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Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the coupling of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization with a nearby field-induced Majorana vortex in iron-based superconductor FeTe 0.55 Se 0.45 . We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures. Braiding Majorana modes is essential for topological quantum computing, but it remains difficult to find a suitable platform. Here, the authors report the evidence of hybridization between field-induced and magnetic adatom induced Majorana modes in an iron-based superconductor FeTe 0.55 Se 0.45 , providing a possible single-material platform for braiding Majorana modes.

The kagome lattice Co 3 Sn 2 S 2 exhibits the quintessential topological phenomena of a magnetic Weyl semimetal such as the chiral anomaly and Fermi-arc surface states. Probing its magnetic properties is crucial for understanding this correlated topological state. Here, using spin-polarized scanning tunneling microscopy/spectroscopy (STM/S) and non-contact atomic force microscopy (nc-AFM) combined with first-principle calculations, we report the discovery of localized spin-orbit polarons (SOPs) with three-fold rotation symmetry nucleated around single S-vacancies in Co 3 Sn 2 S 2. The SOPs carry a magnetic moment and a large diamagnetic orbital magnetization of a possible topological origin associated relating to the diamagnetic circulating current around the S-vacancy. Appreciable magneto-elastic coupling of the SOP is detected by nc-AFM and STM. Our findings suggest that the SOPs can enhance magnetism and more robust time-reversal-symmetry-breaking topological phenomena. Controlled engineering of the SOPs may pave the way toward practical applications in functional quantum devices. Kagome lattice material Co 3 Sn 2 S 2 is identified as a magnetic Weyl semimetal and its magnetic properties are less studied. Here, the authors observe localized spin-orbit polarons nucleated around single S-vacancies carrying a large diamagnetic orbital magnetism in Co 3 Sn 2 S 2 .

The transition metal kagome lattice materials host frustrated, correlated and topological quantum states of matter 1 – 9 . Recently, a new family of vanadium-based kagome metals, AV 3 Sb 5 (A = K, Rb or Cs), with topological band structures has been discovered 10 , 11 . These layered compounds are nonmagnetic and undergo charge density wave transitions before developing superconductivity at low temperatures 11 – 19 . Here we report the observation of unconventional superconductivity and a pair density wave (PDW) in CsV 3 Sb 5 using scanning tunnelling microscope/spectroscopy and Josephson scanning tunnelling spectroscopy. We find that CsV 3 Sb 5 exhibits a V-shaped pairing gap Δ  ~ 0.5 meV and is a strong-coupling superconductor (2 Δ / k B T c  ~ 5) that coexists with 4 a 0 unidirectional and 2 a 0  × 2 a 0 charge order. Remarkably, we discover a 3Q PDW accompanied by bidirectional 4 a 0 /3 spatial modulations of the superconducting gap, coherence peak and gap depth in the tunnelling conductance. We term this novel quantum state a roton PDW associated with an underlying vortex–antivortex lattice that can account for the observed conductance modulations. Probing the electronic states in the vortex halo in an applied magnetic field, in strong field that suppresses superconductivity and in zero field above T c , reveals that the PDW is a primary state responsible for an emergent pseudogap and intertwined electronic order. Our findings show striking analogies and distinctions to the phenomenology of high- T c cuprate superconductors, and provide groundwork for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals. A study reports unconventional superconductivity and a pair density wave in the kagome superconductor CsV 3 Sb 5 , and provides a basis for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals.

The correlation of surface impurity states with the antiferromagnetic ground states is crucial for understanding the formation of the topological surface state in the antiferromagnetic topological insulators MnBi 2 Te 4 . By using low-temperature scanning tunneling microscopy and spectroscopy, we observed a localized bound state around the Mn-Bi antisite defect at the Te-terminated surface of the antiferromagnetic topological insulator MnBi 2 Te 4 . When applying a magnetic field perpendicular to the surface ( B z ) from −1.5 to 3.0 T, the bound state shifts linearly to a lower energy with increasing B z , which is attributed to the Zeeman effect. Remarkably, when applying a large range of B z from −8.0 to 8.0 T, the magnetic field induced reorientation of surface magnetic moments results in an abrupt jump in the local density of states (LDOS), which is characterized by LDOS-change-ratio d σ ˜ / d B quantitatively. Interestingly, two asymmetric critical field, −2.0 and 4.0 T determined by the two peaks in d σ ˜ / d B are observed, which is consistent with simulated results according to a Mills-model, describing a surface spin flop transition (SSF). Our results provide a new flatform for studying the interplay between magnetic order and topological phases in magnetic topological materials.

Landau quantization associated with the quantized cyclotron motion of electrons under magnetic field provides the effective way to investigate topologically protected quantum states with entangled degrees of freedom and multiple quantum numbers. Here we report the cascade of Landau quantization in a strained type-II Dirac semimetal NiTe2 with spectroscopic-imaging scanning tunneling microscopy. The uniform-height surfaces exhibit single-sequence Landau levels (LLs) at a magnetic field originating from the quantization of topological surface state (TSS) across the Fermi level. Strikingly, we reveal the multiple sequence of LLs in the strained surface regions where the rotation symmetry is broken. Firstprinciples calculations demonstrate that the multiple LLs attest to the remarkable lifting of the valley degeneracy of TSS by the in-plane uniaxial or shear strains. Our findings pave a pathway to tune multiple degrees of freedom and quantum numbers of TMDs via strain engineering for practical applications such as high-frequency rectifiers, Josephson diode and valleytronics.

