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At least 145 records · Page 8
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DOE OSTI2020

Realization of an intrinsic ferromagnetic topological state in MnBi 8 Te 13

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 MnBi 8 Te 13 , a natural heterostructure with [MnBi 2 Te 4 ] and [Bi 2 Te 3 ] layers. Thermodynamic, transport, and neutron diffraction measurements show that despite the adjacent [MnBi 2 Te 4 ] being 44.1 Å apart, MnBi 8 Te 13 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, MnBi 8 Te 13 serves as an ideal system to investigate rich emergent phenomena, including the quantized anomalous Hall effect and quantized magnetoelectric effect.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Reentrant Correlated Insulators in Twisted Bilayer Graphene at 25 T ( 2 π Flux)

Twisted bilayer graphene (TBG) is remarkable for its topological flat bands, which drive strongly interacting physics at integer fillings, and its simple theoretical description facilitated by the Bistritzer-MacDonald Hamiltonian, a continuum model coupling two Dirac fermions. Because of the large moiré unit cell, TBG offers the unprecedented opportunity to observe reentrant Hofstadter phases in laboratory-strength magnetic fields near 25 T. This Letter is devoted to magic angle TBG at 2π flux where the magnetic translation group commutes. Here we use a newly developed gauge-invariant formalism to determine the exact single-particle band structure and topology. We find that the characteristic TBG flat bands reemerge at 2π flux, but, due to the magnetic field breaking C 2z T, they split and acquire Chern number ±1. We show that reentrant correlated insulating states appear at 2π flux driven by the Coulomb interaction at integer fillings, and we predict the characteristic Landau fans from their excitation spectrum.

36 MATERIALS SCIENCE↗
DOE OSTI2024

In-plane Wilson loop for measurement of quantized non-Abelian Berry flux

Band topology of anomalous quantum Hall insulators can be precisely addressed by computing the Chern numbers of constituent nondegenerate bands, describing the presence of quantized, Abelian Berry flux through the two-dimensional Brillouin zone. Can Berry flux be captured for the SU (2) Berry connection of two -fold degenerate bands in spinful materials preserving space -inversion ($\mathscr{P}$) and time -reversal ($\mathscr{T}$) symmetries without detailed knowledge of underlying basis? We address this question by investigating the correspondence between a non -Abelian generalization of Stokes' theorem and the manifestly gauge -invariant eigenvalues of Wilson loops computed along in -plane contours which preserve the underlying crystalline symmetry. The importance of this correspondence is elucidated by performing natural number resolved classification of ab initio band structures of three-dimensional, Dirac materials. Further, our work underscores how identification of quantized Berry flux, both Abelian and non -Abelian, offers a unified framework for addressing first -order and higher -order topology of insulators and semimetals.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Hofstadter Topology: Noncrystalline Topological Materials at High Flux

he Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding ~10 4 T magnetic fields to a trivial band structure. In this work, we show that when a magnetic field is added to an initially topological band structure, a wealth of possible phases emerges. Remarkably, we find topological phases that cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with a nonzero Chern number or mirror Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with a nontrivial Kane–Mele invariant can be classified as a 3D topological insulator (TI) or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of twofold rotation and time reversal and show that there exists a higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group that exists at rational values of the flux. The advent of Moiré lattices renders our work relevant experimentally. Due to the enlarged Moiré unit cell, it is possible for laboratory-strength fields to reach one flux per plaquette and allow access to our proposed Hofstadter topological phase.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Emergent superconductivity in topological-kagome-magnet/metal heterostructures

Itinerant kagome lattice magnets exhibit many novel correlated and topological quantum electronic states with broken time-reversal symmetry. Superconductivity, however, has not been observed in this class of materials, presenting a roadblock in a promising path toward topological superconductivity. Here, we report that novel superconductivity can emerge at the interface of kagome Chern magnet TbMn 6 Sn 6 and metal heterostructures when elemental metallic thin films are deposited on either the top (001) surface or the side surfaces. Superconductivity is also successfully induced and systematically studied by using various types of metallic tips on different TbMn 6 Sn 6 surfaces in point-contact measurements. The anisotropy of the superconducting upper critical field suggests that the emergent superconductivity is quasi-two-dimensional. Remarkably, the interface superconductor couples to the magnetic order of the kagome metal and exhibits a hysteretic magnetoresistance in the superconducting states. Taking into account the spin-orbit coupling, the observed interface superconductivity can be a surprising and more realistic realization of the p-wave topological superconductors theoretically proposed for two-dimensional semiconductors proximity-coupled to s-wave superconductors and insulating ferromagnets. Our findings of robust superconductivity in topological-Chern-magnet/metal heterostructures offer a new direction for investigating spin-triplet pairing and topological superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

