Temperature-Dependent Spin-to-Charge Conversion and Efficient Manipulation of Elliptical THz Waves in Bi2Te3/TbFeCo Heterostructures

Topological insulators (TIs) with spin-momentum-locked surface states and considerable spin-to-charge conversion (SCC) efficiency are ideal substitutes for the nonmagnetic layer in the traditional ferromagnetic/nonmagnetic (FM/NM) spintronic terahertz (THz) emitters. Here, the TI/ferrimagnetic structure as an effective polarization tunable THz source is verified by terahertz emission spectroscopy. The emitted THz electric field can be separated into two THz components utilizing their opposite symmetry on pump polarization and the magnetic field. TI not only emits a THz electric field via the linear photogalvanic effect (LPGE) but also serves as the medium of SCC via the inverse Edelstein effect (IEE) in the heterostructure. In addition, the amplitude and polarity of the SCC component can be efficiently manipulated by temperature in our ferrimagnetic TbFeCo layer compared with Co or Fe. Once these two THz components are delicately set orthogonally, an elliptical THz wave is generated by the intrinsic phase difference at the THz frequency range. The feasible control of its polarization and chirality is demonstrated by three means: pump polarization, magnetic field, and temperature. These appealing observations may pave the way for the development of elliptical THz wave emitters and polarization-sensitive THz spectroscopy.

Fabrication-induced even-odd discrepancy of magnetotransport in few-layer MnBi2Te4

The van der Waals antiferromagnetic topological insulator MnBi2Te4 represents a promising platform for exploring the layer-dependent magnetism and topological states of matter. Recently observed discrepancies between magnetic and transport properties have aroused controversies concerning the topological nature of MnBi2Te4 in the ground state. In this article, we demonstrate that fabrication can induce mismatched even-odd layer dependent magnetotransport in few-layer MnBi2Te4. We perform a comprehensive study of the magnetotransport properties in 6- and 7-septuple-layer MnBi2Te4, and reveal that both even- and odd-number-layer device can show zero Hall plateau phenomena in zero magnetic field. Importantly, a statistical survey of the optical contrast in more than 200 MnBi2Te4 flakes reveals that the zero Hall plateau in odd-number-layer devices arises from the reduction of the effective thickness during the fabrication, a factor that was rarely noticed in previous studies of 2D materials. Our finding not only provides an explanation to the controversies regarding the discrepancy of the even-odd layer dependent magnetotransport in MnBi2Te4, but also highlights the critical issues concerning the fabrication and characterization of 2D material devices.

Dimerized Hofstadter model in two-leg ladder quasi-crystals

We theoretically study topological features, band structure, and localization properties of a dimerized two-leg ladder with an oscillating on-site potential. The periodicity of the on-site potential can take either rational or irrational values. We consider two types of dimerized configurations; symmetric and asymmetric models. For rational values of the periodicity as long as inversion symmetry is preserved both symmetric and asymmetric ladders can host topological phases. Additionally, the energy spectrum of the models exhibits a fractal structure known as the Hofstadter butterfly spectrum, dependent on the dimerization of the hopping and the strength of the on-site potential. In the case of irrational values for the periodicity, a metal-insulator phase transition occurs with small values of the critical strength of the on-site potential in the dimerized cases. Our models incorporate the effects of lattice configuration and quasi-periodicity, paving the way for establishing platforms that host both topological and non-topological phase transitions.

Anderson critical metal phase in trivial states protected by average magnetic crystalline symmetry

Transitions between distinct obstructed atomic insulators (OAIs) protected by crystalline symmetries, where electrons form molecular orbitals centering away from the atom positions, must go through an intermediate metallic phase. In this work, we find that the intermediate metals will become a scale-invariant critical metal phase (CMP) under certain types of quenched disorder that respect the magnetic crystalline symmetries on average. We explicitly construct models respecting average C2zT, m, and C4zT and show their scale-invariance under chemical potential disorder by the finite-size scaling method. Conventional theories, such as weak anti-localization and topological phase transition, cannot explain the underlying mechanism. A quantitative mapping between lattice and network models shows that the CMP can be understood through a semi-classical percolation problem. Ultimately, we systematically classify all the OAI transitions protected by (magnetic) groups P m , P 2 ' , P 4 ' , and P 6 ' with and without spin-orbit coupling, most of which can support CMP.

Hidden non-collinear spin-order induced topological surface states

Rare-earth monopnictides are a family of materials simultaneously displaying complex magnetism, strong electronic correlation, and topological band structure. The recently discovered emergent arc-like surface states in these materials have been attributed to the multi-wave-vector antiferromagnetic order, yet the direct experimental evidence has been elusive. Here we report observation of non-collinear antiferromagnetic order with multiple modulations using spin-polarized scanning tunneling microscopy. Moreover, we discover a hidden spin-rotation transition of single-to-multiple modulations 2 K below the Néel temperature. The hidden transition coincides with the onset of the surface states splitting observed by our angle-resolved photoemission spectroscopy measurements. Single modulation gives rise to a band inversion with induced topological surface states in a local momentum region while the full Brillouin zone carries trivial topological indices, and multiple modulation further splits the surface bands via non-collinear spin tilting, as revealed by our calculations. The direct evidence of the non-collinear spin order in NdSb not only clarifies the mechanism of the emergent topological surface states, but also opens up a new paradigm of control and manipulation of band topology with magnetism.

Topological phase transitions with zero indirect band gaps

Topological phase transitions in band models are usually associated to the gap closing between the highest valance band and the lowest conduction band, which can give rise to different types of nodal structures, such as Dirac/Weyl points, lines and surfaces. In this work, we show the existence of a different kind of topological phase transitions in one-dimensional systems, which are instead characterized by the presence of a robust zero indirect gap, which occurs when the top of the valence band coincides with the bottom of the conduction band in energy but not in momentum. More specifically, we consider an one-dimensional model on a trimer chain that is protected by both particle-hole and chiral-inversion symmetries. At the critical point, the system supports a Dirac-like point. After introducing a deforming parameter that breaks both inversion and chiral symmetries but preserves their combination, we observe the emergence of a zero indirect band gap, which results to be related to thepersymmetryof our Hamiltonian. Importantly, the zero indirect gap holds for a range of values of the deforming parameter. We finally discuss the implementation of the deforming parameter in our tight-binding model through time-periodic (Floquet) driving.

