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Tutorial: Defects in topological semimetals

Three-dimensional topological semimetals are a class of electronic materials in which their bulk and surface states contain linear band touching nodes near the Fermi level. Like semiconductors, their properties will be affected by point and extended defects in their crystal structures, although the extent to which defects and disorders influence topological semimetals may differ in key ways due to their unique electronic structures. In this Tutorial, we provide an overview of the defects in topological semimetals, covering both computational and experimental methods for exploring defect-property relationships. We also include a discussion on open questions that still need to be explored further.

36 MATERIALS SCIENCE↗

Topology-enhanced mechanical stability of swelling nanoporous electrodes

Abstract Materials like silicon and germanium offer a 10-fold improvement in charge capacity over conventional graphite anodes in lithium-ion batteries but experience a roughly threefold volume increase during lithiation, which challenges ensuring battery integrity. Nanoporous silicon, created by liquid-metal-dealloying, is a potentially attractive anode design to mitigate this challenge, exhibiting both higher capacity and extended cycle lifetimes. However, how nanoporous structures accommodate the large volume change is unknown. Here, we address this question by using phase-field modeling to produce nanoporous particles and to investigate their elastoplastic swelling behavior and fracture. Our simulations show that enhanced mechanical stability results from the network topology consisting of ligaments connected by bulbous, sphere-like nodes. The ligaments forcefully resist elongation while the nodes, behaving like isolated spherical particles, experience large stresses driving fracture. However, being smaller compared to a sphere of the same volume as the entire nanoporous particle, the nodes are more protected against fracture.

36 MATERIALS SCIENCE↗

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 $\overline{Γ}$ in topological insulators Bi 2 Se(Te) 3 and Dirac cones at Κ and 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.

36 MATERIALS SCIENCE↗

Tunable topological Dirac surface states and van Hove singularities in kagome metal GdV 6 Sn 6

Transition-metal-based kagome materials at van Hove filling are a rich frontier for the investigation of novel topological electronic states and correlated phenomena. To date, in the idealized two-dimensional kagome lattice, topologically Dirac surface states (TDSSs) have not been unambiguously observed, and the manipulation of TDSSs and van Hove singularities (VHSs) remains largely unexplored. Here, we reveal TDSSs originating from a $\mathbb{Z}_2$ bulk topology and identify multiple VHSs near the Fermi level (E F ) in magnetic kagome material GdV 6 Sn 6 . Using in situ surface potassium deposition, we successfully realize manipulation of the TDSSs and VHSs. The Dirac point of the TDSSs can be tuned from above to below E F , which reverses the chirality of the spin texture at the Fermi surface. These results establish GdV 6 Sn 6 as a fascinating platform for studying the nontrivial topology, magnetism, and correlation effects native to kagome lattices. They also suggest potential application of spintronic devices based on kagome materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transition-metal phthalocyanine monolayers as new Chern insulators

To explore new materials for the realization of the quantum anomalous Hall effect (QAHE), we studied the electronic, magnetic and topological properties of transition-metal phthalocyanine (TMPc) monolayers in a square lattice. Many of them have large topologically nontrivial band gaps and integer Chern numbers. In particular, the Fermi level of MoPc lies right in the band gap (E g = 8.1 meV) and has large magnetic anisotropy energy (MAE = 2.0 meV per Mo atom) and a Curie temperature of 16 K, showing its usefulness for applications. The presence of the topologically protected edge state in a MoPc nanoribbon further confirms it as a new two-dimensional topological insulator. This much widens the search for QAHE materials for the design of quantum devices.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Orbital character of the spin-reorientation transition in TbMn 6 Sn 6

