T2. The defect impact zone is in the range of several nanometers. The impact border of T2 is decorated by brown color in Fig. 5g (spectra 4 in Fig. 5j), but the transition is smooth in T1. It is interesting that for T1 the hill and valley of the 2 × 1 strips show different electronic spectra (spectra 2 vs 3 in Fig. 5e), while there is no such difference for T2. As a result, the 2 × 1 reconstruction is clearly visible in the STS maps in Fig. 5c, d, but not in Fig. 5h, i. To better understand the cluster maps, STS maps at different energies are examined. Figure 5c–d and h–i show the −1.5 V and +2.0 V energy slices of the STS maps for T1 and T2, respectively. For T1, the STS map at +2.0 V (Fig. 5d) presents only the defect locations, but the STS map at −1.5 V (Fig. 5c) is similar to the cluster map (Fig. 5b) which plot out the areas modified by defects. On the contrary, for T2, the STS map at −1.5 V (Fig. 5h) shows the defect locations, but the map at +2.0 V (Fig. 5i) shows the influenced areas. The combination of the cluster and STS maps show that defects in the Ba termination (T1) modify the filled states, but modify the empty states in the Sb2 termination (T2).

Fig. 5: Local electronic behavior of T1 (a-e) and T2 (f- j).

STM images (a, f), cluster maps (b, g), −1.5 V STS maps (c, h), 2 V STS maps (d, i) and cluster spectra (e, j) for T1 and T2, respectively. Image size 20 nm × 20 nm, the scale bars represent 4 nm. See text for the meaning of colors in cluster maps and spectra.

QPI analysis

To further understand the nature of T1 and T2 surfaces, we perform the FFT of STS maps to acquire quasiparticle interference (QPI) maps. The QPI analysis is conducted in the energy range between −2 V and 2 V, with the 22 mV (T1) and 26 mV (T2) energy intervals. No interesting states are found in the lower energy range, but a newstate appears in the energy range of 1.6–2.0 eV in T1 only. Figure 6a shows the QPI map obtained from the STS map at +2.0 V for T1, where the reciprocal lattice points of both the atomic lattice and 2 × 1 reconstruction are clearly observable at q_x ≈ 1.4 and 0.7 Å⁻¹, respectively, which is consistent with the FFTs in Fig. 2a, d. Inside the Brillouin zone of the atomic lattice, there is a new set of pattern, marked by a white arrow, from the interference of scattered quasiparticles. Figure 6b, c show the QPI patterns inside the Brillouin zone for T1 and T2, respectively. Note that the dispersion is substantially distinct between T1 and T2. Although QPI maps show similar dispersing signal at $\bar\Gamma$ for both T1 and T2, additional strong QPI signal at q ≈ 0.5 Å⁻¹ along $\bar{\mathrm \Gamma }$-$\bar{\mathrm A}$ direction is found for T1. This is more clearly illustrated in Fig. 6d, e, which display the energy dependent linecuts from the QPI maps along the $\bar{\mathrm \Gamma }$-$\bar{\mathrm A}$ direction for T1 and T2, respectively. The strong signal at q ≈ 0.5 Å⁻¹ appears in T1 for the energy range of 1.6–2.0 eV, but not in T2. This indicates that the surface-projected electronic structure strongly depends on the individual layers/surfaces. Finding out the exact origin of the change in QPI with reconstructions will require extensive theoretical studies including the reconstructed surface, which is out of the scope of this paper. We consider that the reconstruction may affect the scattering potentials that influences the relative intensity between the scattering wavevectors, or even modify the surface band structure and appear as new scattering wavevectors. Compared to the bulk band structure⁶, the dispersion at q ≈ 0.5 Å⁻¹ seems to be related to the Dirac cone. Note that we are aware of the folding of the surface Brillouin zone due to its 2 × 1 lattices.

Fig. 6: QPI comparison of the two terminations.

a An example QPI map from the FFT of the STS map (T1 termination, bias 2.0 V). The reciprocal lattice is marked by white dotted line, and Brillouin zones of 1 × 1 and 2 × 1 lattices are marked by purple and cyan dotted lines, respectively. b, c QPI maps at three different biases for T1 and T2 termination, respectively. d, e Energy vs. QPI signal in $\bar{\mathrm \Gamma }$-$\bar{\mathrm A}$ direction for T1 and T2 termination, respectively.

