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 2D electron gases and the anomalous Hall effect (AHE) in ferromagnets, quantum metric has rarely been explored. Here, we report a nonlinear Hall effect induced by quantum metric dipole by interfacing even-layered MnBi₂Te₄ with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the 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.

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.

Evidence for unconventional superconductivity and nontrivial topology in PdTe

PdTe is a superconductor with T_c ~ 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 T_c, the electronic specific heat initially decreases in T³ behavior (1.5 K < T < T_c) 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 β) 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 (F_α = 65 T, F_β = 658 T, F_γ = 1154 T, and F_η = 1867 T for H // a), consistent with theoretical predictions. Nontrivial α and β 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.

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.

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 physics^1,2. The quantum spin Hall phase^3-6 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.

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{{{\Gamma }}}$$\end{document}Γ¯ in topological insulators Bi₂Se(Te)₃ and Dirac cones at K and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K^{\prime}$$\end{document}K′ 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.

In graphene and on the surfaces of many topological insulators, the Dirac cones are pinned to high symmetry points in reciprocal space. Here, the authors report that the Dirac cones in atomically-thin Sb layers occur at generic reciprocal-space points which can be tuned by lattice strain.

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 (Bi_0.3Sb_0.7)₂Te₃ (BST) based heterostructures with a ferrimagnetic insulator europium iron garnet (EuIG) of perpendicular magnetic anisotropy. Here we demonstrate large anomalous Hall resistance (R_AHE) exceeding 8 Ω (ρ_AHE 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 (ρ_AHE of 0.14 μΩ·cm) at 300 K. The large R_AHE 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.

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 textures^2,3. 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 antiferromagnets^4-9. The layer-locked Berry curvature represents a first step towards spatial engineering of the Berry phase through effects such as layer-specific moiré potential.

Room-temperature nonlinear Hall effect and wireless radiofrequency rectification in Weyl semimetal TaIrTe4

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 doubling^1,2. However, the low-temperature detection of the NLHE limits its applications^3,4. 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.

A Novel Magnetic Material by Design: Observation of Yb3+ with Spin-1/2 in Yb x Pt5P

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 ∼0.6 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.

Fermion-boson many-body interplay in a frustrated kagome paramagnet

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.

Many-Body Resonance in a Correlated Topological Kagome Antiferromagnet

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.

Realization of an intrinsic ferromagnetic topological state in MnBi8Te13

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.

Responses of midbrain auditory neurons to two different environmental sounds-A new approach on cross-sound modeling

When modeling auditory responses to environmental sounds, results are satisfactory if both training and testing are restricted to datasets of one type of sound. To predict 'cross-sound' responses (i.e., to predict the response to one type of sound e.g., rat Eating sound, after training with another type of sound e.g., rat Drinking sound), performance is typically poor. Here we implemented a novel approach to improve such cross-sound modeling (single unit datasets were collected at the auditory midbrain of anesthetized rats). The method had two key features: (a) population responses (e.g., average of 32 units) instead of responses of individual units were analyzed; and (b) the long sound segment was first divided into short segments (single sound-bouts), their similarity was then computed over a new metric involving the response (called Stimulus Response Model map or SRM map), and finally similar sound-bouts (regardless of sound type) and their associated responses (peri-stimulus time histograms, PSTHs) were modelled. Specifically, a committee machine model (artificial neural networks with 20 stratified spectral inputs) was trained with datasets from one sound type before predicting PSTH responses to another sound type. Model performance was markedly improved up to 92%. Results also suggested the involvement of different neural mechanisms in generating the early and late responses to amplitude transients in the broad-band environmental sounds. We concluded that it is possible to perform rather satisfactory cross-sound modeling on datasets grouped together based on their similarities in terms of the new metric of SRM map.

Topology on a new facet of bismuth

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.