Ferromagnetic (FM) order in a two-dimensional kagome layer is predicted to generate a topological Chern insulator without an applied magnetic field. The Chern gap is largest when spin moments point perpendicular to the kagome layer, enabling the capability to switch topological transport properties, such as the quantum anomalous Hall effect, by controlling the spin orientation. In TbMn 6 Sn 6 , the uniaxial magnetic anisotropy of the Tb 3+ ion is effective at generating the Chern state within the FM Mn kagome layers while a spin-reorientation (SR) transition to easy-plane order above T SR = 310 K provides a mechanism for switching. Here, we use inelastic neutron scattering to provide key insights into the fundamental nature of the SR transition. The observation of two Tb excitations, which are split by the magnetic anisotropy energy, indicates an effective two-state orbital character for the Tb ion, with a uniaxial ground state and an isotropic excited state. The simultaneous observation of both modes below T SR confirms that orbital fluctuations are slow on magnetic and electronic time scales < ps and act as a spatially-random orbital alloy. A thermally-driven critical concentration of isotropic Tb ions triggers the SR transition.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Thermal and thermoelectric properties of an antiferromagnetic topological insulator MnBi 2 Te 4

The discovery of an intrinsic antiferromagnetic topological insulator (AFMTI) in MnBi 2 Te 4 has attracted intense attention, most of which lies in its electrical properties. Here in this paper, we report electronic, thermal, and thermoelectric transport studies of this newly found AFMTI. The temperature and magnetic field dependence of its resistivity, thermal conductivity, and Seebeck coefficient indicate strong coupling between charge, lattice, and spin degrees of freedom in this system. Furthermore, MnBi 2 Te 4 exhibits a large anomalous Nernst signal, which is associated with nonzero Berry curvature of the field-induced canted antiferromagnetic state.

36 MATERIALS SCIENCE↗

Topological band and superconductivity in UTe 2

UTe 2 is a likely spin-triplet superconductor that also exhibits evidence for chiral Majorana edge states. A characteristic structural feature of UTe 2 is inversion-symmetry related pairs of U atoms, forming rungs of ladders. Here we show how each rung's two sublattice degrees of freedom play a key role in understanding the electronic structure and the origin of superconductivity. In particular, DFT + U calculations generically reveal a topological band near the chemical potential originating from a band inversion associated with 5f electrons residing on these rungs, necessitating a microscopic description that includes these rung degrees of freedom. Furthermore, we show that a previously identified strong ferromagnetic interaction within a U-U rung leads to a pseudospin-triplet superconducting state that accounts for a nonzero polar Kerr angle, the observed magnetic field-temperature phase diagrams, and nodal Weyl fermions. Finally, our analysis may also be relevant for other U-based superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Defects in Semiconductors

All semiconductors, whether by design or by accident, contain defects. The fundamental properties of defects, such as impurities, native defects, and extended defects, affect a broad range of applications. These technologically important defects may be introduced during growth and processing. Electrical, optical, and magnetic phenomena related to defects have been observed experimentally and studied theoretically in a variety of materials. In addition to traditional semiconductors (elemental, III–V, and II–VI), emerging materials include organic semiconductors, nitrides, oxides, and topological insulators, in bulk crystal and thin-film forms as well as low-dimensional and nanoscale structures.

36 MATERIALS SCIENCE↗

Amorphous topological matter: Theory and experiment

Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. Here, we review the recent progress made on defining amorphous topological phases, their new phenomenology. We discuss the open questions in the field which promise to significantly enlarge the set of materials and synthetic systems benefiting from the robustness of topological matter.

36 MATERIALS SCIENCE↗

Hidden magnetism uncovered in a charge ordered bilayer kagome material ScV 6 Sn 6

Charge ordered kagome lattices have been demonstrated to be intriguing platforms for studying the intertwining of topology, correlation, and magnetism. The recently discovered charge ordered kagome material ScV 6 Sn 6 does not feature a magnetic groundstate or excitations, thus it is often regarded as a conventional paramagnet. Here, using advanced muon-spin rotation spectroscopy, we uncover an unexpected hidden magnetism of the charge order. We observe an enhancement of the internal field width sensed by the muon ensemble, which takes place within the charge ordered state. More importantly, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. Taken together with the hidden magnetism found in AV 3 Sb 5 (A = K, Rb, Cs) and FeGe kagome systems, our results suggest ubiqitous time-reversal symmetry-breaking in charge ordered kagome lattices.

