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DOE OSTI2023

Revealing topology in metals using experimental protocols inspired by K-theory

Topological metals are conducting materials with gapless band structures and nontrivial edge-localized resonances. Their discovery has proven elusive because traditional topological classification methods require band gaps to define topological robustness. Inspired by recent theoretical developments that leverage techniques from the field of C*-algebras to identify topological metals, here, we directly observe topological phenomena in gapless acoustic crystals and realize a general experimental technique to demonstrate their topology. Specifically, we not only observe robust boundary-localized states in a topological acoustic metal, but also re-interpret a composite operator—mathematically derived from the K-theory of the problem—as a new Hamiltonian whose physical implementation allows us to directly observe a topological spectral flow and measure the topological invariants. Our observations and experimental protocols may offer insights for discovering topological behaviour across a wide array of artificial and natural materials that lack bulk band gaps.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Quantum Imaging of Magnetic Phase Transitions and Spin Fluctuations in Intrinsic Magnetic Topological Nanoflakes

Topological materials featuring exotic band structures, unconventional current flow patterns, and emergent organizing principles offer attractive platforms for the development of next-generation transformative quantum electronic technologies. The family of MnBi 2 T e4 (Bi 2 Te 3 )n materials is naturally relevant in this context due to their nontrivial band topology, tunable magnetism, and recently discovered extraordinary quantum transport behaviors. Despite numerous pioneering studies, to date, the local magnetic properties of MnBi 2 Te 4 (Bi 2 Te 3 )n remain an open question, hindering a comprehensive understanding of their fundamental material properties. Exploiting nitrogen-vacancy (NV) centers in diamond, we report nanoscale quantum imaging of magnetic phase transitions and spin fluctuations in exfoliated MnBi 2 Te 4 (Bi 2 Te 3 )n flakes, revealing the underlying spin transport physics and magnetic domains at the nanoscale. Furthermore, our results highlight the unique advantage of NV centers in exploring the magnetic properties of emergent quantum materials, opening new opportunities for investigating the interplay between topology and magnetism.

Antiferromagnetic materials↗

DOE OSTI2021

Plasmons in two-dimensional topological insulators

Here, we analyze collective excitations in models of two-dimensional topological insulators using the random phase approximation. In a two-dimensional extension of the Su-Schrieffer-Heeger model, edge plasmonic excitations with induced charge-density distributions localized at the boundaries of the system are found in the topologically nontrivial phase, dispersing similarly as one-dimensional bulk plasmons in the conventional Su-Schrieffer-Heeger chain. For two-dimensional bulk collective modes, we reveal regimes of enhanced interband wave function correlations, leading to characteristic hardening and softening of inter- and intraband bulk plasmonic branches, respectively. In the two-dimensional Haldane Chern insulator model, chiral, unidirectional edge plasmons in nano-ribbon architectures are observed, which can be characterized by an effective Coulomb interaction cross section. Bulk collective excitations in the two-dimensional Haldane model are shown to be originated by single-particle band structure details in different topological phases.

2-dimensional systems↗

DOE OSTI2021

Spectroscopy of a tunable moiré system with a correlated and topological flat band

Abstract Moiré superlattices created by the twisted stacking of two-dimensional crystals can host electronic bands with flat energy dispersion in which enhanced interactions promote correlated electron states. The twisted double bilayer graphene (TDBG), where two Bernal bilayer graphene are stacked with a twist angle, is such a moiré system with tunable flat bands. Here, we use gate-tuned scanning tunneling spectroscopy to directly demonstrate the tunability of the band structure of TDBG with an electric field and to show spectroscopic signatures of electronic correlations and topology for its flat band. Our spectroscopic experiments are in agreement with a continuum model of TDBG band structure and reveal signatures of a correlated insulator gap at partial filling of its isolated flat band. The topological properties of this flat band are probed with the application of a magnetic field, which leads to valley polarization and the splitting of Chern bands with a large effective g-factor.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Revealing the intrinsic transport properties of antiperovskite Sr 3 SnO thin films