A New Magnetic Topological Quantum Material Candidate by Design

Magnetism, when combined with an unconventional electronic band structure, can give rise to forefront electronic properties such as the quantum anomalous Hall effect, axion electrodynamics, and Majorana fermions. Here we report the characterization of high-quality crystals of EuSn₂P₂, a new quantum material specifically designed to engender unconventional electronic states plus magnetism. EuSn₂P₂ has a layered, Bi₂Te₃-type structure. Ferromagnetic interactions dominate the Curie-Weiss susceptibility, but a transition to antiferromagnetic ordering occurs near 30 K. Neutron diffraction reveals that this is due to two-dimensional ferromagnetic spin alignment within individual Eu layers and antiferromagnetic alignment between layers-this magnetic state surrounds the Sn-P layers at low temperatures. The bulk electrical resistivity is sensitive to the magnetism. Electronic structure calculations reveal that EuSn₂P₂ might be a strong topological insulator, which can be a new magnetic topological quantum material (MTQM) candidate. The calculations show that surface states should be present, and they are indeed observed by angle-resolved photoelectron spectroscopy (ARPES) measurements.

Topological quantum properties of chiral crystals

Chiral crystals are materials with a lattice structure that has a well-defined handedness due to the lack of inversion, mirror or other roto-inversion symmetries. Although it has been shown that the presence of crystalline symmetries can protect topological band crossings, the topological electronic properties of chiral crystals remain largely uncharacterized. Here we show that Kramers-Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin-orbit coupling and are guaranteed by structural chirality, lattice translation and time-reversal symmetry. Unlike conventional Weyl fermions, they appear at time-reversal-invariant momenta. We identify representative chiral materials in 33 of the 65 chiral space groups in which Kramers-Weyl fermions are relevant to the low-energy physics. We determine that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin-orbit coupling carry non-trivial Chern numbers. Kramers-Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window.

Quasiparticle interference and nonsymmorphic effect on a floating band surface state of ZrSiSe

Non-symmorphic crystals are generating great interest as they are commonly found in quantum materials, like iron-based superconductors, heavy-fermion compounds, and topological semimetals. A new type of surface state, a floating band, was recently discovered in the nodal-line semimetal ZrSiSe, but also exists in many non-symmorphic crystals. Little is known about its physical properties. Here, we employ scanning tunneling microscopy to measure the quasiparticle interference of the floating band state on ZrSiSe (001) surface and discover rotational symmetry breaking interference, healing effect and half-missing-type anomalous Umklapp scattering. Using simulation and theoretical analysis we establish that the phenomena are characteristic properties of a floating band surface state. Moreover, we uncover that the half-missing Umklapp process is derived from the glide mirror symmetry, thus identify a non-symmorphic effect on quasiparticle interferences. Our results may pave a way towards potential new applications of nanoelectronics.

Tunable double-Weyl Fermion semimetal state in the SrSi2 materials class

We discuss first-principles topological electronic structure of noncentrosymmetric SrSi2 materials class based on the hybrid exchange-correlation functional. Topological phase diagram of SrSi2 is mapped out as a function of the lattice constant with focus on the semimetal order. A tunable double-Weyl Fermion state in Sr1-xCaxSi2 and Sr1-xBaxSi2 alloys is identified. Ca doping in SrSi2 is shown to yield a double-Weyl semimetal with a large Fermi arc length, while Ba doping leads to a transition from the topological semimetal to a gapped insulator state. Our study indicates that SrSi2 materials family could provide an interesting platform for accessing the unique topological properties of Weyl semimetals.

Unconventional Chiral Fermions and Large Topological Fermi Arcs in RhSi

The theoretical proposal of chiral fermions in topological semimetals has led to a significant effort towards their experimental realization. In particular, the Fermi surfaces of chiral semimetals carry quantized Chern numbers, making them an attractive platform for the observation of exotic transport and optical phenomena. While the simplest example of a chiral fermion in condensed matter is a conventional |C|=1 Weyl fermion, recent theoretical works have proposed a number of unconventional chiral fermions beyond the standard model which are protected by unique combinations of topology and crystalline symmetries. However, materials candidates for experimentally probing the transport and response signatures of these unconventional fermions have thus far remained elusive. In this Letter, we propose the RhSi family in space group No. 198 as the ideal platform for the experimental examination of unconventional chiral fermions. We find that RhSi is a filling-enforced semimetal that features near its Fermi surface a chiral double sixfold-degenerate spin-1 Weyl node at R and a previously uncharacterized fourfold-degenerate chiral fermion at Γ. Each unconventional fermion displays Chern number ±4 at the Fermi level. We also show that RhSi displays the largest possible momentum separation of compensative chiral fermions, the largest proposed topologically nontrivial energy window, and the longest possible Fermi arcs on its surface. We conclude by proposing signatures of an exotic bulk photogalvanic response in RhSi.