Anomalous and Chern topological waves in hyperbolic networks

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental work has been limited to time-reversal invariant systems made of coupled discrete resonances, leaving the more interesting case of robust, unidirectional edge wave transport completely unobserved. Here, we report a non-reciprocal hyperbolic network that exhibits both Chern and anomalous chiral edge modes, and implement it on a planar microwave platform. We experimentally evidence the unidirectional character of the topological edge modes by direct field mapping. We demonstrate the topological origin of these hyperbolic chiral edge modes by an explicit topological invariant measurement, performed from external probes. Our work extends the reach of topological wave physics by allowing for backscattering-immune transport in materials with synthetic non-Euclidean behavior.

Spectral Asymmetry Induces a Re-Entrant Quantum Hall Effect in a Topological Insulator

The band inversion of topological materials in three spatial dimensions is intimately connected to the parity anomaly of 2D massless Dirac fermions, known from quantum field theory. At finite magnetic fields, the parity anomaly reveals itself as a non-zero spectral asymmetry, i.e., an imbalance between the number of conduction and valence band Landau levels, due to the unpaired zero Landau level. This work reports the realization of this 2D Dirac physics at a single surface of the 3D topological insulator (Hg,Mn)Te. An unconventional re-entrant sequence of quantized Hall plateaus in the measured Hall resistance can be directly related to the occurrence of spectral asymmetry in a single topological surface state. The effect should be observable in any topological insulator where the transport is dominated by a single Dirac surface state.

Pressure-driven dome-shaped superconductivity in topological insulator GeBi2Te4

The discovery of new superconductors based on topological insulators always captures special attention due to their unique structural and electronic properties. High pressure is an effective way to regulate the lattice as well as electronic states in the topological insulators, thus altering their electronic properties. Herein, we report the structural and electrical transport properties of the topological insulator GeBi2Te4by using high-pressure techniques. The synchrotron x-ray diffraction revealed that GeBi2Te4underwent two structural phase transitions fromR-3m(phase I) toC2/m(phase II) and then intoIm-3m(phase III). Superconductivity was observed at 6.6 GPa to be associated with the first structural phase transition. The superconducting transition temperatureTcreached a maximum value of 8.4 K, accompanied by theRHsign changing from negative to positive at 14.6 GPa, then gradually decreased with increasing pressure in phase III, showing a dome-shaped phase diagram. The present results provide a platform for understanding the interplay between the crystal structure and superconductivity by the regulation of pressure in the topological insulator materials.

Acoustic Higher-Order Topological Insulators Induced by Orbital-Interactions

The discovery of higher-order topological insulator metamaterials, in analogy with their condensed-matter counterparts, has enabled various breakthroughs in photonics, mechanics, and acoustics. A common way of inducing higher-order topological wave phenomena is through pseudo-spins, which mimic the electron spins as a symmetry-breaking degree of freedom. Here, this work exploits degenerate orbitals in acoustic resonant cavities to demonstrate versatile, orbital-selective, higher-order topological corner states. Type-II corner states are theoretically investigated and experimentally demonstrated based on tailored orbital interactions, without the need for long-range hoppings that has so far served as a key ingredient for Type-II corner states in single-orbital systems. Due to the orthogonal nature of the degenerate p orbitals, this work also introduces a universal strategy to realize orbital-dependent edge modes, featuring high-Q edge states identified in bulk bands. These findings provide an understanding of the interplay between acoustic orbitals and topology, shedding light on orbital-related topological wave physics, as well as its applications for acoustic sensing and trapping.

Focusing Micromechanical Polaritons in Topologically Nontrivial Hyperbolic Metasurfaces

Vertically stacked multiple atomically thin layers have recently widened the landscape of rich optical structures thanks to these quantum metamaterials or van der Waals (vdW) materials, featuring hyperbolic polaritons with unprecedented avenues for light. Despite their far-reaching implications, most of their properties rest entirely on a trivial band topological origin. Here, a 2D approach is adopted toward a micromechanical vdW analogue that, as a result of engineered chiral and mirror symmetries, provides topologically resilient hyperbolic radiation of mechanical vibrations in the ultrasonic regime. By applying laser vibrometry of the micrometer-sized metasurface, we are able to exhibit the exotic fingerprints of robust hyperbolic radiation spanning several frequencies, which beyond their physical relevance, may enable ultrasonic technologies.

Robust temporal adiabatic passage with perfect frequency conversion between detuned acoustic cavities

For classical waves, phase matching is vital for enabling efficient energy transfer in many scenarios, such as waveguide coupling and nonlinear optical frequency conversion. Here, we propose a temporal quasi-phase matching method and realize robust and complete acoustical energy transfer between arbitrarily detuned cavities. In a set of three cavities, A, B, and C, the time-varying coupling is established between adjacent elements. Analogy to the concept of stimulated Raman adiabatic passage, amplitudes of the two couplings are modulated as time-delayed Gaussian functions, and the couplings' signs are periodically flipped to eliminate temporal phase mismatching. As a result, robust and complete acoustic energy transfer from A to C is achieved. The non-reciprocal frequency conversion properties of our design are demonstrated. Our research takes a pivotal step towards expanding wave steering through time-dependent modulations and is promising to extend the frequency conversion based on state evolution in various linear Hermitian systems to nonlinear and non-Hermitian regimes.

Monolithic Strong Coupling of Topological Surface Acoustic Wave Resonators on Lithium Niobate

Coherent phonon transfer via high-quality factor (Q) mechanical resonator strong coupling has garnered significant interest. Yet, the practical applications of these strongly coupled resonator devices are largely constrained by their vulnerability to fabrication defects. In this study, topological strong coupling of gigahertz frequency surface acoustic wave (SAW) resonators with lithium niobate is achieved. The nanoscale grooves are etched onto the lithium niobate surface to establish robust SAW topological interface states (TISs). By constructing phononic crystal (PnC) heterostructures, a strong coupling of two SAW TISs, achieving a maximum Rabi splitting of 22 MHz and frequency quality factor product fQm of ≈1.2 × 1013  Hz, is realized. This coupling can be tuned by adjusting geometric parameters and a distinct spectral anticrossing is experimentally observed. Furthermore, a dense wavelength division multiplexing device based on the coupling of multiple TISs is demonstrated. These findings open new avenues for the development of practical topological acoustic devices for on-chip sensing, filtering, phonon entanglement, and beyond.

Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems

While a significant fraction of topological materials has been characterized using symmetry requirements1-4, the past two years have witnessed the rise of novel multi-gap dependent topological states5-9, the properties of which go beyond these approaches and are yet to be fully explored. Although already of active interest at equilibrium10-15, we show that the combination of out-of-equilibrium processes and multi-gap topological insights galvanize a new direction within topological phases of matter. We show that periodic driving can induce anomalous multi-gap topological properties that have no static counterpart. In particular, we identify Floquet-induced non-Abelian braiding, which in turn leads to a phase characterized by an anomalous Euler class, being the prime example of a multi-gap topological invariant. Most strikingly, we also retrieve the first example of an 'anomalous Dirac string phase'. This gapped out-of-equilibrium phase features an unconventional Dirac string configuration that physically manifests itself via anomalous edge states on the boundary. Our results not only provide a stepping stone for the exploration of intrinsically dynamical and experimentally viable multi-gap topological phases, but also demonstrate periodic driving as a powerful way to observe these non-Abelian braiding processes notably in quantum simulators.

Spin-resolved topology and partial axion angles in three-dimensional insulators

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ([Formula: see text]-) invariant (helical) 3D TCIs-termed higher-order TCIs (HOTIs)-the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), "spin-Weyl" semimetals, and [Formula: see text]-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that β-MoTe2 realizes a spin-Weyl state and that α-BiBr hosts both 3D QSHI and T-DAXI regimes.

Controllable strain-driven topological phase transition and dominant surface-state transport in HfTe5

The fine-tuning of topologically protected states in quantum materials holds great promise for novel electronic devices. However, there are limited methods that allow for the controlled and efficient modulation of the crystal lattice while simultaneously monitoring the changes in the electronic structure within a single sample. Here, we apply significant and controllable strain to high-quality HfTe5 samples and perform electrical transport measurements to reveal the topological phase transition from a weak topological insulator phase to a strong topological insulator phase. After applying high strain to HfTe5 and converting it into a strong topological insulator, we found that the resistivity of the sample increased by 190,500% and that the electronic transport was dominated by the topological surface states at cryogenic temperatures. Our results demonstrate the suitability of HfTe5 as a material for engineering topological properties, with the potential to generalize this approach to study topological phase transitions in van der Waals materials and heterostructures.

Transition to the Haldane phase driven by electron-electron correlations

One of the most famous quantum systems with topological properties, the spin [Formula: see text] antiferromagnetic Heisenberg chain, is well-known to display exotic [Formula: see text] edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons - the two-orbital Hubbard model-with increasing repulsion strength U and Hund interaction JH. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.

Temperature-dependent Fermi surface probed by Shubnikov-de Haas oscillations in topological semimetal candidates DyBi and HoBi

Rare earth-based monopnictides are among the most intensively studied groups of materials in which extremely large magnetoresistance has been observed. This study explores magnetotransport properties of two representatives of this group, DyBi and HoBi. The extreme magnetoresistance is discovered in DyBi and confirmed in HoBi. At [Formula: see text] K and in [Formula: see text] T for both compounds, magnetoresistance reaches the order of magnitude of [Formula: see text]. For both materials, standard Kohler's rule is obeyed only in the temperature range from 50 to 300 K. At lower temperatures, extended Kohler's rule has to be invoked because carrier concentrations and mobilities strongly change with temperature and magnetic field. This is further proven by the observation of a quite rare temperature-dependence of oscillation frequencies in Shubnikov-de Haas effect. Rate of this dependence clearly changes at Néel temperature, reminiscent of a novel magnetic band splitting. Multi-frequency character of the observed Shubnikov-de Haas oscillations points to the coexistence of electron- and hole-type Fermi pockets in both studied materials. Overall, our results highlight correlation of temperature dependence of the Fermi surface with the magnetotransport properties of DyBi and HoBi.

Topological electronic structure and spin texture of quasi-one-dimensional higher-order topological insulator Bi4Br4

The notion of topological insulators (TIs), characterized by an insulating bulk and conducting topological surface states, can be extended to higher-order topological insulators (HOTIs) hosting gapless modes localized at the boundaries of two or more dimensions lower than the insulating bulk. In this work, by performing high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements with submicron spatial and spin resolution, we systematically investigate the electronic structure and spin texture of quasi-one-dimensional (1D) HOTI candidate Bi4Br4. In contrast to the bulk-state-dominant spectra on the (001) surface, we observe gapped surface states on the (100) surface, whose dispersion and spin-polarization agree well with our ab-initio calculations. Moreover, we reveal in-gap states connecting the surface valence and conduction bands, which is a signature of the hinge states inside the (100) surface gap. Our findings provide compelling evidence for the HOTI phase of Bi4Br4. The identification of the higher-order topological phase promises applications based on 1D spin-momentum locked current in electronic and spintronic devices.

Quantum anomalous Hall phase and effective in-plane Lande-gfactor in an inverted quantum well

A suitable magnetic doped InAs/GaSb or HgTe/CdTe quantum well (QW) shows the coexistence of the quantum spin Hall and quantum anomalous Hall (QAH) phases. We study the topological transitions between these two topological states and confirm the possibility of the QAH phase through the calculations of quantum Hall conductance. The Hall plateau occurs ate2/hrather than2e2/hat such a doping state indicating a QAH phase. Also, the latest experiment reported a robust quantized Hall conductance that persists in an in-plane magnetic field as strong as 12 Tesla. Based on the results of the cited experiment, we present here a precise calculation of the effective in-plane Lande-gfactor. The paper predicts a certain range of controllable parameters in an inverted QW for enabling a dissipationless charge transport needed for spintronics application.