A topologically non-trivial band structure and reports of superconductivity have motivated significant investigation into the transport properties of the antiperovskite oxide Sr 3 SnO. Phase-pure films of Sr 3 SnO can be grown by molecular beam epitaxy, but they do not have the required extremely high hole-doping densities (>1 × 10 21 cm –3 ) for which superconductivity has been observed in bulk materials. To date, high hole-doping densities have been achieved via inducing strontium deficiency, which inevitably results in impurity phases. Here, we show that indium acts as an effective hole dopant in Sr 3 SnO and can be used to achieve high hole doping densities in stoichiometric films. Films with carrier densities as high as 1.5 × 10 21 cm –3 remain non-superconducting. We, therefore, suggest that Sr 3 SnO is probably not an intrinsic superconductor. A second question addressed in this work is the measurement of the intrinsic electrical transport properties of Sr 3 SnO, given its rapid degradation in air. We show that even in inert atmospheres, reducing the time needed for establishing electrical contacts and protecting the Sr 3 SnO film result in improved electrical properties. Here, we demonstrate low carrier density films (4 × 10 18 cm –3 ) with carrier mobilities of 400 cm 2 V –1 s –1 at 10 K.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Transport and Imaging of Novel Phases of Moiré Quantum Matter

Moiré materials open an entirely new platform for exploring the interplay between band structure, interactions, symmetry and topology. Strong effects of interaction can result from antiferromagnetic correlations as is commonly found in high temperature superconductors. Alternatively, the effects of interactions can be strengthened by reducing the role of kinetic energy as is commonly done in quantum Hall systems. Interestingly, moiré materials are a new class of materials where both types of effects can be present simultaneously, even at zero magnetic field, leading to a plethora of new correlated topological phases. Here we plan to harness the expertise of our groups in synthesis, fabrication, and novel measurement techniques to unravel and elucidate some of the mysteries of moiré materials. Our goal in this proposal has been to deepen our understanding of correlated phases in moiré materials using a variety of experimental tool developed in the PI’s labs. We used thermodynamic probes based on local and global electrostatic sensing to provide direct information on compressibility, entropy, magnetization and topology. Revealing the fundamental principles of correlated topological matter may pave the way towards a new class of materials with superior electronic characteristics with possible application in quantum science, engineering and energy harvesting platforms.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Targeted Dy intercalation under graphene/SiC for tuning its electronic band structure

Metal intercalation of graphene is a promising method to tune its electronic band structure and generate novel electronic and topological phases. The tuning depends critically on the ability to bond the intercalated atoms at predesigned, subsurface interlayer locations because the emerging band structure depends on metal location. In this work, we have studied Dy intercalation under single-layer graphene (SLG) on SiC using spot profile analysis–low-energy electron diffraction and scanning tunneling microscopy (STM). The experimental work is complemented with density-functional theory (DFT) analysis. Because different diffraction spots originate from different subsurface interlayer regions, it is possible to identify changes in the intercalation location by monitoring the spot intensity as a function of growth conditions. DFT calculations of the chemical potential as a function of intercalated Dy coverage support the variation of the stability of the intercalated phase at different intercalated locations. The preferred location is confirmed from STM studies showing the removal of the 6 × 6 moiré corrugation at the preferred location, observed at higher Dy coverage.