Mirror Protected Dirac Fermions on a Weyl Semimetal NbP Surface

The first Weyl semimetal was recently discovered in the NbP class of compounds. Although the topology of these novel materials has been identified, the surface properties are not yet fully understood. By means of scanning tunneling spectroscopy, we find that NbP's (001) surface hosts a pair of Dirac cones protected by mirror symmetry. Through our high-resolution spectroscopic measurements, we resolve the quantum interference patterns arising from these novel Dirac fermions and reveal their electronic structure, including the linear dispersions. Our data, in agreement with our theoretical calculations, uncover further interesting features of the Weyl semimetal NbP's already exotic surface. Moreover, we discuss the similarities and distinctions between the Dirac fermions here and those in topological crystalline insulators in terms of symmetry protection and topology.

Signatures of a time-reversal symmetric Weyl semimetal with only four Weyl points

Through intense research on Weyl semimetals during the past few years, we have come to appreciate that typical Weyl semimetals host many Weyl points. Nonetheless, the minimum nonzero number of Weyl points allowed in a time-reversal invariant Weyl semimetal is four. Realizing such a system is of fundamental interest and may simplify transport experiments. Recently, it was predicted that TaIrTe₄ realizes a minimal Weyl semimetal. However, the Weyl points and Fermi arcs live entirely above the Fermi level, making them inaccessible to conventional angle-resolved photoemission spectroscopy (ARPES). Here, we use pump-probe ARPES to directly access the band structure above the Fermi level in TaIrTe₄. We observe signatures of Weyl points and topological Fermi arcs. Combined with ab initio calculation, our results show that TaIrTe₄ is a Weyl semimetal with the minimum number of four Weyl points. Our work provides a simpler platform for accessing exotic transport phenomena arising in Weyl semimetals.Weyl semimetals are interesting because they are characterized by topological invariants, but specific examples discovered to date tend to have complicated band structures with many Weyl points. Here, the authors show that TaIrTe₄ has only four Weyl points, the minimal number required by time-reversal symmetry.

Evidence of indirect gap in monolayer WSe2

Monolayer transition metal dichalcogenides, such as MoS2 and WSe2, have been known as direct gap semiconductors and emerged as new optically active materials for novel device applications. Here we reexamine their direct gap properties by investigating the strain effects on the photoluminescence of monolayer MoS2 and WSe2. Instead of applying stress, we investigate the strain effects by imaging the direct exciton populations in monolayer WSe2-MoS2 and MoSe2-WSe2 lateral heterojunctions with inherent strain inhomogeneity. We find that unstrained monolayer WSe2 is actually an indirect gap material, as manifested in the observed photoluminescence intensity-energy correlation, from which the difference between the direct and indirect optical gaps can be extracted by analyzing the exciton thermal populations. Our findings combined with the estimated exciton binding energy further indicate that monolayer WSe2 exhibits an indirect quasiparticle gap, which has to be reconsidered in further studies for its fundamental properties and device applications.Monolayer transition metal dichalcogenides have so far been thought to be direct bandgap semiconductors. Here, the authors revisit this assumption and find that unstrained monolayer WSe2 is an indirect-gap material, as evidenced by the observed photoluminescence intensity-energy correlation.

Atomic-scale visualization of surface-assisted orbital order

Orbital-related physics attracts growing interest in condensed matter research, but direct real-space access of the orbital degree of freedom is challenging. We report a first, real-space, imaging of a surface-assisted orbital ordered structure on a cobalt-terminated surface of the well-studied heavy fermion compound CeCoIn₅. Within small tip-sample distances, the cobalt atoms on a cleaved (001) surface take on dumbbell shapes alternatingly aligned in the [100] and [010] directions in scanning tunneling microscopy topographies. First-principles calculations reveal that this structure is a consequence of the staggered d _xz -d _yz orbital order triggered by enhanced on-site Coulomb interaction at the surface. This so far overlooked surface-assisted orbital ordering may prevail in transition metal oxides, heavy fermion superconductors, and other materials.