Axion insulator state in hundred-nanometer-thick magnetic topological insulator sandwich heterostructures

An axion insulator is a three-dimensional (3D) topological insulator (TI), in which the bulk maintains the time-reversal symmetry or inversion symmetry but the surface states are gapped by surface magnetization. The axion insulator state has been observed in molecular beam epitaxy (MBE)-grown magnetically doped TI sandwiches and exfoliated intrinsic magnetic TI MnBi2Te4 flakes with an even number layer. All these samples have a thickness of ~ 10 nm, near the 2D-to-3D boundary. The coupling between the top and bottom surface states in thin samples may hinder the observation of quantized topological magnetoelectric response. Here, we employ MBE to synthesize magnetic TI sandwich heterostructures and find that the axion insulator state persists in a 3D sample with a thickness of ~ 106 nm. Our transport results show that the axion insulator state starts to emerge when the thickness of the middle undoped TI layer is greater than ~ 3 nm. The 3D hundred-nanometer-thick axion insulator provides a promising platform for the exploration of the topological magnetoelectric effect and other emergent magnetic topological states, such as the high-order TI phase.

Mott insulators with boundary zeros

The topological classification of electronic band structures is based on symmetry properties of Bloch eigenstates of single-particle Hamiltonians. In parallel, topological field theory has opened the doors to the formulation and characterization of non-trivial phases of matter driven by strong electron-electron interaction. Even though important examples of topological Mott insulators have been constructed, the relevance of the underlying non-interacting band topology to the physics of the Mott phase has remained unexplored. Here, we show that the momentum structure of the Green's function zeros defining the "Luttinger surface" provides a topological characterization of the Mott phase related, in the simplest description, to the one of the single-particle electronic dispersion. Considerations on the zeros lead to the prediction of new phenomena: a topological Mott insulator with an inverted gap for the bulk zeros must possess gapless zeros at the boundary, which behave as a form of "topological antimatter" annihilating conventional edge states. Placing band and Mott topological insulators in contact produces distinctive observable signatures at the interface, revealing the otherwise spectroscopically elusive Green's function zeros.

Antiferromagnetic topological insulator with selectively gapped Dirac cones

Antiferromagnetic (AF) topological materials offer a fertile ground to explore a variety of quantum phenomena such as axion magnetoelectric dynamics and chiral Majorana fermions. To realize such intriguing states, it is essential to establish a direct link between electronic states and topology in the AF phase, whereas this has been challenging because of the lack of a suitable materials platform. Here we report the experimental realization of the AF topological-insulator phase in NdBi. By using micro-focused angle-resolved photoemission spectroscopy, we discovered contrasting surface electronic states for two types of AF domains; the surface having the out-of-plane component in the AF-ordering vector displays Dirac-cone states with a gigantic energy gap, whereas the surface parallel to the AF-ordering vector hosts gapless Dirac states despite the time-reversal-symmetry breaking. The present results establish an essential role of combined symmetry to protect massless Dirac fermions under the presence of AF order and widen opportunities to realize exotic phenomena utilizing AF topological materials.

Bulk-local-density-of-state correspondence in topological insulators

In the quest to connect bulk topological quantum numbers to measurable parameters in real materials, current established approaches often necessitate specific conditions, limiting their applicability. Here we propose and demonstrate an approach to link the non-trivial hierarchical bulk topology to the multidimensional partition of local density of states (LDOS), denoted as the bulk-LDOS correspondence. In finite-size topologically nontrivial photonic crystals, we observe the LDOS partitioned into three distinct regions: a two-dimensional interior bulk area, a one-dimensional edge region, and zero-dimensional corner sites. Contrarily, topologically trivial cases exhibit uniform LDOS distribution across the entire two-dimensional bulk area. Our findings provide a general framework for distinguishing topological insulators and uncovering novel aspects of topological directional band-gap materials, even in the absence of in-gap states.

Dirac-fermion-assisted interfacial superconductivity in epitaxial topological-insulator/iron-chalcogenide heterostructures

Over the last decade, the possibility of realizing topological superconductivity (TSC) has generated much excitement. TSC can be created in electronic systems where the topological and superconducting orders coexist, motivating the continued exploration of candidate material platforms to this end. Here, we use molecular beam epitaxy (MBE) to synthesize heterostructures that host emergent interfacial superconductivity when a non-superconducting antiferromagnet (FeTe) is interfaced with a topological insulator (TI) (Bi, Sb)2Te3. By performing in-vacuo angle-resolved photoemission spectroscopy (ARPES) and ex-situ electrical transport measurements, we find that the superconducting transition temperature and the upper critical magnetic field are suppressed when the chemical potential approaches the Dirac point. We provide evidence to show that the observed interfacial superconductivity and its chemical potential dependence is the result of the competition between the Ruderman-Kittel-Kasuya-Yosida-type ferromagnetic coupling mediated by Dirac surface states and antiferromagnetic exchange couplings that generate the bicollinear antiferromagnetic order in the FeTe layer.

Identifying topological corner states in two-dimensional metal-organic frameworks

Due to the diversity of molecular building blocks, the two-dimensional (2D) metal-organic frameworks (MOFs) are ideal platforms to realize exotic lattice models in condensed matter theory. In this work, we demonstrate the universal existence of topological corner states in 2D MOFs with a star lattice configuration, and confirm the intriguing higher-order nontrivial topology in the energy window between two Kagome-bands, or between Dirac-band and four-band. Furthermore, combining first-principles calculations and scanning tunneling microscopy measurements, the unique topological corner state is directly identified in monolayer Ni3(HITP)2 (HITP = 2,3,6,7,10,11-hexaiminotriphenylene) grown on the Au(111) substrate. Our results not only illustrate the first organic topological state in the experiments, but also offer an exciting opportunity to study higher-order topology in 2D MOFs with the large insulating band gap.