The Dirac equation as a model of topological insulators

The Dirac equation with a spatially dependent mass can be used as a simple, exactly soluble, continuum model of a three-dimensional Topological Insulator. For a bulk system, the sign of the mass determines the parity at the only time-reversal point ( k _ = 0 ) and, thus, leads to the designation of the bulk as being topologically trivial or non-trivial. Since the mass changes sign at the interface between a topologically trivial and non-trivial materials, topological surface states appear on that boundary. We present that electron scattering experiments may provide an alternate probe of the topological character of the surface states. For infinitely thick slabs, the states on the opposite sides of the slab decouple. The spatial decoupling results in the surface states become gapless, non-degenerate and, due to the Rashba spin–orbit coupling generated by the loss of inversion symmetry, exhibit spin-momentum locking. We review several characteristic properties of the topological surface states which are dependent on the topological quantum numbers and show that, using this model, they can be calculated exactly using simple approaches.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Universal Magnetic Phases in Twisted Bilayer MoTe 2

Twisted bilayer MoTe 2 (tMoTe 2 ) has emerged as a robust platform for exploring correlated topological phases, yet the evolution of its magnetism and topology with twist angle remains an open question. Here, we systematically map the magnetic phase diagram of tMoTe 2 by using local optical spectroscopy and scanning nanoSQUID-on-tip magnetometry. We identify spontaneous ferromagnetism at filling factors ν = −1 and −3 across twist angles from 2.1° to 3.7°, revealing a universal, twist-angle-insensitive ferromagnetic phase. At 2.1°, we further observe robust ferromagnetism at ν = −5, absent at larger twist angles. Temperature-dependent measurements reveal a contrasting twist-angle dependence of the Curie temperatures between ν = −1 and −3, indicating a distinct interplay between the exchange interactions and bandwidth for the two Chern bands. Despite broken time-reversal symmetry, no topological gap is detected at ν = −3. Furthermore, our results establish a global framework for understanding and controlling magnetic order in tMoTe 2 .

Insulators↗
DOE OSTI2022

Magic-Angle Twisted Bilayer Graphene as a Topological Heavy Fermion Problem

Magic-angle (θ=1.05°) twisted bilayer graphene (MATBG) has shown two seemingly contradictory characters: the localization and quantum-dot-like behavior in STM experiments, and delocalization in transport experiments. We construct a model, which naturally captures the two aspects, from the Bistritzer-MacDonald (BM) model in a first principle spirit. A set of local flat-band orbitals (f) centered at the AA-stacking regions are responsible to the localization. A set of extended topological semimetallic conduction bands (c), which are at small energetic separation from the local orbitals, are responsible to the delocalization and transport. The topological flat bands of the BM model appear as a result of the hybridization of f and c electrons. This model then provides a new perspective for the strong correlation physics, which is now described as strongly correlated f electrons coupled to nearly free c electrons—we hence name our model as the topological heavy fermion model. Using this model, we obtain the U(4) and U(4)×U(4) symmetries of Refs. [1–5] as well as the correlated insulator phases and their energies. Simple rules for the ground states and their Chern numbers are derived. Moreover, features such as the large dispersion of the charge ±1 excitations [2,6,7], and the minima of the charge gap at the Γ M point can now, for the first time, be understood both qualitatively and quantitatively in a simple physical picture. Our mapping opens the prospect of using heavy-fermion physics machinery to the superconducting physics of MATBG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

$2+1$ dimensional Floquet systems and lattice fermions: Exact bulk spectral equivalence

A connection has recently been proposed between periodically driven systems known as Floquet insulators in continuous time and static fermion theories in discrete time. This connection has been established in a (1+1) ( 1 + 1 ) -dimensional free theory, where an explicit mapping between the spectra of a Floquet insulator and a discrete-time Dirac fermion theory has been formulated. Here we investigate the potential of static discrete-time theories to capture Floquet physics in higher dimensions, where so-called anomalous Floquet topological insulators can emerge that feature chiral edge states despite having bulk bands with zero Chern number. Starting from a particular model of an anomalous Floquet system, we provide an example of a static discrete-time theory whose bulk spectrum is an exact analytic match for the Floquet spectrum. The spectra with open boundary conditions in a particular strip geometry also match up to finite-size corrections. However, the models differ in several important respects. The discrete-time theory is spatially anisotropic, so that the spectra do not agree for all lattice terminations, e.g. other strip geometries or on half spaces. This difference can be attributed to the fact that the static discrete-time model is quasi-one-dimensional in nature and therefore has a different bulk-boundary correspondence than the Floquet model.

