*Adv Mater ; : e2205927, 2022 Nov 17.*

##### RESUMO

Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization and spin-orbit coupling (SOC) can engender highly tunable topological states. Here, utilizing angle-resolved photoemission spectroscopy, we directly visualize the Weyl lines with strong out-of-plane dispersion in the A-A stacked kagome magnet GdMn6 Sn6 . Remarkably, the Weyl lines exhibit a strong magnetization-direction tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. Our results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct three-dimensional topological phases, but also demonstrate AMn6 Sn6 (A = rare earth or Li, Mg, Ca) as a versatile material family for exploring diverse emergent topological quantum responses. This article is protected by copyright. All rights reserved.

*Phys Rev Lett ; 129(16): 166401, 2022 Oct 14.*

##### RESUMO

Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge density wave, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to nonkagome surface layers. Here, we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifies a 2×2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin mapping across steps of unit cell height demonstrates the existence of spin-polarized electrons with an antiferromagnetic stacking order. We further uncover the correlation between antiferromagnetism and charge order anisotropy, highlighting the unusual magnetic coupling of the charge order. Finally, we detect a pronounced edge state within the charge order energy gap, which is robust against the irregular shape fluctuations of the kagome lattice edges. We discuss our results with the theoretically considered topological features of the kagome charge order including unconventional magnetism and bulk-boundary correspondence.

*Nat Commun ; 13(1): 4603, 2022 Aug 06.*

##### RESUMO

Two-dimensional (2D) Dirac states with linear dispersion have been observed in graphene and on the surface of topological insulators. 2D Dirac states discovered so far are exclusively pinned at high-symmetry points of the Brillouin zone, for example, surface Dirac states at [Formula: see text] in topological insulators Bi2Se(Te)3 and Dirac cones at K and [Formula: see text] points in graphene. The low-energy dispersion of those Dirac states are isotropic due to the constraints of crystal symmetries. In this work, we report the observation of novel 2D Dirac states in antimony atomic layers with phosphorene structure. The Dirac states in the antimony films are located at generic momentum points. This unpinned nature enables versatile ways such as lattice strains to control the locations of the Dirac points in momentum space. In addition, dispersions around the unpinned Dirac points are highly anisotropic due to the reduced symmetry of generic momentum points. The exotic properties of unpinned Dirac states make antimony atomic layers a new type of 2D Dirac semimetals that are distinct from graphene.

*Nat Mater ; 21(10): 1111-1115, 2022 Oct.*

##### RESUMO

Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics1,2. The quantum spin Hall phase3-6 is a topological quantum phase that features a two-dimensional insulating bulk and a helical edge state. Here we use vector magnetic field and variable temperature based scanning tunnelling microscopy to provide micro-spectroscopic evidence for a room-temperature quantum spin Hall edge state on the surface of the higher-order topological insulator Bi4Br4. We find that the atomically resolved lattice exhibits a large insulating gap of over 200 meV, and an atomically sharp monolayer step edge hosts an in-gap gapless state, suggesting topological bulk-boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent in the underlying band topology. We further identify the geometrical hybridization of such edge states, which not only supports the Z2 topology of the quantum spin Hall state but also visualizes the building blocks of the higher-order topological insulator phase. Our results further encourage the exploration of high-temperature transport quantization of the putative topological phase reported here.

*Nat Commun ; 13(1): 1197, 2022 Mar 07.*

##### RESUMO

In ordinary materials, electrons conduct both electricity and heat, where their charge-entropy relations observe the Mott formula and the Wiedemann-Franz law. In topological quantum materials, the transverse motion of relativistic electrons can be strongly affected by the quantum field arising around the topological fermions, where a simple model description of their charge-entropy relations remains elusive. Here we report the topological charge-entropy scaling in the kagome Chern magnet TbMn6Sn6, featuring pristine Mn kagome lattices with strong out-of-plane magnetization. Through both electric and thermoelectric transports, we observe quantum oscillations with a nontrivial Berry phase, a large Fermi velocity and two-dimensionality, supporting the existence of Dirac fermions in the magnetic kagome lattice. This quantum magnet further exhibits large anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects, all of which persist to above room temperature. Remarkably, we show that the charge-entropy scaling relations of these anomalous transverse transports can be ubiquitously described by the Berry curvature field effects in a Chern-gapped Dirac model. Our work points to a model kagome Chern magnet for the proof-of-principle elaboration of the topological charge-entropy scaling.