Non-trivial topological phases in transition metal rich half-Heusler oxides

Topological insulators with gapless surface states and insulating bulk in non-centrosymmetric cubic systems have been extensively explored following the discovery of two-dimensional quantum spin hall effect in zincblende HgTe. In such systems the negative band inversion strength EBIS(= EΓ6-EΓ8<0) governs the robustness of the non-trivial topological states at ambient conditions. Hence, realizing large negative values of EBIShas been a guiding motivation of several investigations reported in literature. Here, we present a material design approach which can be employed to realize large negative values of EBISin cubic materials such as half-Heusler (HH) oxides with 18 valence electron configurations. We explore 27 HH oxides of the form ABO (A = Li, K, Rb; B = Cu, Ag, Au) inα-,β-, andγ-phase (by placing transition metal atom at different Wyckoff positions) for their non-trivial topological phase. Off these three phases, we found that, theα-phase of nine HH oxides (wherein the transition metal atoms occupy 4a Wyckoff positions in the crystal structure) is the most promising with non-trivial topological phase which is governed by the mass-Darwin fully-relativistic effects enhancing EBIS. Whereas the other phases were found to be either trivial semiconductors or semimetals or metals and most of them being dynamically unstable. We focus on RbAuO inα-phase with EBISof -1.29 eV and the effect of strain fields on the topological surface states of this compound. We conclude that theα-phase of HH oxide presented here can be synthesized experimentally for diverse room temperature applications in spintronics and nanoelectronics.

Exploiting the Close-to-Dirac Point Shift of the Fermi Level in the Sb2Te3/Bi2Te3 Topological Insulator Heterostructure for Spin-Charge Conversion

Properly tuning the Fermi level position in topological insulators is of vital importance to tailor their spin-polarized electronic transport and to improve the efficiency of any functional device based on them. Here, we report the full in situ metal organic chemical vapor deposition (MOCVD) and study of a highly crystalline Bi2Te3/Sb2Te3 topological insulator heterostructure on top of large area (4″) Si(111) substrates. The bottom Sb2Te3 layer serves as an ideal seed layer for the growth of highly crystalline Bi2Te3 on top, also inducing a remarkable shift of the Fermi level to place it very close to the Dirac point, as visualized by angle-resolved photoemission spectroscopy. To exploit such ideal topologically protected surface states, we fabricate the simple spin-charge converter Si(111)/Sb2Te3/Bi2Te3/Au/Co/Au and probe the spin-charge conversion (SCC) by spin pumping ferromagnetic resonance. A large SCC is measured at room temperature and is interpreted within the inverse Edelstein effect, thus resulting in a conversion efficiency of λIEEE ∼ 0.44 nm. Our results demonstrate the successful tuning of the surface Fermi level of Bi2Te3 when grown on top of Sb2Te3 with a full in situ MOCVD process, which is highly interesting in view of its future technology transfer.

Spin-Orbit Torques and Spin Hall Magnetoresistance Generated by Twin-Free and Amorphous Bi0.9 Sb0.1 Topological Insulator Films

Topological insulators have attracted great interest as generators of spin-orbit torques (SOTs) in spintronic devices. Bi1-x Sbx is a prominent topological insulator that has a high charge-to-spin conversion efficiency. However, the origin and magnitude of the SOTs induced by current-injection in Bi1-x Sbx remain controversial. Here, the investigation of the SOTs and spin Hall magnetoresistance resulting from charge-to-spin conversion in twin-free epitaxial layers of Bi0.9 Sb0.1 (0001) coupled to FeCo are investigated, and compared with those of amorphous Bi0.9 Sb0.1 . A large charge-to-spin conversion efficiency of 1 in the first case and less than 0.1 in the second is found, confirming crystalline Bi0.9 Sb0.1 as a strong spin-injector material. The SOTs and spin Hall magnetoresistance are independent of the direction of the electric current, indicating that charge-to-spin conversion in single-crystal Bi0.9 Sb0.1 (0001) is isotropic despite the strong anisotropy of the topological surface states. Further, it is found that the damping-like SOT has a non-monotonic temperature dependence with a minimum at 20 K. By correlating the SOT with resistivity and weak antilocalization measurements, charge-spin conversion is concluded to occur via thermally excited holes from the bulk states above 20 K, and conduction through the isotropic surface states with increasing spin polarization due to decreasing electron-electron scattering below 20 K.

Evidence of unconventional superconductivity on the surface of the nodal semimetal CaAg1-xPdxP

Surface states of topological materials provide extreme electronic states for unconventional superconducting states. CaAg1-xPdxP is an ideal candidate for a nodal-line Dirac semimetal with drumhead surface states and no additional bulk bands. Here, we report that CaAg1-xPdxP has surface states that exhibit unconventional superconductivity (SC) around 1.5 K. Extremely sharp magnetoresistance, tuned by surface-sensitive gating, determines the surface origin of the ultrahigh-mobility "electrons." The Pd-doping elevates the Fermi level towards the surface states, and as a result, the critical temperature (Tc) is increased up to 1.7 K from 1.2 K for undoped CaAgP. Furthermore, a soft point-contact study at the surface of Pd-doped CaAgP proved the emergence of unconventional SC on the surface. We observed the bell-shaped conductance spectra, a hallmark of the unconventional SC. Ultrahigh mobility carriers derived from the surface flat bands generate a new class of unconventional SC.

Realization and topological properties of third-order exceptional lines embedded in exceptional surfaces

As the counterpart of Hermitian nodal structures, the geometry formed by exceptional points (EPs), such as exceptional lines (ELs), entails intriguing spectral topology. We report the experimental realization of order-3 exceptional lines (EL3) that are entirely embedded in order-2 exceptional surfaces (ES2) in a three-dimensional periodic synthetic momentum space. The EL3 and the concomitant ES2, together with the topology of the underlying space, prohibit the evaluation of their topology in the eigenvalue manifold by prevailing topological characterization methods. We use a winding number associated with the resultants of the Hamiltonian. This resultant winding number can be chosen to detect only the EL3 but ignores the ES2, allowing the diagnosis of the topological currents carried by the EL3, which enables the prediction of their evolution under perturbations. We further reveal the connection between the intersection multiplicity of the resultants and the winding of the resultant field around the EPs and generalize the approach for detecting and topologically characterizing higher-order EPs. Our work exemplifies the unprecedented topology of higher-order exceptional geometries and may inspire new non-Hermitian topological applications.