36 MATERIALS SCIENCE↗

Higher harmonics in planar Hall effect induced by cluster magnetic multipoles

Antiferromagnetic (AFM) materials are attracting tremendous attention due to their spintronic applications and associated novel topological phenomena. However, detecting and identifying the spin configurations in AFM materials are quite challenging due to the absence of net magnetization. Herein, we report the practicality of utilizing the planar Hall effect (PHE) to detect and distinguish “cluster magnetic multipoles” in AFM Nd 2 Ir 2 O 7 (NIO-227) fully strained films. By imposing compressive strain on the spin structure of NIO-227, we artificially induced cluster magnetic multipoles, namely dipoles and A 2 - and T 1 -octupoles. Importantly, under magnetic field rotation, each magnetic multipole exhibits distinctive harmonics of the PHE oscillation. Moreover, the planar Hall conductivity has a nonlinear magnetic field dependence, which can be attributed to the magnetic response of the cluster magnetic octupoles. Our work provides a strategy for identifying cluster magnetic multipoles in AFM systems and would promote octupole-based AFM spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Partial charge transfer and absence of induced magnetization in EuS(111)/Bi 2 Se 3 heterostructures

We report that heterostructures made from topological and magnetic insulators promise to form excellent platforms for new electronic and spintronic functionalities mediated by interfacial effects. We report the results of a first-principles density functional theory study of the geometric, electronic structure, and magnetic properties of the EuS( 111 )/Bi 2 Se 3 interface, including van der Waals and relativistic spin-orbit effects. In contrast to previous theoretical studies, we find no appreciable magnetic anisotropy in such a heterostructure. We also do not see additional induced magnetization at the interface or the magnetic proximity effect on the topological states. This is due to the localized nature of Eu moments and because of a partial charge transfer of ~ 0.5 electron from Eu to Se. The formation of the surface dipole shifts the Dirac cone about 0.4 eV below the chemical potential, and the associated electrostatic screening moves the topological state from the first to the second quintuple layer of Bi 2 Se 3 .

36 MATERIALS SCIENCE↗

Influence of point defects on the electronic and topological properties of monolayer WTe 2

In some topological insulators such as monolayers of WTe 2 or graphene with spin-orbit coupling, band inversion originates from chemical bonding and space group symmetry, in contrast to materials such as Bi 2 Se 3 , where the band inversion derives from relativistic effects in the atoms. In the former, band inversion is susceptible to changes of the chemical environment, e.g., by defects, while the latter are less affected by defects due to the larger energy scale associated with atomic relativistic effects. Motivated by recent experiments, we study the effect of Te vacancies and Te adatoms on the electronic properties of WTe 2 . We find that the Te vacancies have a formation energy of 2.21 eV, while the formation energy of the Te adatoms is much lower with 0.72 eV. Here, the vacancies strongly influence the band structure and we present evidence that band inversion is already reversed at the nominal composition of WTe 1.97 . In contrast, we show that the adatoms do not change the electronic structure in the vicinity of the Fermi level and thus the topological properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Three-dimensional flat bands in pyrochlore metal CaNi 2

