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DOE OSTI2025

Classification of fragile topology enabled by matrix homotopy

Flat bands in twisted materials have attracted considerable attention due to the emergence of correlated phases that can be associated with the non-Wannier-representable nature of its single-particle states. Specifically, these bands can exhibit a class of topology that can be nullified by the addition of trivial bands, termed fragile topology, which has required an expansion of prior classification schemes. However, existing approaches for predicting fragile topology rely on momentum-space methods, e.g., Wilson loops, presenting a fundamental challenge for using fragile topology as a predictor of correlated phases in aperiodic systems, such as incommensurate twist angles in moiré materials. Here, we develop a ℤ 2 energy-resolved topological marker for classifying fragile phases using a system’s position-space description, enabling the direct classification of finite, disordered, and aperiodic materials. By translating the physical symmetries protecting the system’s fragile topological phase into matrix symmetries of the system’s Hamiltonian and position operators, we use matrix homotopy to construct our topological marker while simultaneously yielding a quantitative measure of topological robustness. We demonstrate our framework’s effectiveness in both a low-energy tight-binding model and a continuum photonic crystal model of 𝐶 2 ⁢𝒯-symmetric systems, and find that fragile topology can both persist under strong disorder and even exhibit disorder-induced reentrant phase transitions. Our photonic crystal results also demonstrate the robustness of fragile topology, and the applicability of our approach, to heterostructures lacking a bulk spectral gap. Overall, our framework serves as an efficient tool for elucidating fragile topology, offering guidance for the prediction and discovery of correlated phases in both crystalline and aperiodic materials.

Lee, Ki Young [Sandia National Laboratories (SNL-N↗

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

Machine‐Learning Spectral Indicators of Topology

Abstract Topological materials discovery has emerged as an important frontier in condensed matter physics. While theoretical classification frameworks have been used to identify thousands of candidate topological materials, experimental determination of materials’ topology often poses significant technical challenges. X‐ray absorption spectroscopy (XAS) is a widely used materials characterization technique sensitive to atoms’ local symmetry and chemical bonding, which are intimately linked to band topology by the theory of topological quantum chemistry (TQC). Moreover, as a local structural probe, XAS is known to have high quantitative agreement between experiment and calculation, suggesting that insights from computational spectra can effectively inform experiments. In this work, computed X‐ray absorption near‐edge structure (XANES) spectra of more than 10 000 inorganic materials to train a neural network (NN) classifier that predicts topological class directly from XANES signatures, achieving F 1 scores of 89% and 93% for topological and trivial classes, respectively is leveraged. Given the simplicity of the XAS setup and its compatibility with multimodal sample environments, the proposed machine‐learning‐augmented XAS topological indicator has the potential to discover broader categories of topological materials, such as non‐cleavable compounds and amorphous materials, and may further inform field‐driven phenomena in situ, such as magnetic field‐driven topological phase transitions.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Nonlinear Topological Photonics: Capturing Nonlinear Dynamics and Optical Thermodynamics

Combining multiple optical resonators or engineering dispersion of complex media has provided an effective method for demonstrating topological physics controlling photons in unprecedented ways such as unidirectional light propagation and spatially localized modes between an interface or on a corner. Further, adding nonlinear responses to those topological photonic systems has enabled achieving diverse phases of photons in both space and time, allowing for more functionalities in photonic devices that provide a new playground for studying dynamic features of nonlinear topological systems. However, most methods for describing nonlinear topological photonic systems rely on linear topological theories, making it challenging to accurately characterize the topology of nonlinear systems. Thus, substantial efforts have focused on rigorously describing nonlinear topological phases and developing effective tools to analyze nonlinear topological effects. Meanwhile, coupled multimode optical waveguides with nonlinear dynamic responses provide an excellent platform for the statistical description of photons, opening a new paradigm called “optical thermodynamics”. This review will introduce the basic concepts of nonlinear topological photonics and the recent development of theoretical approaches focusing on data-driven approaches for creating phase diagrams as well as the spectral localizer framework and the pseudospectrum method for understanding optical nonlinearities in topological systems. In addition, the new concept of optical thermodynamics will be introduced with some recent theoretical works.

