Atomically-precise engineering of spin-orbit polarons in a kagome magnetic Weyl semimetal

doi:10.21203/rs.3.rs-2801865/v1

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Atomically-precise engineering of spin-orbit polarons in a kagome magnetic Weyl semimetal

https://doi.org/10.21203/rs.3.rs-2801865/v1

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Atomically-precise engineering of defects in topological quantum materials, which is essential for constructing new artificial quantum materials with exotic properties and appealing for practical quantum applications, remains challenging due to the hindrances in modifying complex lattice with atomic precision. Here, we report the atomically-precise engineering of the vacancy-localized spin-orbital polarons (SOP) in a kagome magnetic Weyl semimetal Co₃Sn₂S₂, using scanning tunneling microscope. We achieve the repairing of the selected single vacancy and create atomically-precise sulfur quantum antidots with elaborate geometry through vacancy-by-vacancy repairing. We find that that the bound states of SOP experience a symmetry-dependent energy shift towards Fermi level with increasing vacancy size driven by the anti-bond interactions. Strikingly, as vacancy size increases, the localized magnetic moments of SOPs are tunable and ultimately extended to the negative magnetic moments resulting from spin-orbit coupling in the kagome flat band. These findings establish a new platform for engineering atomic quantum states in topological quantum materials, offering potential for kagome-lattice-based spintronics and quantum technologies.

Physical sciences/Nanoscience and technology/Techniques and instrumentation/Microscopy/Scanning probe microscopy

Physical sciences/Physics/Condensed-matter physics/Topological matter/Topological defects

Physical sciences/Materials science/Condensed-matter physics/Topological matter/Topological defects

Creation and manipulation of many-body quantum states are crucial for developing radically new technologies in quantum computation, communications, security, and sensing^1-4. Individual atomic-scale defects in a solid material provides one of the ideal candidates for generating localized quantum states due to the introduction of symmetry breaking, degeneracy lifting and scattering sources in the vicinity of the defects^5-11. The atomically-precise engineering of defect-localized bound states has been realized in a few material platforms such as insulating film^12-14, diamond¹⁵, graphene¹⁶, h-BN¹⁷ and two-dimensional transition-metal dichalcogenides¹⁸, which is appealing for practical quantum applications. However, so far, the engineering of defect bound states is limited to a few material platforms due to the challenges in modifying the atomic defects of complex lattice.

Topological quantum materials have recently attracted considerable attention due to their fascinating symmetry-protected band structures and cooperative effects involving the interplay of multiple degrees of freedom (charge, spin, orbital, lattice)^19,20. The interactions of multiple degrees of freedom in quantum materials are dynamically intertwined with each other, which results in exotic quantum states^21,22. In recent years, the transition-metal kagome lattice materials which host Dirac points and nearly flat bands that naturally promote topological and correlation effects^23,24 are discovered, providing exciting opportunities for exploring frustrated, correlated, and topological quantum states of matter^25-33. Remarkably, defects-localized quantum states including the single-vacancy-localized magnetic polarons have been discovered in magnetic transition-metal kagome shandites, which provides a promising way to engineer quantum bound states for dilute magnetic topological materials and kagome-lattice-based devices^34,35. On the other hand, the difficulty of reliability of engineering defects leaves it largely unexplored.

Herein, we report the atomically precise engineering of spin-orbit polarons (SOPs) localized around the S vacancy antidots in a kagome Weyl semimetal Co₃Sn₂S₂ by using low-temperature scanning tunneling microscopy (STM). The vacancy quantum antidots with well-organized geometry are precisely constructed though tip-assisted repairing method (Fig. 1a). Spin-polarized STM and magnetic-field dependent measurements demonstrate the SOP nature of the bound states localized at the S vacancy quantum antidots. When the geometric size increases, the bound states of quantum antidots shift towards to the Fermi energy. In addition, the energy shift of bound states depends on the geometric shape of vacancies, which agree with the theoretical simulations based on the anti-bonding interaction between adjacent quantum antidots. Interestingly, as vacancy size increases, the magnetic moments extend from localized magnetic moment to the flat band negative magnetism from Co₃Sn kagome layer.