The transition-metal kagome lattice materials host frustrated, correlated, and topological quantum states of matter. Recently, a new family of vanadium-based kagome metals AV3Sb5 (A=K, Rb, and Cs) with topological band structures has been discovered. These layered compounds are nonmagnetic and undergo charge density wave transitions before developing superconductivity at low temperatures. Here we report the observation of unconventional superconductivity and pair density wave (PDW) in CsV3Sb5 using scanning tunneling microscope/spectroscopy (STM/STS) and Josephson STS. We find that CsV3Sb5 exhibits a V-shaped pairing gap {\\Delta}~0.5 meV and is a strong-coupling superconductor (2{\\Delta}/kBTc~5) that coexists with 4a0 unidirectional and 2a0X2a0 charge order. Remarkably, we discover a 3Q PDW accompanied by bidirectional 4a0/3 spatial modulations of the superconducting gap, coherence peak and gap-depth in the tunneling conductance. We term this novel quantum state a roton-PDW associated with an underlying vortex-antivortex lattice that can account for the observed conductance modulations. Probing the electronic states in the vortex halo in an applied magnetic field, in strong-field that suppresses superconductivity, and in zero-field above Tc reveals that the PDW is a primary state responsible for an emergent pseudogap and intertwined electronic order. Our findings show striking analogies and distinctions to the phenomenology of high-Tc cuprate superconductors, and provide groundwork for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals.

Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the coupling of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization with a nearby field-induced Majorana vortex in iron-based superconductor FeTe0.55Se0.45. We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.

The vanadium-based kagome superconductor CsV3Sb5 has attracted tremendous attention due to its unexcepted anomalous Hall effect (AHE), charge density waves (CDWs), nematicity, and a pseudogap pair density wave (PDW) coexisting with unconventional strong-coupling superconductivity (SC). The origins of CDWs, unconventional SC, and their correlation with different electronic states in this kagome system are of great significance, but so far, are still under debate. Chemical doping in the kagome layer provides one of the most direct ways to reveal the intrinsic physics, but remains unexplored. Here, we report, for the first time, the synthesis of Ti-substituted CsV3Sb5 single crystals and its rich phase diagram mapping the evolution of intertwining electronic states. The Ti atoms directly substitute for V in the kagome layers. CsV3-xTixSb5 shows two distinct SC phases upon substitution. The Ti slightly-substituted phase displays an unconventional V-shaped SC gap, coexisting with weakening CDW, PDW, AHE, and nematicity. The Ti highly-substituted phase has a U-shaped SC gap concomitant with a short-range rotation symmetry breaking CDW, while long-range CDW, twofold symmetry of in-plane resistivity, AHE, and PDW are absent. Furthermore, we also demonstrate the chemical substitution of V atoms with other elements such as Cr and Nb, showing a different modulation on the SC phase and CDWs. These findings open up a way to synthesise a new family of doped CsV3Sb5 materials, and further representing a new platform for tuning the different correlated electronic states and superconducting pairing in kagome superconductors.

The kagome lattice Co\\(_3\\)Sn\\(_2\\)S\\(_2\\) exhibits the quintessential topological phenomena of a magnetic Weyl semimetal such as the chiral anomaly and Fermi-arc surface states. Probing its magnetic properties is crucial for understanding this correlated topological state. Here, using spin-polarized scanning tunneling microscopy/spectroscopy (STM/S), we report the discovery of localized spin-orbit polarons (SOPs) with three-fold rotation symmetry nucleated around single-S vacancies in Co\\(_3\\)Sn\\(_2\\)S\\(_2\\). The SOPs carry a spin-polarized magnetic moment and a large orbital magnetization of a topological origin associated with the Berry phase and the persistent circulating current. Appreciable magneto-elastic coupling of the SOP is detected by atomic force microscope and STM. Our findings suggest that the SOPs can enhance magnetism and stability of the magnetic Weyl nodes for more robust time-reversal-symmetry-breaking topological phenomena. Controlled engineering of the SOPs may pave the way toward practical applications in functional quantum devices.

Accurately predicting air pollutant concentrations can reduce health risks and provide crucial references for environmental governance. In pollution prediction tasks, three key factors are essential: (1) dynamic dependencies among global monitoring stations should be considered in spatial feature extraction due to the diffusion properties of air pollutants; (2) precise temporal correlation modeling is critical because pollutant concentrations change dynamically and periodically; (3) it is vital to avoid propagation of long-term prediction errors across spatiotemporal dimensions. To address these challenges, we propose STGATN, a novel spatiotemporal graph attention network with an encoder-decoder architecture. Both the encoder and decoder incorporate a spatiotemporal embedding mechanism, a spatiotemporal graph attention block, a gated temporal convolutional network, and a fusion gate. Specifically, the spatiotemporal graph attention module is designed to use temporal and graph attention networks to extract dynamic spatiotemporal correlations. The gated temporal convolutional network is constructed to capture the long-term temporal causal relationships. The fusion gate adaptively fuses the spatiotemporal correlations and temporal causal relationships. In addition, a spatiotemporal embedding mechanism, including positional and temporal information, is added to account for pollutants’ periodicity and station-specific properties. Moreover, this paper proposes a transformer attention that establishes direct dependencies between future and historical time steps to avoid prediction error accumulation in the dynamic decoding process. The experimental results show that the proposed prediction model significantly outperforms the latest baseline methods on the air pollution dataset from actual monitoring stations in Beijing City.