Topological photonics↗

DOE OSTI2025

Topological perturbation to a standard dehydrogenation catalyst, Pt 3 Sn

Topological materials, which exhibit protected topological surface states (TSS) near the Fermi level, have been proposed to be good catalysts. Topological catalysis may be more prevalent than we suspect, and not limited to exotic new materials. Here we study a known dehydrogenation catalyst, Pt 3 Sn alloy, which happens to be a topological semimetal, and probe the participation of TSSs in catalytic dehydrogenation of methane catalyzed by this material. Through first principle modeling and detailed analysis of the electronic structure for topological and non-topological surfaces of Pt 3 Sn, we find that TSS get significantly altered by the binding of reaction intermediates, particularly H. However, this effect of TSS on the binding of the reagents is merely perturbative, as the majority of the adsorbate binding is achieved by not-surface-focused electronic states, located much deeper below the Fermi level. Therefore, the reaction energetics and selectivity are predominantly determined by electronic states other than TSS. The fact that TSS are available for the reagent binding does not alone guarantee that the catalysis is strongly driven by TSS. However, TSS are not to be ignored, as small changes in the energetics along the reaction profile can translate into substantial differences in the reaction rate. Hence, in our view, Pt 3 Sn – a topological material – is first and foremost a standard catalyst, with added topological features, and not purely a topological catalyst. Our results point at the need to carefully consider all the bonding effects at the topological material interface.

Chemistry↗

DOE OSTI2023

Controllable superconducting to semiconducting phase transition in topological superconductor 2M-WS 2

The investigation of exotic properties in two-dimensional (2D) topological superconductors has garnered increasing attention in condensed matter physics, particularly for applications in topological qubits. Despite this interest, a reliable way of fabricating topological Josephson junctions (JJs) utilizing topological superconductors has yet to be demonstrated. Controllable structural phase transition presents a unique approach to achieving topological JJs in atomically thin 2D topological superconductors. In this work, we report the pioneering demonstration of a structural phase transition from the superconducting to the semiconducting phase in the 2D topological superconductor 2M-WS 2 . We reveal that the metastable 2M phase of WS 2 remains stable in ambient conditions but transitions to the 2H phase when subjected to temperatures above 150°C. We further locally induced the 2H phase within 2M-WS 2 nanolayers using laser irradiation. Notably, the 2H phase region exhibits a hexagonal shape, and scanning tunneling microscopy (STM) uncovers an atomically sharp crystal structural transition between the 2H and 2M phase regions. Moreover, the 2M to 2H phase transition can be induced at the nanometer scale by a 200 keV electron beam. The electrical transport measurements further confirmed the superconductivity of the pristine 2M-WS 2 and the semiconducting behavior of the laser-irradiated 2M-WS 2 . Furthermore, our results establish a novel approach for controllable topological phase change in 2D topological superconductors, significantly impacting the development of atomically scaled planar topological JJs.

2D materials↗

DOE OSTI2022

Topological alloy engineering and locally linearized gap dependence on concentration

Alloy engineering is a well-established approach to tune various materials’ properties, but its application to topological alloys remains rudimentary. Of special interest is the band gap, the most defining property of topological materials; however, the concentration dependence of energy gaps in topological alloys remains unknown. Here we systematically investigate the band gap evolution of a topological alloy as a function of alloy concentration, using KZnSb 1-x Bi x as a prototype, based on first-principles calculations. In contrast to the well-established smooth bowing curve for a trivial gap in semiconductor alloys, we found that the topological gap evolves generally with a complex fragmented pattern due to topological phase transitions, and most strikingly a linear dependence on concentration locally in each distinct phase. Such gap linearization is fundamentally rooted in the linear dependence on alloy concentration of spin-orbit coupling (SOC) that predominantly determines a topological gap. Furthermore, we demonstrate topological alloy engineering as a general approach to tune the topological order by modulating the band edge composition and degeneracy through the alloying-induced interplay of SOC and atomic orbital on-site energy, while the linear gap dependence on alloy concentration remains independent of the degree of topological order.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Robustness of topological persistence in knowledge distillation for wearable sensor data