Atomically-precise construction of Sulfur quantum antidots

The crystal structure of Co₃Sn₃S₂ consist of the rhombohedral lattice where the kagome Co₃Sn layer are sandwiched between two triangular S layers, which are further encapsulated by two separated triangular Sn layers ³². Cleavage in vacuum typically results in Sn and S terminated surfaces with kagome Co₃Sn surfaces rarely obtained ²⁹.

We start with the S terminated surface, which has been identified by STM and atomic force microscopy (AFM) in previous works^29,35,36. The vacancies, which appear as hole-like features in STM images, are randomly distributed at S-terminated surface. The absence of single atom surrounding the hole-like feature in the STM image is further confirmed by the non-contact AFM (Fig. S1). The vacancies consist of single vacancies and vacancy aggregates with various shapes (Fig. S2).

We then achieve the atomically-precise repairing of S vacancy through applying a voltage pulse from an STM tip. Figures 1b and 1c depict the experimental demonstration of repairing a single S vacancy. Briefly, to repair a single S vacancy, we position the STM tip close to the vacancy center (red arrow in Fig. 1b), followed by applying a tip pulse with a small voltage (approximately range from 0.5 V to 1.0 V). It is evident that the single S vacancy is filled with an additional S atom (highlighted by the blue hexagon in Fig. 1c). The filling of a S atom is also confirmed by the non-contact AFM (Fig. S3).

Prior to the repairing, the dI/dV spectrum obtained at a single vacancy exhibit a series of approximately equal-spaced spectral peaks, emerging just above the valence band inside the region of suppressed density of states. These peaks arise from a localized spin-orbit polaron around the single vacancy ³⁵. However, after applying the tip pulse, the dI/dV spectrum obtained at the same position exhibits features identical to those of vacancy-free region, providing additional evidence that the S single vacancy is repaired by the tip pulse (Fig. S3).

The origin of additional S atom to fill the single vacancy is illustrated in Figure 1d. As there are no topographic changes between the relatively-large scale STM images before and after the tip pulse except for the repair of single S vacancy (Fig. S4), it suggests that the filling S atom originates from the underlying layers rather than the surface layer. Considering that the crystal structure of Co₃Sn₂S₂ is composed of stacked…–Sn-[S-(Co₃-Sn)-S]–…layers, we define that top S layer of the sandwich structure corresponding to the as-cleaved S surface is the S_up layer (brown triangle in Fig. 1d) while the underlying S layer of sandwich structure is S_down layer (light brown triangle in Fig. 1d). During the tip pulse, one of S atoms in the S_down layer transfers to the vacancy site of the S_up layer, repairing the vacancy at the S_up layer. In addition, the calculations indicate that the energy barrier for the S atom transfer from S_down layer to S_up layer is approximately 0.73 eV. The relatively low energy barrier means that it is possible to overcome it the with a small voltage pulse applied at sufficiently close tip-sample distances (Fig. S5).

The capabilities in controlled repairing of specific single vacancies provides a pathway for the controlled fabrication of physically interesting vacancy “quantum antidots” (QADs) at the atomic scale. Motivated by this, we apply a step-to-step manipulation method to transform naturally-formed vacancy aggregates into QADs with well-defined shapes and sizes. For instance, we can manipulate the length of a one-dimensional S vacancy chain by gradually filling S atoms into specific sites (Fig. 1e). Similarly, filling one S atom at a specific site of a cross-shaped vacancy consisting of four S absences leads to the formation of a triangular vacancy (Fig. 1f). In more complex case, we are able to create quasi-regularly-shaped QADs such as quasi-triangular and quasi-hexagonal vacancy by filling specific sites of vacancy aggregates with irregular polygon shapes (Fig. S6).