2-dimensional systems↗

DOE OSTI2025

Higher-order Van Hove singularities in kagome topological bands

Motivated by the growing interest in band structures featuring higher-order Van Hove singularities (HOVHS), we investigate a spinless fermion kagome system characterized by nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes. While NN hopping preserves time-reversal symmetry, NNN hopping, akin to chiral hopping on the Haldane lattice, breaks time-reversal symmetry and leads to the formation of topological bands with Chern numbers ranging from 𝐶 = ±1 to ±4. We perform analytical and numerical analysis of the energy bands near the high-symmetry points Γ, ±𝐊, and 𝐌 𝑖 (𝑖 = 1, 2, and 3), which uncover a rich and complex landscape of HOVHS, controlled by the magnitude and phase of the NNN hopping. We observe power-law divergences in the density of states (DOS), 𝜌⁡(𝜀)∼|𝜀| −𝜈 , with exponents 𝜈 = 1/2, 1/3, 1/4, which can significantly affect the anomalous Hall response at low temperatures when the Fermi level crosses the HOVHS. Additionally, the NNN hopping induces the formation of higher Chern number bands 𝐶 = ±2, ±4 in the middle of the spectrum obeying a sublattice interference whereupon electronic states are maximally localized in each of the sublattices when the momentum approaches the three high-symmetry points 𝐌 𝑖 (𝑖 = 1, 2, and 3) on the Brillouin zone boundary. Finally, this classification of HOVHS in kagome systems provides a platform to explore unconventional electronic orders induced by electronic correlations.

Chern insulators↗

DOE OSTI2025

Influence of Bi alloying on GaAs valence band structure

Bi alloying is predicted to transform GaAs from a semiconductor to a topological insulator or semimetal. To date, studies of the GaAs 1−x Bi x alloy band structure have been limited, and the origins of Bi-induced enhancement of the spin-orbit splitting energy, Δ SO , are unresolved. Here, in this study, we present high-resolution angle-resolved photoemission spectroscopy of droplet-free epitaxial GaAs 1−x Bi x films with x Bi = 0.06. In addition to quantifying the Bi-induced shifts of the light-hole and heavy-hole valence bands, we probe the origins of the Bi-enhanced Δ SO . Using exact-two-component density functional theory calculations, we identify the key role of Bi p-orbitals in the upward shift of the light-hole and heavy-hole bands that results in the Bi-enhanced Δ SO .

Cooper, Joshua J. P. [Univ. of Michigan, Ann Arbor↗

DOE OSTI2026

Evidence for strong electronic correlations in the bulk state of grey arsenic

Here, we investigate the electron band structure of grey arsenic, whose (111) face hosts the topological Shockley state. Interestingly, the bulk band close to the touching point with the surface state exhibits the characteristics of inelastic scattering. Moreover, the band structure analysis reveals linearity in the imaginary part of electron self-energy. These features are analogous to those observed in high-temperature superconductors and marginal Fermi liquid systems, respectively, where strong electronic correlations exist. Our results suggest that correlated many-body states can be connected by non-interacting topological states, providing a viable playground to explore the coupling between topological and correlated states via grey arsenic surface.

ARPES↗

DOE OSTI2023

Unconventional surface state pairs in a high-symmetry lattice with anti-ferromagnetic band-folding

Many complex magnetic structures in a high-symmetry lattice can arise from a superposition of well-defined magnetic wave vectors. These “multi-q” structures have garnered much attention because of interesting real-space spin textures such as skyrmions. However, the role multi-q structures play in the topology of electronic bands in momentum space has remained rather elusive. Here we show that the type-I anti-ferromagnetic 1q, 2q and 3q structures in an face-centered cubic sublattice with band inversion, such as NdBi, can induce unconventional surface state pairs inside the band-folding hybridization bulk gap. Our density functional theory calculations match well with the recent experimental observation of unconventional surface states with hole Fermi arc-like features and electron pockets below the Neel temperature. We further show that these multi-q structures have Dirac and Weyl nodes. Our work reveals the special role that band-folding from anti-ferromagnetism and multi-q structures can play in developing new types of surface states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe 2 bilayers

Twisted bilayer transition metal dichalcogenides, such as MoTe 2 , provide a versatile platform for exploring correlated topological phases. This work investigates the interplay between perpendicular magnetic and electric fields in tuning the electronic structure and emergent topological orders of twisted bilayer MoTe 2 (t-MoTe 2 ) across two distinct regimes: a low-twist-angle phase (θ ≈ 2.1°) hosting multiple Chern bands of identical Chern numbers per valley, and a higher-angle phase (θ ≈ 3.89°) featuring Haldane-like bands with opposite Chern numbers. Using a continuum model incorporating moiré potentials up to second harmonics, we compute the Hofstadter fractal spectra under applied fields, revealing Landau fan structures and magnetic-flux-dependent band topology. These fractal spectra are useful in studying emergent topological orders in terms of the composite fermion picture, where the statistical Chern-Simons flux is approximated as a uniform gauge field. We demonstrate that the system hosts both Jain-sequence fractional Chern insulators (FCIs) and non-Jain fractal FCIs with higher Chern numbers. As a result, the electric field suppresses composite fermion gaps and induces topological quantum phase transitions. Furthermore, our analysis extends to valley-contrasting flux attachment, proposing pathways to describe fractional quantum spin Hall states.