Topological data analysis (TDA) has shown great success in various applications involving wearable sensor data. However, there are difficulties in leveraging topological features in machine learning and wearable sensors because of the large time consumption and computational resources required to extract the features. To address this problem, knowledge distillation (KD) is utilized to generate a small model and accommodate topological features with persistence image (PI) representations from the raw time series data. Deploying topological knowledge in KD enables the student to achieve better performance compared to the one trained solely on raw time series data. However, it is not yet known if there are coherent characteristics for topological features in PI, which can aid in improving the performance during KD. In this paper, we investigate the suitability and challenges of utilizing topological features in KD for wearable sensor data, thereby contributing to the advancement of the field. Our study explores the impact of transferred topological features by comparing the Teacher-to-Student framework with Multiple Teachers-to-Student where teachers utilize both time series data and persistence images obtained by TDA as inputs. Additionally, we conduct a rigorous examination of topological knowledge effects by testing under various corruptions, knowledge types, and learning strategies in the context of human activity recognition tasks. Our analysis of topological features in KD presents the optimal strategy for incorporating these features. This study includes datasets of varying scales, window lengths, and activity classes, providing a comprehensive evaluation. Our results demonstrate that leveraging topological features in KD to enhance performance across databases.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Near‐Field Characterization of Higher‐Order Topological Photonic States at Optical Frequencies

Abstract Higher‐order topological insulators (HOTIs) represent a new type of topological system, supporting boundary states localized over boundaries, two or more dimensions lower than the dimensionality of the system itself. Interestingly, photonic HOTIs can possess a richer physics than their original condensed matter counterpart, supporting conventional HOTI states based on tight‐binding coupling, and a new type of topological HOTI states enabled by long‐range interactions. Here, a new mechanism to establish all‐dielectric infrared HOTI metasurfaces exhibiting both types of HOTI states is proposed, supported by a topological transition accompanied by the emergence of topological Wannier‐type polarization. Two kinds of near‐field experimental studies are performed: i) the solid immersion spectroscopy and ii) near‐field imaging using scattering scanning near‐field optical microscopy to directly observe the topological transition and the emergence of HOTI states of two types. It is shown that the near‐field profiles indicate the displacement of the Wannier center across the topological transition leading to the topological dipole polarization and emergence of the topological boundary states. The proposed all‐dielectric HOTI metasurface offers a new approach to confine the optical field in micro‐ and nano‐scale topological cavities and thus paves the way to achieve a novel nanophotonic technology.

Vakulenko, Anton↗

DOE OSTI2025

Hybridization of colloidal handlebodies with singular defects and topological solitons in chiral liquid crystals

Topology can manifest itself in colloids when quantified by invariants like Euler characteristics of nonzero-genus colloidal surfaces, albeit spherical colloidal particles are most often studied, and colloidal particles with complex topology are rarely considered. On the other hand, singular defects and topological solitons often define the physical behavior of the molecular alignment director fields in liquid crystals. Interestingly, nematic liquid crystalline dispersions of colloidal particles allow for probing the interplay between topologies of surfaces and fields, but only a limited number of such cases have been explored so far. Here, we study the hybridization of topological solitons, singular defects, and topologically nontrivial colloidal particles with the genus of surfaces different from zero in a chiral nematic liquid crystal phase. Hybridization occurs when distortions separately induced by colloidal particles and LC solitons overlap, leading to energy minimization-driven redistribution of director field deformations and defects. As a result, hybrid director configurations emerge, combining topological features from both components. We uncover a host of director field configurations complying with topological theorems, which can be controlled by applying electric fields. Rotational and translational dynamics arise due to the nonreciprocal evolution of the director fields in response to alternating electric fields of different frequencies. These findings help define a platform for controlling topologically hyper-complex colloidal structures and dynamics with electrically reconfigurable singular defects and topological solitons induced by colloidal handlebodies.