Interacting bound states with controlled spacings of two neighboring S vacancies

The atomically-precise construction of well-defined QADs immediately provides an excellent opportunity to systematically investigate the evolution of the localized bound states with the geometric size. We firstly study the simplest case of two spatially-separated single S vacancies with decreasing spacings (Fig. 2a). The dI/dV spectra obtained around one single vacancy show that a series of approximately equal-spaced spectral peaks at −322, −300, and −283 mV gradually become suppressed as another vacancy approaches closer. Upon the formation of dimer vacancy, the series of bound states vanishes and a new series of sharp peaks at -292, -277, -265 and -254 meV appear (Fig. 2b).

To further study the evolution of density of states, we simultaneously collect the dI/dV maps at the energy corresponding to bound states (Fig. 2a). Prior to the merging of two vacancies, the bound states in each vacancy exhibit localized flower-petal shaped patterns with three-fold rotation symmetry. After merging, the spatial distribution of the new four distinguishable dI/dV peaks show two-fold rotation-symmetry patterns, with the shared S atoms connecting two single vacancies exhibiting the highest density of states (Fig. 2a and Fig. S7). The peak located at−254 mV (Fig. S5) is the sharpest and the most localized one, which is referred to the primary bound state.

Since the bound states around the single vacancy is emergent from the exotic SOP³⁵, it is natural to investigate the bound states around the dimer vacancy. Thus, we further study the magnetic properties of the primary bound states around the dimer vacancy through spin-polarized STM. The dI/dV spectra using a magnetic Ni tip demonstrate that both the primary bound states localized at single vacancy and dimer vacancy are magnetic with a spin-down majority (Fig. 2c). The polarization of bound states for the dimer vacancy is larger than the one for single vacancy. In addition, by applying a magnetic field perpendicular to the surface (B_z) and a non-magnetic STM tip, we observe anomalous Zeeman effect that primary bound states shift linearly toward the higher energy side independent of the direction of the magnetic field (Fig. 2d). According to the above evidences, we conclude that the bound states observed around the dimer vacancy are originated from SOP with a larger magnetic moment than that of single vacancy³⁵. We also study the lattice distortion around the S vacancies by applying a geometric phase analysis method^37,38 based on the Lawler–Fujita drift-correction algorithm³⁹ (Fig. 2e). The antisymmetric strain map U(r) and symmetric strain map S(r) show that the strain is mainly localized around the S vacancies, further supporting the polaron nature of the bound states around the dimer vacancies and other vacancies.

Tunable bound states of SOPs with custom-designed geometry

In spired by the exotic bound states around dimer vacancy, we further study the evolution of the bound states with the length of single-chain vacancies. We construct a series of linear vacancy with atomic length N using tip-assisted controlled repairing method (Fig. 3a) and collect the dI/dV spectra on the vacancies (N=1, 2, 3 …) respectively. All linear vacancies exhibit series of several peaks with equally spacing energy that emergent from the localized bound states. To facilitate comparison, we defined the sharpest one of the peaks with highest energy position to be the primary bound states of each vacancy (P(N)). We find that the P(N) shift to the Fermi energy with increasing N, and eventually reaches a critical energy position at about -240 meV at N>4, as highlighted by the black arrows (Fig. 3b and Fig. S8).

In addition to the single-chain vacancy, the tunability of the bound states extends to the vacancies with more elaborate shapes, including double-chains, equilateral-triangle and equilateral-hexagon vacancies (Figs. 3c-g). All vacancies exhibit series of several peaks with equally spacing energy and the sharpest peak with highest energy position is similarly assigned as the primary bound states P(N). As summarized in Figure 3I, the evolution of P(N) for each symmetric shape follows an exponential function, with all P(N) shifting exponentially towards a critical energy value near the Fermi level as the size increases. The critical energy level of P(N) depends on the vacancy shape (highlighted by different color in Fig. 3), with higher symmetry shapes possessing higher critical energy levels (Fig. 3i). For instance, the critical energy of P(N) of single chain vacancies is about -240 meV while one of the hexagonal vacancies is almost at Fermi levels.