Anyons↗

DOE OSTI2020

Strongly correlated and topological states in [111] grown transition metal oxide thin films and heterostructures

We highlight recent advances in the theory, materials fabrication, and experimental characterization of strongly correlated and topological states in [111] oriented transition metal oxide thin films and heterostructures, which are notoriously difficult to realize compared to their [001] oriented counterparts. We focus on two classes of complex oxides, with the chemical formulas ABO 3 and A 2 B 2 O 7 , where the B sites are occupied by an open-shell transition metal ion with a local moment and the A sites are typically a rare earth element. The [111] oriented quasi-two-dimensional lattices derived from these parent compound lattices can exhibit peculiar geometries and symmetries, namely, a buckled honeycomb lattice, as well as kagome and triangular lattices. These lattice motifs form the basis for emergent strongly correlated and topological states expressed in exotic magnetism, various forms of orbital ordering, topological insulators, topological semimetals, quantum anomalous Hall insulators, and quantum spin liquids. For transition metal ions with high atomic number, spin–orbit coupling plays a significant role and may give rise to additional topological features in the electronic band structure and in the spectrum of magnetic excitations. We conclude this perspective by articulating open challenges and opportunities in this actively developing field.

36 MATERIALS SCIENCE↗

DOE OSTI2024

When van der Waals Met Kagome: A 2D Antimonide with a Vanadium-Kagome Network

2D materials showcase unconventional properties emerging from quantum confinement effects. In this work, a “soft chemical” route allows for the deintercalation of K + from the layered antimonide KV 6 Sb 6 , resulting in the discovery of a new metastable 2D-Kagome antimonide K 0.1(1) V 6 Sb 6 with a van der Waals gap of 3.2 Å. The structure of K 0.1(1) V 6 Sb 6 was determined via the synergistic techniques, including X-ray pair distribution function analysis, advanced transmission electron microscopy, and density functional theory calculations. The K 0.1(1) V 6 Sb 6 compound crystallizes in the monoclinic space group C2/m (a = 9.57(2) Å, b = 5.502(8) Å, c = 10.23(2) Å, β = 97.6(2)°, Z = 2). The [V 6 Sb 6 ] layers in K 0.1(1) V 6 Sb 6 are retained upon deintercalation and closely resemble the layers in the parent compound, yet deintercalation results in a relative shift of the adjacent [V 6 Sb 6 ] layers. The magnetic properties of the K 0.1(1) V 6 Sb 6 phase in the 2–300 K range are comparable to those of KV 6 Sb 6 and another Kagome antimonide KV 3 Sb 5 , consistent with nearly temperature-independent paramagnetism. Electronic band structure calculation suggests a nontrivial band topology with flat bands and opening of band crossing afforded by deintercalation. Transport property measurements reveal a metallic nature for K 0.1(1) V 6 Sb 6 and a low thermal conductivity of 0.6 W K –1 m –1 at 300 K. Additionally, ion exchange in KV 6 Sb 6 via a solvothermal route leads to a successful partial exchange of K + with A + (A = Na, Rb, and Cs). Here, this study highlights the tunability of the layered structure of the KV 6 Sb 6 compound, providing a rich playground for the realization of new 2D materials.