Lee, Jun-Yong [Hiroshima Univ. (Japan)]↗

DOE OSTI2020

Wannier representation of Floquet topological states

A universal feature of topological insulators is that they cannot be adiabatically connected to an atomic limit, where individual lattice sites are completely decoupled. This property is intimately related to a topological obstruction to constructing a localized Wannier function from Bloch states of an insulator. In this work, we generalize this characterization of topological phases toward periodically driven systems. We show that nontrivial connectivity of hybrid Wannier centers in momentum space and time can characterize various types of topology in periodically driven systems, which include Floquet topological insulators, anomalous Floquet topological insulators with micromotion-induced boundary states, and gapless Floquet states realized with topological Floquet operators. In particular, nontrivial time dependence of hybrid Wannier centers indicates impossibility of continuous deformation of a driven system into an undriven insulator, and a topological Floquet operator implies an obstruction to constructing a generalized Wannier function which is localized in real and frequency spaces. Our results pave a way to a unified understanding of topological states in periodically driven systems as a topological obstruction in Floquet states.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A topological superconductor tuned by electronic correlations

A topological superconductor, characterized by either a chiral order parameter or a topological surface state in proximity to bulk superconductivity, is foundational to topological quantum computing. A key open challenge is whether electron-electron interactions can tune such topological superconducting phases. Here, we provide experimental signatures of a unique topological superconducting phase in competition with electronic correlations in 10-unit-cell thick FeTe x Se 1-x films grown on SrTiO 3 substrates. When the Te content x exceeds 0.7, we observe a topological transition marked by the emergence of a superconducting surface state. Near the FeTe limit, the system undergoes another transition where the surface state disappears, and superconductivity is suppressed. Theory suggests that electron-electron interactions in the odd-parity xy− band drives this second topological transition. The flattening and eventual decoherence of d xy -derived bands track the superconducting dome, linking correlation effects directly to superconducting coherent transport. Our work establishes many-body electronic correlations as a sensitive knob for tuning topology and superconductivity, offering a pathway to engineer new topological phases in correlated materials.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Intertwined Topological and Magnetic Orders in Atomically Thin Chern Insulator MnBi 2 Te 4

The interplay between band topology and magnetic order plays a key role in quantum states of matter. MnBi 2 Te 4 , a van der Waals magnet, has recently emerged as an exciting platform for exploring Chern insulator physics. Its layered antiferromagnetic order was predicted to enable even-odd layer-number dependent topological states, supported by promising edge transport measurements. Furthermore, it becomes a Chern insulator when all spins are aligned by an applied magnetic field. However, the evolution of the bulk electronic structure as the magnetic state is continuously tuned and its dependence on layer number remains unexplored. Here, employing multimodal probes, we establish oneto-one correspondence between bulk electronic structure, magnetic state, topological order, and layer thickness in atomically thin MnBi 2 Te 4 devices. As the magnetic state is tuned through the canted magnetic phase, we observe a band crossing, i.e., the closing and reopening of the bulk bandgap, corresponding to the concurrent topological phase transition. Surprisingly, we find that the even- and odd-layer number devices exhibit a similar topological phase transition coupled to magnetic states, distinct from recent theoretical and experimental reports. Our findings shed new light on the interplay between band topology and magnetic order in this newly discovered topological magnet and validate the band crossing with concurrent measurements of topological invariant in a continuously tuned topological phase transition.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Topological quantum interference in a pumped Su-Schrieffer-Heeger lattice

Topological quantum interference emerges from the interplay between quantum mechanics and topology. We present evidence for two types of such interference phenomenon that can result from the quantum dynamics of initial topological states. We realize both types of topological quantum interference in a pumped non-Hermitian Su-Schrieffer-Heeger lattice that can be implemented by creation and coherent control of excitonic states of trapped neutral atoms. On quenching the system from the topological to the gapless phases and then back again, we find that interference patterns develop in the gapless phase and also after switching back to the topological phase. These patterns occur both as many-excitation interferences generated in the presence of pumping the atoms at the end sites, and as one- and two-excitation interferences seen in the absence of pumping when starting with edge excitations. Investigation of the excitation dynamics shows that these interference patterns originate from the topological nature of the initial states and are very different from quantum interferences originating from nontopological states of the lattice. Our results also reveal that unlike well-known situations where topological states are protected against local perturbations, in the non-Hermitian SSH systems resulting from driving the excited-state populations, a local dissipation at each lattice site can suppress both the topological interference and the total population of the lattice.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Topological quantum devices: a review

The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Optical N-plasmon: topological hydrodynamic excitations in graphene from repulsive Hall viscosity