The geometry-dependent bound states suggest the strong interactions between adjacent single vacancies. Furthermore, the spatial distributions of the bound states across the single chain vacancies (Fig. S9) exhibit quasi one-dimensional band behaviors^40-42, indicating the existences of vacancy-vacancy interactions. To gain insight into the shape-dependent energy shift behaviors of P(N), we develop a simple model (see method in Supplementary Materials and Fig. S10) to simulate the bound states around vacancies. We simulate vacancies with a simple tight-binding model with a nearest neighbor hopping t. We construct four types of vacancy patterns with different number of S vacancies, which consist of single chain, double chain, triangle and hexagon. In each vacancy configuration, the highest energy level is extracted as the anti-bonding state. We find that the anti-bonding state undergoes a similar exponential shift towards higher energy (Fig. 3j), which is consistent with experimental observations in Figure 3I. This suggests that the anti-bonding interaction between the single-vacancy-localized quantum states plays a crucial role in shaping the bound states of vacancy antidots.

Engineering the magnetic moment of SOPs

In addition to the energy position, the magnetic moment of the bound states is also tuned by the geometric size of vacancy antidots. We focus on the magnetic moment of triangular vacancy antidots due to their high yields and relatively-large lattice distortions (Fig. S11). The bound states of triangular vacancy antidots present the anomalous Zeeman effect with external magnetic field (Figs. 4a,b). Fitting the energy position as a function of the magnetic field, we obtained the effective magnetic moment value |µ(N)|. For example, |µ(N=3)| = 0.09meV/T =1.55 µ_B (Fig. 4a) and |µ(N=10)| = 0.17 meV/T = 2.93 µ_B (Fig. 4b). These results indicate that the magnetic moment of bound states localized at vacancy is directly related to the size of vacancy.

The Co₃Sn terrace, confined by the step edges of adjacent S terraces (Fig. 4c), is considered as a naturally occurring vacancy antidot with an enormous size (N=∞). The spatially-averaged dI/dV spectrum obtained at the Co₃Sn terrace shows a sharp peak in the vicinity of Fermi level, which is consistent with previous STM results on the Co₃Sn surface^29,36. The magnetic dependent dI/dV curves show similar anomalous Zeeman effect with an effective magnetic moment of µ(N=∞) = -0.19 meV/T = -3.28 µ_B (Fig. 4d). The negative orbital magnetic moment results from the spin-orbital coupling in the kagome flat band considering the non-trivial Berry phase of the flat band ⁴³. Evolution of the magnetic moment with the atomic number of vacancies shows that the magnetic moments extend from localized magnetic moment around vacancies to the flat band negative magnetism from Co₃Sn kagome layer (Fig. 4e).

The atomically-precise manipulation of atomic vacancies opens a new playground for investigating fundamental physical properties of vacancy nanostructures with custom-designed geometries and their coupling with physical parameters such as magnetic moment, orbital and charges. In addition, the controlled integration of individual functional vacancies of topological quantum materials into extended, scalable atomic circuits, which is promising for practical applications such as atomic memory ¹³ and quantum qubit ⁴⁴. Through precise engineering of vacancies, the artificial vacancy lattice can be achieved, which is essential for realizing designer quantum materials with tailored properties ¹⁴. The antibonding interactions among the vacancies in Co₃Sn₂S₂could improve the understanding of polaron-like bound states in coupled quantum systems ⁴², to explore artificial coupled quantum systems with great control.

