Atomic scale quantum anomalous hall effect in monolayer graphene/MnBi2Te4 heterostructure.

The two-dimensional quantum anomalous Hall (QAH) effect is direct evidence of non-trivial Berry curvature topology in condensed matter physics. Searching for QAH in 2D materials, particularly with simplified fabrication methods, poses a significant challenge in future applications. Despite numerous theoretical works proposed for the QAH effect with C = 2 in graphene, neglecting magnetism sources such as proper substrate effects lacks experimental evidence. In this work, we propose the QAH effect in graphene/MnBi2Te4 (MBT) heterostructure based on density-functional theory (DFT) calculations. The monolayer MBT introduces spin-orbital coupling, Zeeman exchange field, and Kekulé distortion as a substrate effect into graphene, resulting in QAH with C = 1 in the heterostructure. Our effective Hamiltonian further presents a rich phase diagram that has not been studied previously. Our work provides a new and practical way to explore the QAH effect in monolayer graphene and the magnetic topological phases by the flexibility of MBT family materials.

Optical excitations of graphene-like materials: group III-nitrides.

By using first-principles calculations, we have studied the electronic and optical characteristics of group III-nitrides, such as BN, AlN, GaN, and InN monolayers. The optimized geometry, quasi-particle energy spectra, charge density distributions, band-decomposed charge densities, and Van Hove singularities in density of states are described in the work using physical and chemical pictures and orbital hybridizations found in B-N, Al-N, Ga-N, and In-N chemical bonds. Moreover, the dielectric functions, energy loss functions, absorption coefficients, and reflectance spectra with electron-hole interactions of optical properties are successfully achieved. More importantly, the close relations between electronic and optical properties are successfully demonstrated. The theoretical framework will be useful to research other graphene-like materials.

Correction: Theoretical investigations of the electronic and optical properties of a GaGeTe monolayer.

[This corrects the article DOI: 10.1039/D3RA03160H.].

Theoretical investigations of the electronic and optical properties of a GaGeTe monolayer.

Our study focused on exploring the electronic and optical characteristics of the GaGeTe monolayer using first-principles calculations. Our findings showed that this material has remarkable physical and chemical properties attributed to its unique band structure, van Hove singularities in the density of states (DOS), charge density distributions, and charge density differences. We also observed excitonic effects, multiple optical excitation peaks, and strong plasmon modes in the energy loss functions, absorption coefficients, and reflectance spectra, which contribute to its enriched optical response. Moreover, we were able to establish a close relationship between the orbital hybridizations of the initial and final states with each optical excitation peak. Our results suggest that GaGeTe monolayers hold great potential for various semiconductor applications, especially those involving optics. Furthermore, the theoretical framework we used can be applied to study the electronic and optical properties of other graphene-like semiconductor materials.

Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure.

Quantum geometry in condensed-matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in two-dimensional electron gases and the anomalous Hall effect (AHE) in ferromagnets, the quantum metric has rarely been explored. Here, we report a nonlinear Hall effect induced by the quantum metric dipole by interfacing even-layered MnBi2Te4 with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the antiferromagnetic (AFM) spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.

Evidence for unconventional superconductivity and nontrivial topology in PdTe.

PdTe is a superconductor with Tc ~ 4.25 K. Recently, evidence for bulk-nodal and surface-nodeless gap features has been reported in PdTe. Here, we investigate the physical properties of PdTe in both the normal and superconducting states via specific heat and magnetic torque measurements and first-principles calculations. Below Tc, the electronic specific heat initially decreases in T3 behavior (1.5 K < T < Tc) then exponentially decays. Using the two-band model, the superconducting specific heat can be well described with two energy gaps: one is 0.372 meV and another 1.93 meV. The calculated bulk band structure consists of two electron bands (α and ß) and two hole bands (γ and η) at the Fermi level. Experimental detection of the de Haas-van Alphen (dHvA) oscillations allows us to identify four frequencies (Fα = 65 T, Fß = 658 T, Fγ = 1154 T, and Fη = 1867 T for H // a), consistent with theoretical predictions. Nontrivial α and ß bands are further identified via both calculations and the angle dependence of the dHvA oscillations. Our results suggest that PdTe is a candidate for unconventional superconductivity.

Causal structure of interacting Weyl fermions in condensed matter systems.

The spacetime light cone is central to the definition of causality in the theory of relativity. Recently, links between relativistic and condensed matter physics have been uncovered, where relativistic particles can emerge as quasiparticles in the energy-momentum space of matter. Here, we unveil an energy-momentum analogue of the spacetime light cone by mapping time to energy, space to momentum, and the light cone to the Weyl cone. We show that two Weyl quasiparticles can only interact to open a global energy gap if they lie in each other's energy-momentum dispersion cones-analogous to two events that can only have a causal connection if they lie in each other's light cones. Moreover, we demonstrate that the causality of surface chiral modes in quantum matter is entangled with the causality of bulk Weyl fermions. Furthermore, we identify a unique quantum horizon region and an associated 'thick horizon' in the emergent causal structure.