Abstract Edge states occurring in Chern and quantum spin-Hall phases are signatures of the topological electronic band structure in two-dimensional (2D) materials. Recently, a new topological electromagnetic phase of graphene characterized by the optical N-invariant was proposed. Optical N-invariant arises from repulsive Hall viscosity in hydrodynamic many-body electron systems, distinct from the Chern and Z 2 invariants. In this paper, we introduce the topologically protected edge excitation—optical N-plasmon of interacting many-body electron systems in the topological optical N-phase. These optical N-plasmons are signatures of the topological plasmonic band structure in 2D materials. We demonstrate that optical N-plasmons exhibit unique dispersion relations, stability against various boundary conditions, and edge profiles when compared with the topologically trivial edge magneto plasmons. Based on the optical N-plasmon, we design an ultra sub-wavelength broadband topological hydrodynamic circulator, which is a chiral quantum radio-frequency circuit component crucial for information routing and interfacing quantum–classical computing systems. Furthermore, we reveal that optical N-plasmons can be effectively tuned by the neighboring dielectric environment without breaking the topological properties. Our work provides a smoking gun signature of topological electromagnetic phases occurring in 2D materials arising from repulsive Hall viscosity.

Physics↗

DOE OSTI2025

Emergent Dimer-Model Topological Order and Quasiparticle Excitations in Liquid Crystals: Combinatorial Vortex Lattices

Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological phases and topological order has been introduced in the context of spin liquids to investigate emergent phenomena like quantum Hall effects and high-temperature superconductivity. Here, we bridge these two seemingly disparate perspectives on topology in physics. Combining experiments and simulations, we show how topological defects in liquid crystals can be used as versatile building blocks to create complex, highly degenerate topological phases, which we refer to as “combinatorial vortex lattices” (CVLs). CVLs exhibit extensive residual entropy and support locally stable quasiparticle excitations in the form of charge-conserving topological monopoles, which can act as mobile information carriers and be linked via Dirac strings. CVLs can be rewritten and reconfigured on demand, endowed with various symmetries, and modified through laser-induced topological surgery—an essential capability for information storage and retrieval. We demonstrate experimentally the realization, stability, and precise optical manipulation of CVLs, thus opening new avenues for understanding and technologically exploiting higher-hierarchy topology in liquid crystals and other ordered media.

36 MATERIALS SCIENCE↗

NASA NTRS2018

Optimization of the Magnetic Field Topology in the Hall Effect Rocket with Magnetic Shielding

NASA's Hall Effect Rocket with Magnetic Shielding (HERMeS) 12.5 kilowatt Technology Demonstration Unit-1 (TDU-1) has been the subject of extensive technology maturation in preparation for flight system development. The TDU-1 thruster implements a magnetically shielded field topology and has demonstrated the elimination of the discharge channel erosion. Extensive wear testing of the TDU Hall thrusters has identified the thruster front pole covers as the next life limiting component. This effort aims to explore and investigate alternate magnetic field topologies to assess whether reductions in the front pole cover erosion can be attained while still maintaining very low erosion rates on the discharge channel walls. NASA GRC (Glenn Research Center) and JPL (Jet Propulsion Laboratory) have begun a magnetic field topology characterization and optimization study by designing four candidate magnetic field topologies that reduce the effectiveness of the shielding along the discharge channel walls with the intent to also reduce the erosion rates along the pole covers. Three of the four candidate magnetic field topologies have been manufactured subjected to an extensive test campaign that includes performance, plume, and stability characterization. In the Phase I test segment, the thruster's oscillation magnitude and laser-induced fluorescence (LIF) measurements of the plasma plume were performed for the three candidate topologies. In Phase I, the thruster's oscillation magnitude and LIF measurements were performed for the three candidate topologies. Phase I test results found that the B1 configuration attained lower oscillation levels than the baseline topology (B0). Additionally, laser induced fluorescence measurements along the discharge chamber centerline found that upstream retraction of the thruster’s peak magnetic field does result in an upstream shift of the acceleration zone but the magnitude of the shift does not correspond one-to-one to the shift in the location of the peak radial magnetic field magnitude. Phase II test segment will include performing performance, stability, plume, and erosion measurements for the various candidate magnetic field topologies..

Kamhawi, Hani↗