Quasiparticle Interference on Cubic Perovskite Oxide Surfaces

We report the observation of coherent surface states on cubic perovskite oxide SrVO_{3}(001) thin films through spectroscopic-imaging scanning tunneling microscopy. A direct link between the observed quasiparticle interference patterns and the formation of a d_{xy}-derived surface state is supported by first-principles calculations. We show that the apical oxygens on the topmost VO_{2} plane play a critical role in controlling the coherent surface state via modulating orbital state.

Monoclinic 122-Type BaIr₂Ge₂ with a Channel Framework: A Structural Connection between Clathrate and Layered Compounds

A new 122-type phase, monoclinic BaIr₂Ge₂ is successfully synthesized by arc melting; X-ray diffraction and scanning electron microscopy are used to purify the phase and determine its crystal structure. BaIr₂Ge₂ adopts a clathrate-like channel framework structure of the monoclinic BaRh₂Si₂-type, with space group P2₁/c. Structural comparisons of clathrate, ThCr₂Si₂, CaBe₂Ge₂, and BaRh₂Si₂ structure types indicate that BaIr₂Ge₂ can be considered as an intermediate between clathrate and layered compounds. Magnetic measurements show it to be diamagnetic and non-superconducting down to 1.8 K. Different from many layered or clathrate compounds, monoclinic BaIr₂Ge₂ displays a metallic resistivity. Electronic structure calculations performed for BaIr₂Ge₂ support its observed structural stability and physical properties.

Type-II Symmetry-Protected Topological Dirac Semimetals

The recent proposal of the type-II Weyl semimetal state has attracted significant interest. In this Letter, we propose the concept of the three-dimensional type-II Dirac fermion and theoretically identify this new symmetry-protected topological state in the large family of transition-metal icosagenides, MA_{3} (M=V, Nb, Ta; A=Al, Ga, In). We show that the VAl_{3} family features a pair of strongly Lorentz-violating type-II Dirac nodes and that each Dirac node can be split into four type-II Weyl nodes with chiral charge ±1 via symmetry breaking. Furthermore, we predict that the Landau level spectrum arising from the type-II Dirac fermions in VAl_{3} is distinct from that of known Dirac or Weyl semimetals. We also demonstrate a topological phase transition from a type-II Dirac semimetal to a quadratic Weyl semimetal or a topological crystalline insulator via crystalline distortions.

Discovery of Lorentz-violating type II Weyl fermions in LaAlGe

In quantum field theory, Weyl fermions are relativistic particles that travel at the speed of light and strictly obey the celebrated Lorentz symmetry. Their low-energy condensed matter analogs are Weyl semimetals, which are conductors whose electronic excitations mimic the Weyl fermion equation of motion. Although the traditional (type I) emergent Weyl fermions observed in TaAs still approximately respect Lorentz symmetry, recently, the so-called type II Weyl semimetal has been proposed, where the emergent Weyl quasiparticles break the Lorentz symmetry so strongly that they cannot be smoothly connected to Lorentz symmetric Weyl particles. Despite some evidence of nontrivial surface states, the direct observation of the type II bulk Weyl fermions remains elusive. We present the direct observation of the type II Weyl fermions in crystalline solid lanthanum aluminum germanide (LaAlGe) based on our photoemission data alone, without reliance on band structure calculations. Moreover, our systematic data agree with the theoretical calculations, providing further support on our experimental results.

Nexus fermions in topological symmorphic crystalline metals

Topological metals and semimetals (TMs) have recently drawn significant interest. These materials give rise to condensed matter realizations of many important concepts in high-energy physics, leading to wide-ranging protected properties in transport and spectroscopic experiments. It has been well-established that the known TMs can be classified by the dimensionality of the topologically protected band degeneracies. While Weyl and Dirac semimetals feature zero-dimensional points, the band crossing of nodal-line semimetals forms a one-dimensional closed loop. In this paper, we identify a TM that goes beyond the above paradigms. It shows an exotic configuration of degeneracies without a well-defined dimensionality. Specifically, it consists of 0D nexus with triple-degeneracy that interconnects 1D lines with double-degeneracy. We show that, because of the novel form of band crossing, the new TM cannot be described by the established results that characterize the topology of the Dirac and Weyl nodes. Moreover, triply-degenerate nodes realize emergent fermionic quasiparticles not present in relativistic quantum field theory. We present materials candidates. Our results open the door for realizing new topological phenomena and fermions including transport anomalies and spectroscopic responses in metallic crystals with nontrivial topology beyond the Weyl/Dirac paradigm.