*ACS Nano ; 16(2): 2369-2380, 2022 Feb 22.*

##### RESUMO

To realize the quantum anomalous Hall effect (QAHE) at elevated temperatures, the approach of magnetic proximity effect (MPE) was adopted to break the time-reversal symmetry in the topological insulator (Bi0.3Sb0.7)2Te3 (BST) based heterostructures with a ferrimagnetic insulator europium iron garnet (EuIG) of perpendicular magnetic anisotropy. Here we demonstrate large anomalous Hall resistance (RAHE) exceeding 8 Ω (ρAHE of 3.2 µΩ·cm) at 300 K and sustaining to 400 K in 35 BST/EuIG samples, surpassing the past record of 0.28 Ω (ρAHE of 0.14 µΩ·cm) at 300 K. The large RAHE is attributed to an atomically abrupt, Fe-rich interface between BST and EuIG. Importantly, the gate dependence of the AHE loops shows no sign change with varying chemical potential. This observation is supported by our first-principles calculations via applying a gradient Zeeman field plus a contact potential on BST. Our calculations further demonstrate that the AHE in this heterostructure is attributed to the intrinsic Berry curvature. Furthermore, for gate-biased 4 nm BST on EuIG, a pronounced topological Hall effect-like (THE-like) feature coexisting with AHE is observed at the negative top-gate voltage up to 15 K. Interface tuning with theoretical calculations has realized topologically distinct phenomena in tailored magnetic TI-based heterostructures.

_{2}P

_{2}.

*Proc Natl Acad Sci U S A ; 119(4)2022 Jan 25.*

##### RESUMO

We unravel the interplay of topological properties and the layered (anti)ferromagnetic ordering in EuSn2P2, using spin and chemical selective electron and X-ray spectroscopies supported by first-principle calculations. We reveal the presence of in-plane long-range ferromagnetic order triggering topological invariants and resulting in the multiple protection of topological Dirac states. We provide clear evidence that layer-dependent spin-momentum locking coexists with ferromagnetism in this material, a cohabitation that promotes EuSn2P2 as a prime candidate axion insulator for topological antiferromagnetic spintronics applications.

*ACS Nano ; 15(9): 15085-15095, 2021 Sep 28.*

##### RESUMO

Antimonene is a promising two-dimensional (2D) material that is calculated to have a significant fundamental bandgap usable for advanced applications such as field-effect transistors, photoelectric devices, and the quantum-spin Hall (QSH) state. Herein, we demonstrate a phenomenon termed topological proximity effect, which occurs between a 2D material and a three-dimensional (3D) topological insulator (TI). We provide strong evidence derived from hydrogen etching on Sb2Te3 that large-area and well-ordered antimonene presents a 2D topological state. Delicate analysis with a scanning tunneling microscope of the evolutionary intermediates reveals that hydrogen etching on Sb2Te3 resulted in the formation of a large area of antimonene with a buckled structure. A topological state formed in the antimonene/Sb2Te3 heterostructure was confirmed with angle-resolved photoemission spectra and density-functional theory calculations; in particular, the Dirac point was located almost at the Fermi level. The results reveal that Dirac fermions are indeed realized at the interface of a 2D normal insulator (NI) and a 3D TI as a result of strong hybridization between antimonene and Sb2Te3. Our work demonstrates that the position of the Dirac point and the shape of the Dirac surface state can be tuned by varying the energy position of the NI valence band, which modifies the direction of the spin texture of Sb-BL/Sb2Te3 via varying the Fermi level. This topological phase in 2D-material engineering has generated a paradigm in that the topological proximity effect at the NI/TI interface has been realized, which demonstrates a way to create QSH systems in 2D-material TI heterostructures.