Iadecola, Thomas (ORCID:0000000251456441)↗
DOE OSTI2020

Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene

Motivated by the recent observation of an anomalous Hall effect in twisted bilayer graphene, here we use a lowest Landau level model to understand the origin of the underlying symmetry-broken correlated state. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene device and its encapsulating substrate. Our model exhibits a phase transition from a spin-valley polarized insulator to a partial or fully valley unpolarized metal as the bandwidth is increased relative to the interaction strength, consistent with experimental observations. In sharp contrast to standard quantum Hall ferromagnetism, the Chern number structure of the flat bands precludes an instability to an intervalley coherent phase, but allows for an excitonic vortex lattice at large interaction anisotropy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Topological Phenomena in Artificial Quantum Materials Revealed by Local Chern Markers

A striking example of frustration in physics is Hofstadter’s butterfly, a fractal structure that emerges from the competition between a crystal’s lattice periodicity and the magnetic length of an applied field. Current methods for predicting the topological invariants associated with Hofstadter’s butterfly are challenging or impossible to apply to a range of materials, including those that are disordered or lack a bulk spectral gap. Here, in this work, we demonstrate a framework for predicting a material’s local Chern markers using its position-space description and validate it against experimental observations of quantum transport in artificial graphene in a semiconductor heterostructure, inherently accounting for fabrication disorder strong enough to close the bulk spectral gap. By resolving local changes in the system’s topology, we reveal the topological origins of antidot-localized states that appear in artificial graphene in the presence of a magnetic field. Moreover, we show the breadth of this framework by simulating how Hofstadter’s butterfly emerges from an initially unpatterned 2D electron gas as the system’s potential strength is increased and predict that artificial graphene becomes a topological insulator at the critical magnetic field. Overall, we anticipate that a position-space approach to determine a material’s Chern invariant without requiring prior knowledge of its occupied states or bulk spectral gaps will enable a broad array of fundamental inquiries and provide a novel route to material discovery, especially in metallic, aperiodic, and disordered systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Higher Chern numbers in multilayer Lieb lattices ( N ≥ 2 ): Topological transitions and quadratic band crossing lines

In this work, we consider a hitherto unexplored setting of a stacked multilayer (N) Lieb lattice which undergoes an unusual topological transition in the presence of intralayer spin-orbit coupling (SOC). The specific stacking configuration induces an effective nonsymmorphic two-dimensional lattice structure, even though the constituent monolayer Lieb lattice is characterized by a symmorphic space group. This emergent nonsymmorphicity leads to multiple doubly degenerate bands extending over the edge of the Brillouin zone (i.e., quadratic band crossing lines). In the presence of intralayer SOC, these doubly degenerate bands typically form three N-band subspaces, mutually separated by two band gaps. We analyze the topological properties of these multiband subspaces, using specially devised Wilson loop operators to compute non-Abelian Berry phases in order to show that they carry a higher Chern number N.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Quantum anomalous Hall effect in two-dimensional magnetic insulator heterojunctions

Abstract Recent years have witnessed tremendous success in the discovery of topological states of matter. Particularly, sophisticated theoretical methods in time-reversal-invariant topological phases have been developed, leading to the comprehensive search of crystal database and the prediction of thousands of topological materials. In contrast, the discovery of magnetic topological phases that break time reversal is still limited to several exemplary materials because the coexistence of magnetism and topological electronic band structure is rare in a single compound. To overcome this challenge, we propose an alternative approach to realize the quantum anomalous Hall (QAH) effect, a typical example of magnetic topological phase, via engineering two-dimensional (2D) magnetic van der Waals heterojunctions. Instead of a single magnetic topological material, we search for the combinations of two 2D (typically trivial) magnetic insulator compounds with specific band alignment so that they can together form a type-III broken-gap heterojunction with topologically non-trivial band structure. By combining the data-driven materials search, first-principles calculations, and the symmetry-based analytical models, we identify eight type-III broken-gap heterojunctions consisting of 2D ferromagnetic insulators in the MXY compound family as a set of candidates for the QAH effect. In particular, we directly calculate the topological invariant (Chern number) and chiral edge states in the MnNF/MnNCl heterojunction with ferromagnetic stacking. This work illustrates how data-driven material science can be combined with symmetry-based physical principles to guide the search for heterojunction-based quantum materials hosting the QAH effect and other exotic quantum states in general.