Single crystal growth of Co₃Sn₂S₂

The single crystals of Co₃Sn₂S₂ were grown by flux method with Sn/Pb mixed flux. The starting materials of Co (99.95% Alfa), Sn (99.999% Alfa), S (99.999% Alfa) and Pb (99.999% Alfa) arewere mixed in molar ratio of Co : S : Sn : Pb = 12 : 8 : 35 : 45. The mixture was placed in Al₂O₃ crucible sealed in a quartz tube. The quartz tube was slowly heated to 673 K over 6 h and kept over 6 h to avoid the heavy loss of sulfur. The quartz tube was further heated to 1323 K over 6 h and kept for 6 h. Then the melt was cooled down slowly to 973 K over 70 h. At 973 K, the flux was removed by rapid decanting and subsequent spinning in a centrifuge. The hexagonal-plate single crystals with diameters of 2 ~ 5 mm are obtained. The composition and phase structure of the crystals were checked by energy-dispersive x-ray spectroscopy and x-ray diffraction, respectively.

Scanning tunneling microscopy/spectroscopy

The samples used in the experiments were cleaved in situ at 6 K and immediately transferred to an STM head. Experiments were performed in an ultrahigh vacuum (1×10^-10 mbar) ultra-low temperature STM system (40 mK) equipped with 9-2-2 T magnetic field. All the scanning parameter (setpoint voltage and current) of the STM topographic images are listed in the captions of the figures. Unless otherwise noted, the differential conductance (dI/dV) spectra were acquired by a standard lock-in amplifier at a modulation frequency of 973.1 Hz. Non-magnetic tungsten tip was fabricated via electrochemical etching and calibrated on a clean Au(111) surface prepared by repeated cycles of sputtering with argon ions and annealing at 500 ℃. Ferromagnetic Ni tip was applied in the spin-polarized STM measurement. The Ni tip was fabricated via electrochemical etching of Ni wire in a constant-current mode. To calibrate the spin-polarization of Ni tip, the as-prepared Ni tip has been applied to resolve magnetic-state-dependent contrast of Co islands grown on a Cu(111) surface in spin-polarized STM experiments⁴⁵.

Q-Plus nc-AFM measurements

Non-contact AFM measurements were performed on a combined nc-AFM/STM system (Createc) at 4.7 K with a base pressure lower than 2 × 10^-10 mbar. All measurements were performed using a commercial qPlus tuning fork sensor in the frequency modulation mode with a Pt/Ir tip at 4.5 K. The resonance frequency of the AFM tuning fork is 27.9 kHz, and the stiffness is approximately 1800 N/m.

Model Hamiltonian

DFT calculations indicate the vacancy-vacancy forms anti-bonding states and contribute the peak DOS observed in experiment. Therefore, we simulated vacancies with a simple tight-binding model with a nearest neighbor hopping t. We constructed four vacancy patterns (linear, bi-linear, triangular, and hexagonal) with different number of S vacancies. In each vacancy configuration, the highest energy level is extracted as the anti-bonding state.

First-principles calculations

The Nudged Elastic Band (NEB) calculations for the surfaces are simulated with a slab model of 4×4 in-plane supercell and four kagome layers along the out-of-plane direction. The vacuum level is about 14 Å. The NEB calculations were performed within Density Functional theory as implemented in VASP^46,47. The generalized gradient approximation parametrized by Perdew-Burke-Ernzerhof ⁴⁸ is used to mimic the exchange-correlation interaction between electrons. A kinetic energy cutoff of 268 eV is used for the plane wave basis set. Single Gamma point is employed to sample the Brillouin zone. In the NEB structural relaxation, the force and total energy thresholds are about 10^-4 eV and 0.01 eV/Å, respectively. The spring constant of 5 eV/Å² between neighboring images is used.

Acknowledgments: The work is supported by grants from the National Natural Science Foundation of China (61888102 and 52022105), the National Key Research and Development Projects of China (2019YFA0308500, and 2018YFA0305800), and the Chinese Academy of Sciences (XDB30000000, YSBR-003, and ZDBS-SSW-WHC001). Z.Q.W. is supported by the US DOE, Basic Energy Sciences Grant No. DE-FG02-99ER45747. B.Y. was supported by financial support by the European Research Council (ERC Consolidator Grant, No. 815869) and the Israel Science Foundation (ISF No. 1251/19).