Anisotropic superconducting property studies of single crystal PbTaSe2

The anisotropic superconducting properties of PbTaSe₂ single crystal is reported. Superconductivity with T _c  =  3.83  ±  0.02 K has been characterized fully with electrical resistivity ρ(T), magnetic susceptibility χ(T), and specific heat C _p (T) measurements using single crystal samples. The superconductivity is type-II with lower critical field H _c1 and upper critical field H _c2 of 65 and 450 Oe (H⊥  to the ab-plane), 140 and 1500 Oe (H|| to the ab-plane), respectively. These results indicate that the superconductivity of PbTaSe₂ is anisotropic. The superconducting anisotropy, electron-phonon coupling λ _ep, superconducting energy gap Δ₀, and the specific heat jump ΔC/γT _c at T _c confirms that PbTaSe₂ can be categorized as a bulk superconductor.

Inter-Layer Coupling Induced Valence Band Edge Shift in Mono- to Few-Layer MoS2

Recent progress in the synthesis of monolayer MoS2, a two-dimensional direct band-gap semiconductor, is paving new pathways toward atomically thin electronics. Despite the large amount of literature, fundamental gaps remain in understanding electronic properties at the nanoscale. Here, we report a study of highly crystalline islands of MoS2 grown via a refined chemical vapor deposition synthesis technique. Using high resolution scanning tunneling microscopy and spectroscopy (STM/STS), photoemission electron microscopy/spectroscopy (PEEM) and μ-ARPES we investigate the electronic properties of MoS2 as a function of the number of layers at the nanoscale and show in-depth how the band gap is affected by a shift of the valence band edge as a function of the layer number. Green's function based electronic structure calculations were carried out in order to shed light on the mechanism underlying the observed bandgap reduction with increasing thickness, and the role of the interfacial Sulphur atoms is clarified. Our study, which gives new insight into the variation of electronic properties of MoS2 films with thickness bears directly on junction properties of MoS2, and thus impacts electronics application of MoS2.

Metal-Semiconductor Phase-Transition in WSe2(1-x) Te2x Monolayer

A metal-semiconductor phase transition in a ternary transition metal dichalcogenide (TMD) monolayer is achieved by alloying Te into WSe₂ (WSe_2(1-x) Te_2x , where x = 0%-100%). The optical bandgaps of the WSe_2(1-x) Te_2x monolayer can be tuned from 1.67 to 1.44 eV (2H semiconductor) and drops to 0 eV (1Td metal), which opens up an exciting opportunity in functional electronic/optoelectronic devices.

Large-Area and High-Quality 2D Transition Metal Telluride

Large-area and high-quality 2D transition metal tellurides are synthesized by the chemical vapor deposition method. The as-grown WTe₂ maintains two different stacking sequences in the bilayer, where the atomic structure of the stacking boundary is revealed by scanning transmission electron microscopy. The low-temperature transport measurements reveal a novel semimetal-to-insulator transition in WTe₂ layers and an enhanced superconductivity in few-layer MoTe₂ .

Atomic-Scale Visualization of Quasiparticle Interference on a Type-II Weyl Semimetal Surface

We combine quasiparticle interference simulation (theory) and atomic resolution scanning tunneling spectromicroscopy (experiment) to visualize the interference patterns on a type-II Weyl semimetal Mo_{x}W_{1-x}Te_{2} for the first time. Our simulation based on first-principles band topology theoretically reveals the surface electron scattering behavior. We identify the topological Fermi arc states and reveal the scattering properties of the surface states in Mo_{0.66}W_{0.34}Te_{2}. In addition, our result reveals an experimental signature of the topology via the interconnectivity of bulk and surface states, which is essential for understanding the unusual nature of this material.