Electronic flat-band materials host quantum states characterized by a quenched kinetic energy. These flat bands are often conducive to enhanced electron correlation effects and emergent quantum phases of matter. Long studied in theoretical models, these systems have received renewed interest after their experimental realization in van der Waals heterostructures and quasi-two-dimensional (2D) crystalline materials. An outstanding experimental question is if such flat bands can be realized in three-dimensional (3D) networks, potentially enabling new materials platforms and phenomena. Here we investigate the C15 Laves phase metal CaNi 2 , which contains a nickel pyrochlore lattice predicted at a model network level to host a doubly-degenerate, topological flat band arising from 3D destructive interference of electronic hopping. Using angle-resolved photoemission spectroscopy, we observe a band with vanishing dispersion across the full 3D Brillouin zone that we identify with the pyrochlore flat band as well as two additional flat bands that we show arise from multi-orbital interference of Ni d -electrons. Furthermore, we demonstrate chemical tuning of the flat-band manifold to the Fermi level that coincides with enhanced electronic correlations and the appearance of superconductivity. Extending the notion of intrinsic band flatness from 2D to 3D, this provides a potential pathway to correlated behaviour predicted for higher-dimensional flat-band systems ranging from tunable topological to fractionalized phases.

36 MATERIALS SCIENCE↗

Quantum oscillations and transport properties of layered single-crystal SrCu 4 ⁢As 2

Here, we report a systematic investigation of the physical properties and Fermi-surface topology of layered single-crystal SrCu 4⁢ As 2 using electrical transport, magnetotransport, and quantum-oscillation experiments plus band-structure calculations. The temperature-dependent electrical resistivity reveals a hysteretic phase transition at 𝑇 𝑃 =59 K, most likely associated with a structural change. Hall resistivity data suggest a marked change in the average hole density resulting from the latter phase transition near 𝑇 𝑃 . A large, linear, and nonsaturating magnetoresistance is observed at low temperatures in SrCu 4 ⁢As 2 , likely attributable to the multipocket Fermi surface. Quantum-oscillation data measured in magnetic fields of up to 60 T show several oscillation frequencies exhibiting low effective masses, indicating the presence of Dirac-like band dispersion in SrCu 4 ⁢As 2 , as suggested by the band structure calculations.

36 MATERIALS SCIENCE↗

Ghost states and surface structures of the charge density wave kagome metal ScV 6 Sn 6

In this work, we investigate the high-temperature phase of the kagome metal ScV 6 Sn 6 using scanning tunneling microscopy/spectroscopy (STM/S) and density functional theory calculations. STM topographic images of the cleaved sample reveal two distinct surface terminations: flat islands with Sn termination and trenches terminated by kagome layers with Sn as the outermost atomic layer. STS measurements on the Sn-terminated and kagome-terminated surfaces show significant differences, in particular the presence of large density of states near the Fermi level in the former case. Our first-principles calculations reveal that the charge density on the kagome-terminated surface gives rise to “ghost states” which show intensity away from surface atoms, arising due to hybridization of orbitals above the surface. These states can obscure the intrinsic properties of the surface, potentially leading to misattribution of the surface termination. This underscores the need for careful interpretation in STM studies, especially when discerning surface states of localized states. Understanding the surface structure of this versatile quantum material provides essential information for interpreting surface-sensitive experiments, tailoring material properties, engineering interfaces, and controlling stability and reactivity. This knowledge paves the way for further exploration and potential applications of kagome lattice materials in various fields, including quantum computing, topological physics, and advanced electronic devices.

36 MATERIALS SCIENCE↗

Computational design of metamaterials with self contact

Inverse homogenization in combination with contact modeling, topology optimization and shape optimization is used to design metamaterials with optimized macroscopic response. The homogenization assumes length scale separation which allows the non-linear macroscopic behavior to be obtained by analyzing a single unit cell in a lattice structure. Self contact in the unit cell, which is modeled using a third medium contact method, is leveraged to obtain a complex homogenized response. The inverse homogenization problem is initially formulated as a topology optimization problem, where the macroscopic stress–strain behavior is tuned to our liking. However, it is well known that boundary phenomena are difficult to model in topology optimization and that interface modeling is crucial to accurately analyze contact. For that reason, the boundary representation of the topology optimized design is extracted and used as initial design in a subsequent shape optimization. The behaviors of our designs are verified by performing rigorous post-processing analyzes using conforming meshes and conventional contact formulations.

42 ENGINEERING↗