Nondegenerate Integer Quantum Hall Effect from Topological Surface States in Ag2Te Nanoplates

The quantum Hall effect is one of the exclusive properties displayed by Dirac Fermions in topological insulators, which propagates along the chiral edge state and gives rise to quantized electron transport. However, the quantum Hall effect formed by the nondegenerate Dirac surface states has been elusive so far. Here, we demonstrate the nondegenerate integer quantum Hall effect from the topological surface states in three-dimensional (3D) topological insulator β-Ag2Te nanostructures. Surface-state dominant conductance renders quantum Hall conductance plateaus with a step of e2/h, along with typical thermopower behaviors of two-dimensional (2D) massless Dirac electrons. The 2D nature of the topological surface states is proven by the electrical and thermal transport responses under tilted magnetic fields. Moreover, the degeneracy of the surface states is removed by structure inversion asymmetry (SIA). The evidenced SIA-induced nondegenerate integer quantum Hall effect in low-symmetry β-Ag2Te has implications for both fundamental study and the realization of topological magneto-electric effects.

Colossal negative magnetoresistance in field-induced Weyl semimetal of magnetic half-Heusler compound

The discovery of topological insulators and semimetals triggered enormous interest in exploring emergent electromagnetic responses in solids. Particular attention has been focused on ternary half-Heusler compounds, whose electronic structure bears analogy to the topological zinc-blende compounds while also including magnetic rare-earth ions coupled to conduction electrons. However, most of the research in this system has been in band-inverted zero-gap semiconductors such as GdPtBi, which still does not fully exhaust the large potential of this material class. Here, we report a less-studied member of half-Heusler compounds, HoAuSn, which we show is a trivial semimetal or narrow-gap semiconductor at zero magnetic field but undergoes a field-induced transition to a Weyl semimetal, with a negative magnetoresistance exceeding four orders of magnitude at low temperatures. The combined study of Shubnikov-de Haas oscillations and first-principles calculation suggests that the exchange field from Ho 4f moments reconstructs the band structure to induce Weyl points which play a key role in the strong suppression of large-angle carrier scattering. Our findings demonstrate the unique mechanism of colossal negative magnetoresistance and provide pathways towards realizing topological electronic states in a large class of magnetic half-Heusler compounds.

Emergent metallicity at the grain boundaries of higher-order topological insulators

Topological lattice defects, such as dislocations and grain boundaries (GBs), are ubiquitously present in the bulk of quantum materials and externally tunable in metamaterials. In terms of robust modes, localized near the defect cores, they are instrumental in identifying topological crystals, featuring the hallmark band inversion at a finite momentum (translationally active type). Here we show that the GB superlattices in both two-dimensional and three-dimensional translationally active higher-order topological insulators harbor a myriad of dispersive modes that are typically placed at finite energies, but always well-separated from the bulk states. However, when the Burgers vector of the constituting edge dislocations points toward the gapless corners or hinges, both second-order and third-order topological insulators accommodate self-organized emergent topological metals near the zero energy (half-filling) in the GB mini Brillouin zone. We discuss possible material platforms where our proposed scenarios can be realized through the band-structure and defect engineering.

Quantized resistance revealed at the criticality of the quantum anomalous Hall phase transitions

In multilayered magnetic topological insulator structures, magnetization reversal processes can drive topological phase transitions between quantum anomalous Hall, axion insulator, and normal insulator states. Here we report an examination of the critical behavior of two such transitions: the quantum anomalous Hall to normal insulator (QAH-NI), and quantum anomalous Hall to axion insulator (QAH-AXI) transitions. By introducing a new analysis protocol wherein temperature dependent variations in the magnetic coercivity are accounted for, the critical behavior of the QAH-NI and QAH-AXI transitions are evaluated over a wide range of temperature and magnetic field. Despite the uniqueness of these different transitions, quantized longitudinal resistance and Hall conductance are observed at criticality in both cases. Furthermore, critical exponents were extracted for QAH-AXI transitions occurring at magnetization reversals of two different magnetic layers. The observation of consistent critical exponents and resistances in each case, independent of the magnetic layer details, demonstrates critical behaviors in quantum anomalous Hall transitions to be of electronic rather than magnetic origin. Our finding offers a new avenue for studies of phase transition and criticality in QAH insulators.

Gate-Defined Josephson Weak-Links in Monolayer WTe2

Systems combining superconductors with topological insulators offer a platform for the study of Majorana bound states and a possible route to realize fault tolerant topological quantum computation. Among the systems being considered in this field, monolayers of tungsten ditelluride (WTe2 ) have a rare combination of properties. Notably, it has been demonstrated to be a quantum spin Hall insulator (QSHI) and can easily be gated into a superconducting state. Measurements on gate-defined Josephson weak-link devices fabricated using monolayer WTe2 are reported. It is found that consideration of the 2D superconducting leads are critical in the interpretation of magnetic interference in the resulting junctions. The reported fabrication procedures suggest a facile way to produce further devices from this technically challenging material and the results mark the first step toward realizing versatile all-in-one topological Josephson weak-links using monolayer WTe2 .

Thermoelectric properties of ballistic Normal-Weyl semimetal-Normal junction

Weyl semimetals are a new class of topological materials possessing outstanding physical properties. We investigate the thermoelectric properties of a ballistic Weyl semimetal specimen connected to two normal contacts. We introduce a model to evaluate the thermoelectric coefficients of the junction and analyze its features along two distinct directions, one along the chiral axis of the Weyl semimetal and the other perpendicular to it. We demonstrate that the thermoelectric response of this junction depends on whether it is along the chiral axis of the Weyl semimetal or not. Electrical and thermal conductances of this junction reveal considerable dependence on the length and chemical potential of the Weyl semimetal layer. In particular, we observe that, decreasing the chemical potential in the normal contacts enhances the Seebeck coefficient and thermoelectric figure of merit of the junction to substantial values. Hence, we unveil that a ballistic junction of Weyl semimetal can serve as a fundamental segment for application in future thermoelectric devices for thermal energy harvesting.

Topology stabilized fluctuations in a magnetic nodal semimetal

The interplay between magnetism and electronic band topology enriches topological phases and has promising applications. However, the role of topology in magnetic fluctuations has been elusive. Here, we report evidence for topology stabilized magnetism above the magnetic transition temperature in magnetic Weyl semimetal candidate CeAlGe. Electrical transport, thermal transport, resonant elastic X-ray scattering, and dilatometry consistently indicate the presence of locally correlated magnetism within a narrow temperature window well above the thermodynamic magnetic transition temperature. The wavevector of this short-range order is consistent with the nesting condition of topological Weyl nodes, suggesting that it arises from the interaction between magnetic fluctuations and the emergent Weyl fermions. Effective field theory shows that this topology stabilized order is wavevector dependent and can be stabilized when the interband Weyl fermion scattering is dominant. Our work highlights the role of electronic band topology in stabilizing magnetic order even in the classically disordered regime.