Author Contributions: H.-J.G. and H. C. designed the experiments. H.C. Y.X. B.H. Z. H. and X. H. performed STM experiments with guidance of H.-J.G. L.H., Q. Z. Y.L., Y.X. performed AFM measurements. E.L., HY, XQ, EL, HL prepared samples. Z.W. proposed the model and H. T. and B. Y. carried out theoretical calculations. H. C. and H.-J. G. analyzed experimental data, plotted figures, and wrote the manuscript with the inputs from all authors. H.-J. G. supervised the project.

Competing interests: Authors declare that they have no competing interests.

Piquero-Zulaica, I. et al. Engineering quantum states and electronic landscapes through surface molecular nanoarchitectures. Rev. Mod. Phys. 94, 045008 (2022).
Prada, E. et al. From Andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires. Nat. Rev. Phys. 2, 575-594 (2020).
Wang, D. et al. Evidence for Majorana bound states in an iron-based superconductor. Science 362, 333-335 (2018).
Chou, C. W. et al. Preparation and coherent manipulation of pure quantum states of a single molecular ion. Nature 545, 203-207 (2017).
Pacchioni, G. Spin qubits: Useful defects in silicon carbide. Nat. Rev. Mater. 2, 17052 (2017).
Freysoldt, C. et al. First-principles calculations for point defects in solids. Rev. Mod. Phys. 86, 253-305 (2014).
Doherty, M. W. et al. The nitrogen-vacancy colour centre in diamond. Phys. Rep. 528, 1-45 (2013).
Khajetoorians, A. A., Wegner, D., Otte, A. F. & Swart, I. Creating designer quantum states of matter atom-by-atom. Nat. Rev. Phys. 1, 703-715 (2019).
Massee, F., Huang, Y. K. & Aprili, M. Atomic manipulation of the gap in Bi₂Sr₂CaCu₂O_8+x. Science 367, 68-71 (2020).
Fan, P. et al. Observation of magnetic adatom-induced Majorana vortex and its hybridization with field-induced Majorana vortex in an iron-based superconductor. Nat. Commun. 12, 1348 (2021).
Qian, G. et al. Spin-flop transition and Zeeman effect of defect-localized bound states in the antiferromagnetic topological insulator MnBi2Te4. Nano Res. 16, 1101-1106 (2023).
Li, Z. et al. Lateral Manipulation of Atomic Vacancies in Ultrathin Insulating Films. ACS Nano 9, 5318-5325 (2015).
Kalff, F. E. et al. A kilobyte rewritable atomic memory. Nat. Nanotechnol. 11, 926-929 (2016).
Drost, R., Ojanen, T., Harju, A. & Liljeroth, P. Topological states in engineered atomic lattices. Nat. Phys. 13, 668-671 (2017).
Dietl, T. & Ohno, H. Dilute ferromagnetic semiconductors: Physics and spintronic structures. Rev. Mod. Phys. 86, 187 (2014).
González-Herrero, H. et al. Atomic-scale control of graphene magnetism by using hydrogen atoms. Science 352, 437-441 (2016).
Su, C. et al. Tuning colour centres at a twisted hexagonal boron nitride interface. Nat. Mater. 21, 896-902 (2022).
Liang, Q., Zhang, Q., Zhao, X., Liu, M. & Wee, A. T. S. Defect Engineering of Two-Dimensional Transition-Metal Dichalcogenides: Applications, Challenges, and Opportunities. ACS Nano 15, 2165-2181 (2021).
Tokura, Y., Kawasaki, M. & Nagaosa, N. Emergent functions of quantum materials. Nat. Phys. 13, 1056-1068 (2017).
Yan, B. & Felser, C. Topological Materials: Weyl Semimetals. Annu. Rev. Condens. Matter Phys. 8, 337-354 (2017).
de la Torre, A. et al. Colloquium: Nonthermal pathways to ultrafast control in quantum materials. Rev. Mod. Phys. 93, 041002 (2021).
Yin, J.-X., Pan, S. H. & Zahid Hasan, M. Probing topological quantum matter with scanning tunnelling microscopy. Nat. Rev. Phys. 3, 249-263 (2021).