Axion optical induction of antiferromagnetic order.

Using circularly polarized light to control quantum matter is a highly intriguing topic in physics, chemistry and biology. Previous studies have demonstrated helicity-dependent optical control of chirality and magnetization, with important implications in asymmetric synthesis in chemistry; homochirality in biomolecules; and ferromagnetic spintronics. We report the surprising observation of helicity-dependent optical control of fully compensated antiferromagnetic order in two-dimensional even-layered MnBi2Te4, a topological axion insulator with neither chirality nor magnetization. To understand this control, we study an antiferromagnetic circular dichroism, which appears only in reflection but is absent in transmission. We show that the optical control and circular dichroism both arise from the optical axion electrodynamics. Our axion induction provides the possibility to optically control a family of [Formula: see text]-symmetric antiferromagnets ([Formula: see text], inversion; [Formula: see text], time-reversal) such as Cr2O3, even-layered CrI3 and possibly the pseudo-gap state in cuprates. In MnBi2Te4, this further opens the door for optical writing of a dissipationless circuit formed by topological edge states.

Observation of Gapped Topological Surface States and Isolated Surface Resonances in PdTe2 Ultrathin Films.

The superconductor PdTe2 is known to host bulk Dirac bands and topological surface states. The coexistence of superconductivity and topological surface states makes PdTe2 a promising platform for exploring topological superconductivity and Majorana bound states. In this work, we report the spectroscopic characterization of ultrathin PdTe2 films with thickness down to three monolayers (ML). In the 3 ML PdTe2 film, we observed spin-polarized surface resonance states, which are isolated from the bulk bands due to the quantum size effects. In addition, the hybridization of surface states on opposite faces leads to a thickness-dependent gap in the topological surface Dirac bands. Our photoemission results show clearly that the size of the hybridization gap increases as the film thickness is reduced. The observation of isolated surface resonances and gapped topological surface states sheds light on the applications of PdTe2 quantum films in spintronics and topological quantum computation.

Visualizing Higher-Fold Topology in Chiral Crystals.

Novel topological phases of matter are fruitful platforms for the discovery of unconventional electromagnetic phenomena. Higher-fold topology is one example, where the low-energy description goes beyond standard model analogs. Despite intensive experimental studies, conclusive evidence remains elusive for the multigap topological nature of higher-fold chiral fermions. In this Letter, we leverage a combination of fine-tuned chemical engineering and photoemission spectroscopy with photon energy contrast to discover the higher-fold topology of a chiral crystal. We identify all bulk branches of a higher-fold chiral fermion for the first time, critically important for allowing us to explore unique Fermi arc surface states in multiple interband gaps, which exhibit an emergent ladder structure. Through designer chemical gating of the samples in combination with our measurements, we uncover an unprecedented multigap bulk boundary correspondence. Our demonstration of multigap electronic topology will propel future research on unconventional topological responses.

Coexistence of Bulk-Nodal and Surface-Nodeless Cooper Pairings in a Superconducting Dirac Semimetal.

The interplay of nontrivial topology and superconductivity in condensed matter physics gives rise to exotic phenomena. However, materials are extremely rare where it is possible to explore the full details of the superconducting pairing. Here, we investigate the momentum dependence of the superconducting gap distribution in a novel Dirac material PdTe. Using high resolution, low temperature photoemission spectroscopy, we establish it as a spin-orbit coupled Dirac semimetal with the topological Fermi arc crossing the Fermi level on the (010) surface. This spin-textured surface state exhibits a fully gapped superconducting Cooper pairing structure below T_{c}∼4.5 K. Moreover, we find a node in the bulk near the Brillouin zone boundary, away from the topological Fermi arc. These observations not only demonstrate the band resolved electronic correlation between topological Fermi arc states and the way it induces Cooper pairing in PdTe, but also provide a rare case where surface and bulk states host a coexistence of nodeless and nodal gap structures enforced by spin-orbit coupling.

Visualization of Tunable Weyl Line in A-A Stacking Kagome Magnets.

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, the Weyl lines are directly visualized 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. These results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct 3D topological phases, but also demonstrate AMn6 Sn6 (A = rare earth, or Li, Mg, or Ca) as a versatile material family for exploring diverse emergent topological quantum responses.

Discovery of Charge Order and Corresponding Edge State in Kagome Magnet FeGe.

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.

Realization of unpinned two-dimensional dirac states in antimony atomic layers.

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.

Evidence of a room-temperature quantum spin Hall edge state in a higher-order topological insulator.

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.

Topological charge-entropy scaling in kagome Chern magnet TbMn6Sn6.

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.

Enormous Berry-Curvature-Based Anomalous Hall Effect in Topological Insulator (Bi,Sb)2Te3 on Ferrimagnetic Europium Iron Garnet beyond 400 K.

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.

Evidence of magnetism-induced topological protection in the axion insulator candidate EuSn2P2.

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.

Topological Proximity-Induced Dirac Fermion in Two-Dimensional Antimonene.

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.

Layer Hall effect in a 2D topological axion antiferromagnet.

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.