It is difficult to make a direct comparison between these STM/STS results and the recent ARPES result⁸ or calculations. Firstly, the samples were cleaved and measured at room temperature for the ARPES results⁸, while our samples were cleaved and measured at low temperatures. We found the sample surface is very sensitive to the environment. As an example, under the 60 eV electron beam of LEED at 77 K, the ordered surface structure can be changed gradually to white background, the 2 × 1 reconstruction pattern can only survive about 20 min. Note that the 2 × 1 reconstruction was not reported in the ARPES paper⁸. Secondly, although ARPES has great surface sensitivity as STM/STS, the lateral dimension it explores is much large. So the ARPES results from this sample actually is the combination of T1 and T2. This might explain why the measured electronic structure from ARPES is unusual and deviates strongly from the band structure calculations⁸. Further theroritical calculations by considering reconstruction and defects as revealed in this study are necessary in order to understand the surface properties.

Low-temperature cleaved BaMnSb₂ surfaces were studied by STM/S and low energy electron diffraction. We found two natural cleavage terminations: one is the Ba layer (T1) and another is the Sb2 layer (T2). The former is above the Sb1 sheet consisting of zig-zag chains, while the latter is the top of the (Sb2)/Mn/(Sb2) slab. Both T1 and T2 exhibit the 2 × 1 surface reconstruction, which is undistinguishable in LEED patterns. However, STM/S results reveal drastic difference in their morphologies and electronic properties of two terminations, which allows us to determine the two surfaces. The QPI analysis reveals that the surface-projected electronic band structures strongly depend on the surface termination. Although the QPI maps of both terminations show dispersing QPI signals at $\bar{\mathrm \Gamma }$, only the Ba termination shows an additional strong QPI signal at q ≈ 0.5 Å⁻¹ along the $\bar{\mathrm \Gamma }$-$\bar{\mathrm A}$ direction at energies above 1.6 V, which may be related to the Dirac cone. We found that the existence of defects/vacancies can greatly modify the local density of states, creating electronic phase separation on the surfaces in the order of tens of nm scale. Our observation of the atomic structures of two terminations with reconstruction as well as the well-defined electronic structures provide critical information for understanding the surface structural and physical properties. Although the topological band structure is yet to be confirmed on the surface, our STM/S and LEED results will guide future research in this matter. Of particularly important are band calculations based on two reconstructed surfaces with and without defects.

Methods

Crystal synthesis

The composition of single crystals used in this study can be expressed as BaMn_1−δSb₂ with 0 < δ < 0.05⁶. Barium pieces (99+% Alfa Aesar), manganese powder (99.5% Alfa Aesar), and antimony powder (99.5% Alfa Aesar) were used for synthesizing BaMnSb₂⁶. Elements were weighed out using a molar ratio of Ba: Mn: Sb = 1:1:2, placed into an alumina crucible, and loaded into a fused silica tube which was then evacuated (∼10 millitorr) and sealed. For initial powder preparation, the mixture was heated to 650 °C at 150 °C/h, held at 650 °C for 1 h, further heated to 750 °C at 50 °C/h, held at 750 °C for 1 h, and cooled down to room temperature by turning off the power. Single crystals were grown with the growth speed of 3 mm/hr in a floating-zone furnace.

STM/S and LEED characterizations

Single crystals of BaMnSb₂ were cleaved in ultra-high vacuum (UHV) at ~100 K and then immediately transferred to the STM head which was precooled to 4.2 K. STM/STS experiments were carried out in an UHV low-temperature scanning tunneling microscope with base pressure of 2 × 10⁻¹⁰ Torr using a mechanically cut Pt-Ir tip¹¹. All Pt-Ir tips were conditioned and checked using a clean Au (111) surface before each measurement. Topographic images were acquired in a constant current mode with a bias voltage applied to samples. All the spectroscopies were obtained using a lock-in amplifier with bias modulation V_rms = 1 mV at 973 Hz. Spectroscopic imaging was preformed over a grid at various energies. The local barrier height (LBH) mapping was carried out over a grid by measuring the derivative of the tunneling current by varying the tip-sample distance ∆Z _rms = 10 pm. To calculate the cluster image, the measured I-V and dI/dV data were first filtered via singular value decomposition filtering followed by a Gaussian filter. We further performed a moving window average of 3 × 3 pixel areas to reduce noise in dI/dV data. Finally, we performed K-means clustering to find the spatial distribution of the principal responses in the data¹². For the LEED experiment, a BaMnSb₂ single crystal was cleaved in situ in an UHV chamber with a base pressure of 2 × 10⁻⁹ Torr, producing a shiny and flat surface. After cleaving at 77 K, the sample was immediately transferred into a μ-metal shielded LEED chamber with a base pressure of 7 × 10⁻¹¹ Torr. A LEED pattern was obtained at 77 K by applying an energy of 60 eV.