2D↗

DOE OSTI2020

Low-energy excitations in type-II Weyl semimetal T d - MoTe 2 evidenced through optical conductivity

Molybdenum ditelluride, MoTe 2 , is a versatile material where the topological phase can be readily tuned by manipulating the associated structural phase transition. The fine details of the band structure of MoTe 2 , key to understanding its topological properties, have proven difficult to disentangle experientially due to the multiband character of the material. Through experimental optical conductivity spectra, we detect two strong low-energy interband transitions. Both are linked to excitations between spin-orbit split bands. The lowest interband transition shows a strong thermal shift, pointing to a chemical potential that dramatically decreases with temperature. Finally, with the help of ab initio calculations and a simple two-band model, we give qualitative and quantitative explanations of the main features in the temperature-dependent optical spectra up to 400 meV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Robust Surface States and Coherence Phenomena in Magnetically Alloyed SmB 6

Samarium hexaboride is a candidate for the topological Kondo insulator state, in which Kondo coherence is predicted to give rise to an insulating gap spanned by topological surface states. Here we investigate the surface and bulk electronic properties of magnetically alloyed Sm 1-x M x B 6 (M = Ce, Eu), using angle-resolved photoemission spectroscopy and complementary characterization techniques. Remarkably, topologically nontrivial bulk and surface band structures are found to persist in highly modified samples with up to 30% Sm substitution and with an antiferromagnetic ground state in the case of Eu doping. The results are interpreted in terms of a hierarchy of energy scales, in which surface state emergence is linked to the formation of a direct Kondo gap, while low-temperature transport trends depend on the indirect gap.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Helicity-dependent photocurrents in the chiral Weyl semimetal RhSi

Weyl semimetals are crystals in which electron bands cross at isolated points in momentum space. Associated with each crossing point (or Weyl node) is a topological invariant known as the Berry monopole charge. The circular photogalvanic effect (CPGE), whereby circular polarized light generates a helicity-dependent photocurrent, is a notable example of a macroscopic property that emerges directly from the topology of the Weyl semimetal band structure. Recently, it was predicted that the amplitude of the CPGE associated with optical transitions near a Weyl node is proportional to its monopole charge. In chiral Weyl systems, nodes of opposite charge are nondegenerate, opening a window of wavelengths where the CPGE resulting from uncompensated Berry charge can emerge. Here, we report measurements of CPGE in the chiral Weyl semimetal RhSi, revealing a CPGE response in an energy window that closes at 0.65 eV, in agreement with the predictions of density functional theory.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Chiral Topological Surface States on a Finite Square Photonic Crystal Bounded by Air

Chiral, topologically protected, photonic surface states can be found at the boundary between gyrotropic photonic crystals where a changing magnetic field induces different topology across the interface. Typically, photonic crystals with either a suitable band structure on both sides of the interface to provide a band gap and evanescent decay of the surface states away from the interface, or an outer layer with engineered material properties is required. In this paper, we show the emergence of topological, unidirectional surface states at the termination of finite gyrotropic photonic crystals with a simple square lattice and C 4 rotational symmetry bounded by a vacuum, eliminating the need for an outside layer to enable chiral surface modes. Here, we start from an infinite, time-reversal-symmetry-breaking photonic crystal with a band gap associated with bands with nonzero Chern numbers, different from all-zero Chern numbers in air. We then modify the photonic crystal to move this band gap below the light line, while maintaining the Chern-number discontinuities. Band-structure calculations for a supercell approximating a photonic crystal finite in the direction normal to the surface demonstrate the existence, dispersion, and chirality of the surface mode. Extensive direct scattering calculations for a point source and spatial Fourier analysis further reveal a unidirectional free-space topological surface state, which propagates counterclockwise around the surface of a finite photonic crystal, providing a nearly foolproof way to cross-check the surface-mode band structure unaffected by backscattering from local defects. Additionally, scattering simulations allow an independent characterization of the state dispersion and unveil the robustness of the topological plasmonic mode propagation around the 90° bends of the structure, being due to only radiation leakage. In contrast to buried topological surface states, the observed surface modes at the photonic crystal–air interface have the advantage of being accessible to the outside world, allowing one to take advantage of the defect-tolerant backscattering-free surface modes to engineer emission from photonic crystal surfaces into arbitrary free-space beam shapes and directions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