*Nature ; 595(7868): 521-525, 2021 07.*

##### RESUMO

Whereas ferromagnets have been known and used for millennia, antiferromagnets were only discovered in the 1930s1. At large scale, because of the absence of global magnetization, antiferromagnets may seem to behave like any non-magnetic material. At the microscopic level, however, the opposite alignment of spins forms a rich internal structure. In topological antiferromagnets, this internal structure leads to the possibility that the property known as the Berry phase can acquire distinct spatial textures2,3. Here we study this possibility in an antiferromagnetic axion insulator-even-layered, two-dimensional MnBi2Te4-in which spatial degrees of freedom correspond to different layers. We observe a type of Hall effect-the layer Hall effect-in which electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under zero electric field, even-layered MnBi2Te4 shows no anomalous Hall effect. However, applying an electric field leads to the emergence of a large, layer-polarized anomalous Hall effect of about 0.5e2/h (where e is the electron charge and h is Planck's constant). This layer Hall effect uncovers an unusual layer-locked Berry curvature, which serves to characterize the axion insulator state. Moreover, we find that the layer-locked Berry curvature can be manipulated by the axion field formed from the dot product of the electric and magnetic field vectors. Our results offer new pathways to detect and manipulate the internal spatial structure of fully compensated topological antiferromagnets4-9. The layer-locked Berry curvature represents a first step towards spatial engineering of the Berry phase through effects such as layer-specific moiré potential.

*Nat Commun ; 12(1): 2492, 2021 May 03.*

##### RESUMO

While the discovery of two-dimensional (2D) magnets opens the door for fundamental physics and next-generation spintronics, it is technically challenging to achieve the room-temperature ferromagnetic (FM) order in a way compatible with potential device applications. Here, we report the growth and properties of single- and few-layer CrTe2, a van der Waals (vdW) material, on bilayer graphene by molecular beam epitaxy (MBE). Intrinsic ferromagnetism with a Curie temperature (TC) up to 300 K, an atomic magnetic moment of ~0.21 [Formula: see text]/Cr and perpendicular magnetic anisotropy (PMA) constant (Ku) of 4.89 × 105 erg/cm3 at room temperature in these few-monolayer films have been unambiguously evidenced by superconducting quantum interference device and X-ray magnetic circular dichroism. This intrinsic ferromagnetism has also been identified by the splitting of majority and minority band dispersions with ~0.2 eV at Ð point using angle-resolved photoemission spectroscopy. The FM order is preserved with the film thickness down to a monolayer (TC ~ 200 K), benefiting from the strong PMA and weak interlayer coupling. The successful MBE growth of 2D FM CrTe2 films with room-temperature ferromagnetism opens a new avenue for developing large-scale 2D magnet-based spintronics devices.

*Nat Nanotechnol ; 16(4): 421-425, 2021 Apr.*

##### RESUMO

The nonlinear Hall effect (NLHE), the phenomenon in which a transverse voltage can be produced without a magnetic field, provides a potential alternative for rectification or frequency doubling1,2. However, the low-temperature detection of the NLHE limits its applications3,4. Here, we report the room-temperature NLHE in a type-II Weyl semimetal TaIrTe4, which hosts a robust NLHE due to broken inversion symmetry and large band overlapping at the Fermi level. We also observe a temperature-induced sign inversion of the NLHE in TaIrTe4. Our theoretical calculations suggest that the observed sign inversion is a result of a temperature-induced shift in the chemical potential, indicating a direct correlation of the NLHE with the electronic structure at the Fermi surface. Finally, on the basis of the observed room-temperature NLHE in TaIrTe4 we demonstrate the wireless radiofrequency (RF) rectification with zero external bias and magnetic field. This work opens a door to realizing room-temperature applications based on the NLHE in Weyl semimetals.

*ACS Cent Sci ; 6(11): 2023-2030, 2020 Nov 25.*

##### RESUMO

The localized f-electrons enrich the magnetic properties in rare-earth-based intermetallics. Among those, compounds with heavier 4d and 5d transition metals are even more fascinating because anomalous electronic properties may be induced by the hybridization of 4f and itinerant conduction electrons primarily from the d orbitals. Here, we describe the observation of trivalent Yb3+ with S = 1/2 at low temperatures in Yb x Pt5P, the first of a new family of materials. Yb x Pt5P (0.23 ≤ x ≤ 0.96) phases were synthesized and structurally characterized. They exhibit a large homogeneity width with the Yb ratio exclusively occupying the 1a site in the anti-CeCoIn5 structure. Moreover, a sudden resistivity drop could be found in Yb x Pt5P below â¼0.6 K, which requires further investigation. First-principles electronic structure calculations substantiate the antiferromagnetic ground state and indicate that two-dimensional nesting around the Fermi level may give rise to exotic physical properties, such as superconductivity. Yb x Pt5P appears to be a unique case among materials.