Room temperature energy-efficient spin-orbit torque switching in two-dimensional van der Waals Fe3GeTe2 induced by topological insulators

Two-dimensional (2D) ferromagnetic materials with unique magnetic properties have great potential for next-generation spintronic devices with high flexibility, easy controllability, and high heretointegrability. However, realizing magnetic switching with low power consumption at room temperature is challenging. Here, we demonstrate the room-temperature spin-orbit torque (SOT) driven magnetization switching in an all-van der Waals (vdW) heterostructure using an optimized epitaxial growth approach. The topological insulator Bi2Te3 not only raises the Curie temperature of Fe3GeTe2 (FGT) through interfacial exchange coupling but also works as a spin current source allowing the FGT to switch at a low current density of ~2.2×106 A/cm2. The SOT efficiency is ~2.69, measured at room temperature. The temperature and thickness-dependent SOT efficiency prove that the larger SOT in our system mainly originates from the nontrivial topological origin of the heterostructure. Our experiments enable an all-vdW SOT structure and provides a solid foundation for the implementation of room-temperature all-vdW spintronic devices in the future.

Electrical analogue of one-dimensional and quasi-one-dimensional Aubry-André-Harper lattices

This work explores the potential for achieving correlated disorder in electrical circuits by utilizing reactive elements. By establishing a direct correspondence between the tight-binding Hamiltonian and the admittance matrix of the circuit, a novel approach is presented. The localization phenomena within the circuit are investigated through the analysis of the two-port impedance. To introduce correlated disorder, the Aubry-André-Harper (AAH) model is employed. Both one-dimensional and quasi-one-dimensional AAH structures are examined and effectively mapped to their tight-binding counterparts. Notably, transitions from a high-conducting phase to a low-conducting phase are observed in these circuits, highlighting the impact of correlated disorder.

Towards layer-selective quantum spin hall channels in weak topological insulator Bi4Br2I2

Weak topological insulators, constructed by stacking quantum spin Hall insulators with weak interlayer coupling, offer promising quantum electronic applications through topologically non-trivial edge channels. However, the currently available weak topological insulators are stacks of the same quantum spin Hall layer with translational symmetry in the out-of-plane direction-leading to the absence of the channel degree of freedom for edge states. Here, we study a candidate weak topological insulator, Bi4Br2I2, which is alternately stacked by three different quantum spin Hall insulators, each with tunable topologically non-trivial edge states. Our angle-resolved photoemission spectroscopy and first-principles calculations show that an energy gap opens at the crossing points of different Dirac cones correlated with different layers due to the interlayer interaction. This is essential to achieve the tunability of topological edge states as controlled by varying the chemical potential. Our work offers a perspective for the construction of tunable quantized conductance devices for future spintronic applications.

Utilizing Topological Insulator Two-Dimensional Bismuth for Ultrasensitive Acoustic Detection

Topological insulators (TIs) are characterized by a full insulating gap in the bulk and gapless edge or surface states, which have attracted tremendous attention. 2D Bi (110), as a typical TI, is of particular interest due to its low symmetry structure and topologically protected and spin-momentum-locked Dirac surface states. However, the material's potential applications are hindered by difficulties in fabrication, due to its strong semi-metallic bonding and poor stability. In this study, a novel electrochemical intercalation method for the fabrication of ultrathin Bi (110) nanosheets with the highest yield ever reported is presented. These nanosheets are stabilized through cathodic exfoliation in a reductive environment and further modification with polymer ionic liquids. The versatility of these nanosheets is demonstrated by fabricating flexible acoustic sensors with ultrahigh sensitivity. These sensors can even detect sounds as quiet as 45 dB. Furthermore, these sensors are utilized for acoustic-to-electric energy conversion and information transfer. This work offers a promising approach for scalable fabrication and preservation of ultrathin 2D TI Bi (110) nanosheets and paves the way for their integration into smart devices.

Anomalous Landau quantization in intrinsic magnetic topological insulators

The intrinsic magnetic topological insulator, Mn(Bi1-xSbx)2Te4, has been identified as a Weyl semimetal with a single pair of Weyl nodes in its spin-aligned strong-field configuration. A direct consequence of the Weyl state is the layer dependent Chern number, [Formula: see text]. Previous reports in MnBi2Te4 thin films have shown higher [Formula: see text] states either by increasing the film thickness or controlling the chemical potential. A clear picture of the higher Chern states is still lacking as data interpretation is further complicated by the emergence of surface-band Landau levels under magnetic fields. Here, we report a tunable layer-dependent [Formula: see text] = 1 state with Sb substitution by performing a detailed analysis of the quantization states in Mn(Bi1-xSbx)2Te4 dual-gated devices-consistent with calculations of the bulk Weyl point separation in the doped thin films. The observed Hall quantization plateaus for our thicker Mn(Bi1-xSbx)2Te4 films under strong magnetic fields can be interpreted by a theory of surface and bulk spin-polarised Landau level spectra in thin film magnetic topological insulators.

Rigorous analysis of the topologically protected edge states in the quantum spin Hall phase of the armchair ribbon geometry

Studying the edge states of a topological system and extracting their topological properties is of great importance in understanding and characterizing these systems. In this paper, we present a novel analytical approach for obtaining explicit expressions for the edge states in the Kane-Mele model within a ribbon geometry featuring armchair boundaries. Our approach involves a mapping procedure that transforms the system into an extended Su-Schrieffer-Heeger model, specifically a two-leg ladder, in momentum space. Through rigorous derivation, we determine various analytical properties of the edge states, including their wave functions and energy dispersion. Additionally, we investigate the condition for topological transition by solely analyzing the edge states, and we elucidate the underlying reasons for the violation of the bulk-edge correspondence in relatively narrow ribbons. Our findings shed light on the unique characteristics of the edge states in the quantum spin Hall phase of the Kane-Mele model and provide valuable insights into the topological properties of such systems.

