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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Topological Invariant of Manifolds in Slawianowski’s Field Theory [Slides]

Witten constructed topological invariants of manifolds by introducing actions depending only on smooth structures of the manifold without using a metric. He focused on an example of Chern-Simons’ theory on 3D manifolds. Slawianowski based his field theory on frame/coframe fields without a metric. A Witten-type topological invariant can be introduced in Slawianowski’s framework, using an integral over the reper fields. Such invariant behaves differently for group manifolds than for all others. It additionally distinguishes semi-simple Lie group manifolds from other group manifolds. Further study of this new invariant is needed, including possible generalizations to other field theories.

42 ENGINEERING↗
DOE OSTI2022

Local Noether theorem for quantum lattice systems and topological invariants of gapped states

Here, we study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed d + 2-form on the parameter space, which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Fréchet–Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Topological invariants of a filling-enforced quantum band insulator

Traditional ionic and covalent compound insulators arise from a commensuration between electron count and system volume. On the other hand, conventional topological insulators, outside of quantum Hall effect systems, do not typically display such a commensuration. Instead, they can undergo a phase transition to a trivial insulator that preserves the electron filling. Nevertheless, in some crystalline insulators, termed filling-enforced quantum band insulators (feQBIs), electron filling can dictate nontrivial topology in the insulating ground state. Currently, little is known about the relation between feQBIs and conventional topological invariants. In this work, we study such relations for a particularly interesting example of a half-filling feQBI that is realized in space group 106 with spinless electrons. In this work, we prove that any four-band feQBI in space group 106 with filling 2 must have a nontrivial topological invariant, namely, the $\mathbb{Z}$ 2 glide invariant, and thus must have a quantized magnetoelectric polarizability θ = π. We thus have found a three-dimensional example where electron filling and band topology are tied. Such a locking raises intriguing questions about the generality of the band-inversion paradigm in describing the transition between trivial and topological phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Note on the Green’s function formalism and topological invariants

It has been discovered previously that the topological order parameter could be identified from the topological data of the Green's function, namely the (generalized) TKNN invariant in general dimensions, for both non-interacting and interacting systems. In this note, we show that this phenomenon has a clear geometric derivation. In conclusion, this proposal could be regarded as an alternative proof for the identification of the corresponding topological invariant and the topological order parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems

We derive a Kubo-like formula for the thermal Hall conductance of a 2d lattice systems which is free from ambiguities associated with the definition of energy magnetization. We use it to define a relative topological invariant of gapped 2d lattice systems at zero temperature. Up to a numerical factor, it can be identified with the difference of chiral central charges for the corresponding edge modes. This establishes the bulk-boundary correspondence for the chiral central charge. Here, we also show that for any local commuting projector Hamiltonian, the relative chiral central charge vanishes, while for free fermionic systems, it is related to the zero-temperature electric Hall conductance via the Wiedemann-Franz law.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups

The two classes of 3D, time-reversal-invariant insulators are known to subdivide into four classes in the presence of glide symmetry. Here, we extend this classification of insulators to include glide-symmetric Weyl metals and find a finer $\mathbb{Z}_4 ⊕\mathbb {Z}$ classification. We further elucidate the smoking-gun experimental signature of each class in the photoemission spectroscopy of surface states. Measuring the $\mathbb{Z}_4$ topological invariant by photoemission relies on identifying the glide representation of the initial Bloch state before photoexcitation—we show how this is accomplished with relativistic selection rules, combined with standard spectroscopic techniques to resolve both momentum and spin. In this work, our method relies on a spin-momentum locking that is characteristic of all glide-symmetric solids (inclusive of insulators and metals in trivial and topological categories). As an orthogonal application, given a glide-symmetric solid with an ideally symmetric surface, we may utilize this spin-momentum locking to generate a source of fully spin-polarized photoelectrons, which have diverse applications in solid-state spectroscopy. Our ab initio calculations predict Ba 2 Pb, stressed Na 3 Bi, and KHgSb to realize all three, nontrivial insulating phases in the $\mathbb{Z}_4$ classification.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Helicity is a topological invariant of massless particles: C = - 2 h

There is an elementary but indispensable relationship between the topology and geometry of massive particles. The geometric spin s is related to the topological dimension of the internal space V by dim⁡ V = 2⁢s + 1. This breaks down for massless particles, which are geometrically characterized by their helicity ℎ, but all have 1D internal spaces. We show that a subtler relation exists between the topology and geometry of massless particles. Wave functions of massless particles are sections of nontrivial line bundles over the light cone whose topology is completely characterized by their first Chern number C. We prove that in general C = -2⁢ℎ. In doing so, we also exhibit a method of generating all massless bundle representations via an Abelian group structure of massless particles.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Time-reversal invariant topological moiré flat band: A platform for the fractional quantum spin Hall effect