*Phys Rev Lett ; 125(4): 046401, 2020 Jul 24.*

##### RESUMO

We use scanning tunneling microscopy to elucidate the atomically resolved electronic structure in the strongly correlated kagome Weyl antiferromagnet Mn_{3}Sn. In stark contrast to its broad single-particle electronic structure, we observe a pronounced resonance with a Fano line shape at the Fermi level resembling the many-body Kondo resonance. We find that this resonance does not arise from the step edges or atomic impurities but the intrinsic kagome lattice. Moreover, the resonance is robust against the perturbation of a vector magnetic field, but broadens substantially with increasing temperature, signaling strongly interacting physics. We show that this resonance can be understood as the result of geometrical frustration and strong correlation based on the kagome lattice Hubbard model. Our results point to the emergent many-body resonance behavior in a topological kagome magnet.

*Sci Adv ; 6(30): eaba4275, 2020 Jul.*

##### RESUMO

Novel magnetic topological materials pave the way for studying the interplay between band topology and magnetism. However, an intrinsically ferromagnetic topological material with only topological bands at the charge neutrality energy has so far remained elusive. Using rational design, we synthesized MnBi8Te13, a natural heterostructure with [MnBi2Te4] and [Bi2Te3] layers. Thermodynamic, transport, and neutron diffraction measurements show that despite the adjacent [MnBi2Te4] being 44.1 Å apart, MnBi8Te13 manifests long-range ferromagnetism below 10.5 K with strong coupling between magnetism and charge carriers. First-principles calculations and angle-resolved photoemission spectroscopy measurements reveal it is an axion insulator with sizable surface hybridization gaps. Our calculations further demonstrate the hybridization gap persists in the two-dimensional limit with a nontrivial Chern number. Therefore, as an intrinsic ferromagnetic axion insulator with clean low-energy band structures, MnBi8Te13 serves as an ideal system to investigate rich emergent phenomena, including the quantized anomalous Hall effect and quantized magnetoelectric effect.

*Nat Commun ; 11(1): 4003, 2020 Aug 10.*

##### RESUMO

Kagome-nets, appearing in electronic, photonic and cold-atom systems, host frustrated fermionic and bosonic excitations. However, it is rare to find a system to study their fermion-boson many-body interplay. Here we use state-of-the-art scanning tunneling microscopy/spectroscopy to discover unusual electronic coupling to flat-band phonons in a layered kagome paramagnet, CoSn. We image the kagome structure with unprecedented atomic resolution and observe the striking bosonic mode interacting with dispersive kagome electrons near the Fermi surface. At this mode energy, the fermionic quasi-particle dispersion exhibits a pronounced renormalization, signaling a giant coupling to bosons. Through the self-energy analysis, first-principles calculation, and a lattice vibration model, we present evidence that this mode arises from the geometrically frustrated phonon flat-band, which is the lattice bosonic analog of the kagome electron flat-band. Our findings provide the first example of kagome bosonic mode (flat-band phonon) in electronic excitations and its strong interaction with fermionic degrees of freedom in kagome-net materials.

*Nature ; 583(7817): 533-536, 2020 07.*

##### RESUMO

The quantum-level interplay between geometry, topology and correlation is at the forefront of fundamental physics1-15. Kagome magnets are predicted to support intrinsic Chern quantum phases owing to their unusual lattice geometry and breaking of time-reversal symmetry14,15. However, quantum materials hosting ideal spin-orbit-coupled kagome lattices with strong out-of-plane magnetization are lacking16-21. Here, using scanning tunnelling microscopy, we identify a new topological kagome magnet, TbMn6Sn6, that is close to satisfying these criteria. We visualize its effectively defect-free, purely manganese-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state shows distinct Landau quantization on application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk-boundary correspondence between the Chern gap and the topological edge state, as well as the Berry curvature field correspondence of Chern gapped Dirac fermions. Our results point to the realization of a quantum-limit Chern phase in TbMn6Sn6, and may enable the observation of topological quantum phenomena in the RMn6Sn6 (where R is a rare earth element) family with a variety of magnetic structures. Our visualization of the magnetic bulk-boundary-Berry correspondence covering real space and momentum space demonstrates a proof-of-principle method for revealing topological magnets.