Topological Insulator Bi2 Se3 -Assisted Heterostructure for Ultrafast Charging Sodium-Ion Batteries

The development of fast charging materials offers a viable solution for large-scale and sustainable energy storage needs. However, it remains a critical challenge to improve the electrical and ionic conductivity for better performance. Topological insulator (TI), a topological quantum material that has attracted worldwide attention, hosts unusual metallic surface states and consequent high carrier mobility. Nevertheless, its potential in promising high-rate charging capability has not been fully realized and explored. Herein, a novel Bi2 Se3 -ZnSe heterostructure as excellent fast charging material for Na+ storage is reported. Ultrathin Bi2 Se3 nanoplates with rich TI metallic surfaces are introduced as an electronic platform inside the material, which greatly reduces the charge transfer resistance and improves the overall electrical conductivity. Meanwhile, the abundant crystalline interfaces between these two selenides promote Na+ migration and provide additional active sites as well. As expected, the composite delivers the excellent high-rate performance of 360.5 mAh g-1 at 20 A g-1 and maintains its electrochemical stability of 318.4 mAh g-1 after 3000 long cycles, which is the record high for all reported selenide-based anodes. This work is anticipated to provide alternative strategies for further exploration of topological insulators and advanced heterostructures.

Quantum Spin Hall Effect in Two-Monolayer-Thick InN/InGaN Coupled Multiple Quantum Wells

In this study, we present a theoretical study of the quantum spin Hall effect in InN/InGaN coupled multiple quantum wells with the individual well widths equal to two atomic monolayers. We consider triple and quadruple quantum wells in which the In content in the interwell barriers is greater than or equal to the In content in the external barriers. To calculate the electronic subbands in these nanostructures, we use the eight-band k∙p Hamiltonian, assuming that the effective spin-orbit interaction in InN is negative, which represents the worst-case scenario for achieving a two-dimensional topological insulator. For triple quantum wells, we find that when the In contents of the external and interwell barriers are the same and the widths of the internal barriers are equal to two monolayers, a topological insulator with a bulk energy gap of 0.25 meV can appear. Increasing the In content in the interwell barriers leads to a significant increase in the bulk energy gap of the topological insulator, reaching about 0.8 meV. In these structures, the topological insulator can be achieved when the In content in the external barriers is about 0.64, causing relatively low strain in quantum wells and making the epitaxial growth of these structures within the range of current technology. Using the effective 2D Hamiltonian, we study the edge states in strip structures containing topological triple quantum wells. We demonstrate that the opening of the gap in the spectrum of the edge states caused by decreasing the width of the strip has an oscillatory character regardless of whether the pseudospin-mixing elements of the effective Hamiltonian are omitted or taken into account. The strength of the finite size effect in these structures is several times smaller than that in HgTe/HgCdTe and InAs/GaSb/AlSb topological insulators. Therefore, its influence on the quantum spin Hall effect is negligible in strips with a width larger than 150 nm, unless the temperature at which electron transport is measured is less than 1 mK. In the case of quadruple quantum wells, we find the topological insulator phase only when the In content in the interwell barriers is larger than in the external barriers. We show that in these structures, a topological insulator with a bulk energy gap of 0.038 meV can be achieved when the In content in the external barriers is about 0.75. Since this value of the bulk energy gap is very small, quadruple quantum wells are less useful for realizing a measurable quantum spin Hall system, but they are still attractive for achieving a topological phase transition and a nonlocal topological semimetal phase.

Giant and Tunable Out-of-Plane Spin Polarization of Topological Antimonene

Topological insulators are bulk insulators with metallic and fully spin-polarized surface states displaying Dirac-like band dispersion. Due to spin-momentum locking, these topological surface states (TSSs) have a predominant in-plane spin polarization in the bulk fundamental gap. Here, we show by spin-resolved photoemission spectroscopy that the TSS of a topological insulator interfaced with an antimonene bilayer exhibits nearly full out-of-plane spin polarization within the substrate gap. We connect this phenomenon to a symmetry-protected band crossing of the spin-polarized surface states. The nearly full out-of-plane spin polarization of the TSS occurs along a continuous path in the energy-momentum space, and the spin polarization within the gap can be reversibly tuned from nearly full out-of-plane to nearly full in-plane by electron doping. These findings pave the way to advanced spintronics applications that exploit the giant out-of-plane spin polarization of TSSs.

Spin-charge separation and quantum spin Hall effect of [Formula: see text]-bismuthene

Multiple works suggest the possibility of classification of quantum spin Hall effect with magnetic flux tubes, which cause separation of spin and charge degrees of freedom and pumping of spin or Kramers-pair. However, the proof of principle demonstration of spin-charge separation is yet to be accomplished for realistic, ab initio band structures of spin-orbit-coupled materials, lacking spin-conservation law. In this work, we perform thought experiments with magnetic flux tubes on [Formula: see text]-bismuthene, and demonstrate spin-charge separation, and quantized pumping of spin for three insulating states, that can be accessed by tuning filling fractions. With a combined analysis of momentum-space topology and real-space response, we identify important role of bands supporting even integer invariants, which cannot be addressed with symmetry-based indicators. Our work sets a new standard for the computational diagnosis of two-dimensional, quantum spin-Hall materials by going beyond the [Formula: see text] paradigm and providing an avenue for precise determination of the bulk invariant through computation of quantized, real-space response.

Macroscopic Quantum Tunneling of a Topological Ferromagnet

The recent advent of topological states of matter spawned many significant discoveries. The quantum anomalous Hall (QAH) effect is a prime example due to its potential for applications in quantum metrology, as well as its influence on fundamental research into the underlying topological and magnetic states and into axion electrodynamics. Here, electronic transport studies on a (V,Bi,Sb)₂ Te₃ ferromagnetic topological insulator nanostructure in the QAH regime are presented. This allows access to the dynamics of an individual ferromagnetic domain. The domain size is estimated to be in the 50-100 nm range. Telegraph noise resulting from the magnetization fluctuations of this domain is observed in the Hall signal. Careful analysis of the influence of temperature and external magnetic field on the domain switching statistics provides evidence for quantum tunneling (QT) of magnetization in a macrospin state. This ferromagnetic macrospin is not only the largest magnetic object in which QT is observed, but also the first observation of the effect in a topological state of matter.