36 MATERIALS SCIENCE↗
DOE OSTI2021

High-throughput search for magnetic topological materials using spin-orbit spillage, machine learning, and experiments

Magnetic topological insulators and semi-metals have a variety of properties that make them attractive for applications including spintronics and quantum computation. Here, we use systematic high-throughput density functional theory calculations to identify magnetic topological materials from the ≈ 40000 three-dimensional materials in the JARVIS-DFT database. First, we screen materials with net magnetic moment > 0.5 μB and spin-orbit spillage > 0.25, resulting in 25 insulating and 564 metallic candidates. The spillage acts as a signature of spin-orbit induced band-inversion. Then, we carry out calculations of Wannier charge centers, Chern numbers, anomalous Hall conductivities, surface bandstructures, and Fermi-surfaces to determine interesting topological characteristics of the screened compounds. We also train machine learning models for predicting the spillage, bandgaps, and magnetic moments of new compounds, to further accelerate the screening process. We experimentally synthesize and characterize a few candidate materials to support our theoretical predictions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Signatures of fractional quantum anomalous Hall states in twisted MoTe 2

The interplay between spontaneous symmetry breaking and topology can result in exotic quantum states of matter. A celebrated example is the quantum anomalous Hall (QAH) state, which exhibits an integer quantum Hall effect at zero magnetic field owing to intrinsic ferromagnetism. In the presence of strong electron–electron interactions, fractional QAH (FQAH) states at zero magnetic field can emerge. These states could host fractional excitations, including non-Abelian anyons—crucial building blocks for topological quantum computation9. Here we report experimental signatures of FQAH states in a twisted molybdenum ditelluride (MoTe 2 ) bilayer. Magnetic circular dichroism measurements reveal robust ferromagnetic states at fractionally hole-filled moiré minibands. Using trion photoluminescence as a sensor, we obtain a Landau fan diagram showing linear shifts in carrier densities corresponding to filling factor v = −2/3 and v = −3/5 ferromagnetic states with applied magnetic field. These shifts match the Streda formula dispersion of FQAH states with fractionally quantized Hall conductance of ${\sigma }_{xy}=-\,\frac{2}{3}\frac{{e}^{2}}{h}$ and ${\sigma }_{xy}=-\,\frac{3}{5}\frac{{e}^{2}}{h}$ , respectively. Moreover, the v = −1 state exhibits a dispersion corresponding to Chern number −1, consistent with the predicted QAH state. In comparison, several non-ferromagnetic states on the electron-doping side do not disperse, that is, they are trivial correlated insulators. The observed topological states can be electrically driven into topologically trivial states. Our findings provide evidence of the long-sought FQAH states, demonstrating MoTe 2 moiré superlattices as a platform for exploring fractional excitations.

Quantum Hall↗
DOE OSTI2020

Quantum anomalous Hall insulator phases in Fe-doped GaBi honeycomb

We discuss electronic and magnetic properties of the Fe-doped GaBi honeycomb using first principles calculations. Our analysis shows that the pristine GaBi honeycomb transitions from being a two-dimensional quantum spin Hall (QSH) insulator to a quantum anomalous Hall (QAH) insulator when it is doped with one Fe atom in a 4 × 4 GaBi honeycomb. Additionally, the QAH phase in Fe-doped GaBi is found to be robust in that it maintains its Chern number (C = 1) under fairly large strains (~ 4%) and supports a gap as large as 112 meV at 2.21% strain. The QAH phase is also retained when the Fe-doped GaBi is placed on a CdTe substrate, suggesting that Fe-doped GaBi films could be useful for spintronics applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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

Classification of (2 + 1) D invertible fermionic topological phases with symmetry

Here we provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups G f and general values of the chiral central charge c - . Here G f is a central extension of a bosonic symmetry group G b by fermion parity, (-1) F , specified by a second cohomology class [ω 2 ]∈ $\mathscr{H}^2$(Gb,$\mathbb{Z}_2$). Our approach proceeds by gauging fermion parity and classifying the resulting G b symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c - ) 1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c - = 0. We show how the tenfold way classification of topological insulators and superconductors fits into our scheme, along with general nonperturbative constraints due to certain choices of c - and G f . Mathematically, our results also suggest an explicit general parametrization of deformation classes of (2 + 1)D invertible topological quantum field theories with G f symmetry.

36 MATERIALS SCIENCE↗