*Proc Natl Acad Sci U S A ; 117(27): 15517-15523, 2020 Jul 07.*

##### RESUMO

Topological electrons in semimetals are usually vulnerable to chemical doping and environment change, which restricts their potential application in future electronic devices. In this paper, we report that the type-II Dirac semimetal [Formula: see text] hosts exceptional, robust topological electrons which can tolerate extreme change of chemical composition. The Dirac electrons remain intact, even after a substantial part of V atoms have been replaced in the [Formula: see text] solid solutions. This Dirac semimetal state ends at [Formula: see text], where a Lifshitz transition to p-type trivial metal occurs. The V-Al bond is completely broken in this transition as long as the bonding orbitals are fully depopulated by the holes donated from Ti substitution. In other words, the Dirac electrons in [Formula: see text] are protected by the V-Al bond, whose molecular orbital is their bonding gravity center. Our understanding on the interrelations among electron count, chemical bond, and electronic properties in topological semimetals suggests a rational approach to search robust, chemical-bond-protected topological materials.

*Nature ; 578(7796): 545-549, 2020 02.*

##### RESUMO

Chirality is ubiquitous in nature, and populations of opposite chiralities are surprisingly asymmetric at fundamental levels1,2. Examples range from parity violation in the subatomic weak force to homochirality in biomolecules. The ability to achieve chirality-selective synthesis (chiral induction) is of great importance in stereochemistry, molecular biology and pharmacology2. In condensed matter physics, a crystalline electronic system is geometrically chiral when it lacks mirror planes, space-inversion centres or rotoinversion axes1. Typically, geometrical chirality is predefined by the chiral lattice structure of a material, which is fixed on formation of the crystal. By contrast, in materials with gyrotropic order3-6, electrons spontaneously organize themselves to exhibit macroscopic chirality in an originally achiral lattice. Although such order-which has been proposed as the quantum analogue of cholesteric liquid crystals-has attracted considerable interest3-15, no clear observation or manipulation of gyrotropic order has been achieved so far. Here we report the realization of optical chiral induction and the observation of a gyrotropically ordered phase in the transition-metal dichalcogenide semimetal 1T-TiSe2. We show that shining mid-infrared circularly polarized light on 1T-TiSe2 while cooling it below the critical temperature leads to the preferential formation of one chiral domain. The chirality of this state is confirmed by the measurement of an out-of-plane circular photogalvanic current, the direction of which depends on the optical induction. Although the role of domain walls requires further investigation with local probes, the methodology demonstrated here can be applied to realize and control chiral electronic phases in other quantum materials4,16.

*Science ; 365(6459): 1278-1281, 2019 09 20.*

##### RESUMO

Topological matter is known to exhibit unconventional surface states and anomalous transport owing to unusual bulk electronic topology. In this study, we use photoemission spectroscopy and quantum transport to elucidate the topology of the room temperature magnet Co2MnGa. We observe sharp bulk Weyl fermion line dispersions indicative of nontrivial topological invariants present in the magnetic phase. On the surface of the magnet, we observe electronic wave functions that take the form of drumheads, enabling us to directly visualize the crucial components of the bulk-boundary topological correspondence. By considering the Berry curvature field associated with the observed topological Weyl fermion lines, we quantitatively account for the giant anomalous Hall response observed in this magnet. Our experimental results suggest a rich interplay of strongly interacting electrons and topology in quantum matter.

*Proc Natl Acad Sci U S A ; 116(27): 13255-13259, 2019 Jul 02.*

##### RESUMO

Bismuth-based materials have been instrumental in the development of topological physics, even though bulk bismuth itself has been long thought to be topologically trivial. A recent study has, however, shown that bismuth is in fact a higher-order topological insulator featuring one-dimensional (1D) topological hinge states protected by threefold rotational and inversion symmetries. In this paper, we uncover another hidden facet of the band topology of bismuth by showing that bismuth is also a first-order topological crystalline insulator protected by a twofold rotational symmetry. As a result, its [Formula: see text] surface exhibits a pair of gapless Dirac surface states. Remarkably, these surface Dirac cones are "unpinned" in the sense that they are not restricted to locate at specific k points in the [Formula: see text] surface Brillouin zone. These unpinned 2D Dirac surface states could be probed directly via various spectroscopic techniques. Our analysis also reveals the presence of a distinct, previously uncharacterized set of 1D topological hinge states protected by the twofold rotational symmetry. Our study thus provides a comprehensive understanding of the topological band structure of bismuth.