Neupert, T., Denner, M. M., Yin, J.-X., Thomale, R. & Hasan, M. Z. Charge order and superconductivity in kagome materials. Nat. Phys. 18, 137-143 (2022).
Yin, J. X., Lian, B. & Hasan, M. Z. Topological kagome magnets and superconductors. Nature 612, 647-657 (2022).
Chen, H. et al. Roton pair density wave in a strong-coupling kagome superconductor. Nature 599, 222-228 (2021).
Nie, L. et al. Charge-density-wave-driven electronic nematicity in a kagome superconductor. Nature 604, 59-64 (2022).
Zhao, H. et al. Cascade of correlated electron states in the kagome superconductor CsV₃Sb₅. Nature 599, 216-221 (2021).
Liu, D. F. et al. Magnetic Weyl semimetal phase in a Kagomé crystal. Science 365, 1282-1285 (2019).
Morali, N. et al. Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co₃Sn₂S₂. Science 365, 1286-1291 (2019).
Mielke, C. et al. Time-reversal symmetry-breaking charge order in a kagome superconductor. Nature 602, 245-250 (2022).
Teng, X. et al. Discovery of charge density wave in a kagome lattice antiferromagnet. Nature 609, 490-495 (2022).
Liu, E. K. et al. Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14, 1125-1131 (2018).
Ortiz, B. R. et al. Superconductivity in the Z₂ kagome metal KV₃Sb₅. Phys. Rev. Mater. 5, 034801 (2021).
Yin, J. X. et al. Spin-orbit quantum impurity in a topological magnet. Nat. Commun. 11, 4415 (2020).
Xing, Y. et al. Localized spin-orbit polaron in magnetic Weyl semimetal Co₃Sn₂S₂. Nat. Commun. 11, 5613 (2020).
Howard, S. et al. Evidence for one-dimensional chiral edge states in a magnetic Weyl semimetal Co3Sn2S2. Nat. Commun. 12, 4269 (2021).
Ren, Z. et al. Nanoscale decoupling of electronic nematicity and structural anisotropy in FeSe thin films. Nat. Commun. 12, 10 (2021).
Walkup, D. et al. Interplay of orbital effects and nanoscale strain in topological crystalline insulators. Nat. Commun. 9, 1550 (2018).
Lawler, M. J. et al. Intra-unit-cell electronic nematicity of the high-T_c copper-oxide pseudogap states. Nature 466, 347-351 (2010).
Crain, J. N. & Pierce, D. T. End states in one-dimensional atom chains. Science 307, 703-706 (2005).
Nilius, N., Wallis, T. M. & Ho, W. Development of one-dimensional band structure in artificial gold chains. Science 297, 1853-1856 (2002).
Schuler, B. et al. Effect of electron-phonon interaction on the formation of one-dimensional electronic states in coupled Cl vacancies. Phys. Rev. B 91, 235443 (2015).
Yin, J.-X. et al. Negative flat band magnetism in a spin–orbit-coupled correlated kagome magnet. Nat. Phys. 15, 443-448 (2019).
Weber, J. R. et al. Quantum computing with defects. PNAS 107, 8513-8518 (2010).
Chen, H., Xiao, W. D., Wu, X., Yang, K. & Gao, H. J. Electrochemically etched Ni tips in a constant-current mode for spin-polarized scanning tunneling microscopy. J Vac Sci Technol B 32, 061801 (2014).
Kresse, G. & Furthmuller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comp. Mater. Sci. 6, 15-50 (1996).
Kresse, G. & Furthmuller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169-11186 (1996).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865-3868 (1996).

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Atomically-precise engineering of spin-orbit polarons in a kagome magnetic Weyl semimetal

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