Motivated by recent observation of the quantum spin Hall effect in monolayer germanene and twisted bilayer transition-metal-dichalcogenides (TMDs), we study the topological phases of moir twisted bilayers with time-reversal symmetry and spin sz conservation. By using a continuum model description which can be applied to both germanene and TMD bilayers, we show that at small twist angles the emergent moir flat bands can be topologically nontrivial due to inversion symmetry breaking. Each of these flat bands admits a lowest-Landau-level description for each spin projection in the chiral limit and at magic twist angle. Furthermore, this allows for the construction of a many-body Laughlin state with time-reversal symmetry which can be stabilized by a short-range pseudopotential, and therefore serves as an ideal platform for realizing the so-far elusive fractional quantum spin Hall effect with emergent spin-1/2 U(1) symmetry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Robust measurement of wave function topology on NISQ quantum computers

Topological quantum phases of quantum materials are defined through their topological invariants. These topological invariants are quantities that characterize the global geometrical properties of the quantum wave functions and thus are immune to local noise. Here, we present a strategy to measure topological invariants on quantum computers. We show that our strategy can be easily integrated with the variational quantum eigensolver (VQE) so that the topological properties of generic quantum many-body states can be characterized on current quantum hardware. We demonstrate the robust nature of the method by measuring topological invariants for both non-interacting and interacting models, and map out interacting quantum phase diagrams on quantum simulators and IBM quantum hardware.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Classifying Topology in Photonic Heterostructures with Gapless Environments

Photonic topological insulators exhibit bulk-boundary correspondence, which requires that boundary-localized states appear at the interface formed between topologically distinct insulating materials. However, many topological photonic devices share a boundary with free space, which raises a subtle but critical problem as free space is gapless for photons above the light line. Here, we use a local theory of topological materials to resolve bulk-boundary correspondence in heterostructures containing gapless materials and in radiative environments. In particular, we construct the heterostructure’s spectral localizer, a composite operator based on the system’s real-space description that provides a local marker for the system’s topology and a corresponding local measure of its topological protection; both quantities are independent of the material’s bulk band gap (or lack thereof). Moreover, we show that approximating radiative outcoupling as material absorption overestimates a heterostructure’s topological protection. Importantly, as the spectral localizer is applicable to systems in any physical dimension and in any discrete symmetry class (i.e., any Altland-Zirnbauer class), our results show how to calculate topological invariants, quantify topological protection, and locate topological boundary-localized resonances in topological materials that interface with gapless media in general.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
NASA NTRS1999

Maxwell Duality, Lorentz Invariance, and Topological Phase

We discuss the Maxwell electromagnetic duality relations between the Aharonov-Bohm, Aharonov-Casher, and He-McKellar-Wilkens topological phases, which allows a unified description of all three phenomena.

Maxwell Duality Lorentz Invariance Topological Pha↗
DOE OSTI2023

Spectral phase singularity and topological behavior in perfect absorption

Perfect absorbers, which can achieve total absorption of all incoming energy, have been extensively studied in the last decades for various important technologies in general wave systems. Here, we show that perfect absorption (PA) is generically associated with topological spectral phase singularity (SPS), carrying conserved and tunable quantized topological invariants in spectral space. The order of topological invariant $\tilde{v}$ depends on the number of degenerate outgoing channels. Two commonly studied absorbers, mirror-backed and all-dielectric structures, are reexamined from a topological perspective to reveal the generation, evolution, and annihilation of SPSs with $\tilde{v}$ = ±1 or even high orders (i.e., $\tilde{v}$ = ±2,±4). A strategy based on charge conservation of SPSs to design dual-band perfect absorbers has been established. Our findings establish the topological origin of the robust existence of PA. More broadly, in this letter, we highlight topology as the fundamental property of conventional scattering behaviors. Finally, this insight could lead to opportunities in applications such as biosensing, topological metasurfaces, and micro/nano thermal radiation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 OSTI2022

Artificial Graphene Nanoribbons: A Test Bed for Topology and Low-Dimensional Dirac Physics

Here, we synthesize artificial graphene nanoribbons by positioning carbon monoxide molecules on a copper surface to confine its surface state electrons into artificial atoms positioned to emulate the low-energy electronic structure of graphene derivatives. We demonstrate that the dimensionality of artificial graphene can be reduced to one dimension with proper "edge" passivation, with the emergence of an effectively gapped one-dimensional nanoribbon structure. These one-dimensional structures show evidence of topological effects analogous to graphene nanoribbons. Guided by first-principles calculations, we spatially explore robust, zero-dimensional topological states by altering the topological invariants of quasi-one-dimensional artificial graphene nanostructures. The robustness and flexibility of our platform allow us to toggle the topological invariants between trivial and nontrivial on the same nanostructure. Ultimately, we spatially manipulate the states to understand fundamental coupling between adjacent topological states that are finely engineered and simulate complex Hamiltonians.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