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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Topology of large-scale structure. IV - Topology in two dimensions

In a recent series of papers, an algorithm was developed for quantitatively measuring the topology of the large-scale structure of the universe and this algorithm was applied to numerical models and to three-dimensional observational data sets. In this paper, it is shown that topological information can be derived from a two-dimensional cross section of a density field, and analytic expressions are given for a Gaussian random field. The application of a two-dimensional numerical algorithm for measuring topology to cross sections of three-dimensional models is demonstrated.

Melott, Adrian L.↗
DOE OSTI2020

Topological Hall Effect in a Topological Insulator Interfaced with a Magnetic Insulator

A topological insulator (TI) interfaced with a magnetic insulator (MI) may host an anomalous Hall effect (AHE), a quantum AHE, and a topological Hall effect (THE). Recent studies, however, suggest that coexisting magnetic phases in TI/MI heterostructures may result in an AHE-associated response that resembles a THE but in fact is not. Here, we report a genuine THE in a TI/MI structure that has only one magnetic phase. The structure shows a THE in the temperature range of T = 2–3 K and an AHE at T = 80–300 K. Over T = 3–80 K, the two effects coexist but show opposite temperature dependencies. Control measurements, calculations, and simulations together suggest that the observed THE originates from skyrmions, rather than the coexistence of two AHE responses. The skyrmions are formed due to a Dzyaloshinskii–Moriya interaction (DMI) at the interface; the DMI strength estimated is substantially higher than that in heavy metal-based systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Chiral-Bubble-Induced Topological Hall Effect in Ferromagnetic Topological Insulator Heterostructures

In this letter, we report compelling evidence of emergent topological Hall effect (THE) from chiral bubbles in a two-dimensional uniaxial ferromagnet, V-doped Sb 2 Te 3 heterostructure. The sign of THE signal is determined by the net curvature of domain walls in different domain configuration, and the strength of THE signal is correlated with the density of nucleation or pinned bubble domains. The experimental results are in good agreement with the integrated linear transport and Monte Carlo simulations, corroborating the emergent gauge field at chiral magnetic bubbles. Lastly, our findings not only reveal a general mechanism of THE in two-dimensional ferromagnets, but also pave the way for the creation and manipulation of topological spin textures for spintronic applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Superconductivity, Pairing Symmetry, and Disorder in the Doped Topological Insulator Sn 1-x In x Te for x >= 0.10.

The temperature dependence of the London penetration depth Delta lambda(T) in the superconducting doped topological crystalline insulator Sn1-xInxTe was measured down to 450 mK for two different doping levels, x approximate to 0.45 (optimally doped) and x approximate to 0.10 (underdoped), bookending the range of cubic phase in the compound. The results indicate no deviation from fully gapped BCS-like behavior, eliminating several candidate unconventional gap structures. Critical field values below 1 K and other superconducting parameters are also presented. The introduction of disorder by repeated particle irradiation with 5 MeV protons does not enhance T-c, indicating that ferroelectric interactions do not compete with superconductivity.

Smylie, M. P.↗
DOE OSTI2022

Topological Crystalline Insulator Candidate ErAsS with Hourglass Fermion and Magnetic-Tuned Topological Phase Transition

Topological crystalline insulators (TCIs) with hourglass fermion surface state have attracted a lot of attention and are further enriched by crystalline symmetries and magnetic order. Here, the emergence of hourglass fermion surface state and exotic phases in the newly discovered, air-stable ErAsS single crystals are shown. In the paramagnetic phase, ErAsS is expected to be a TCI with hourglass fermion surface state protected by the nonsymmorphic symmetry. Dirac-cone-like bands and nearly linear dispersions in large energy range are experimentally observed, consistent well with theoretical calculations. Below T N ≈ 3.27 K, ErAsS enters a collinear antiferromagnetic state, which is a trivial insulator breaking the time-reversal symmetry. An intermediate incommensurate magnetic state appears in a narrow temperature range (3.27–3.65 K), exhibiting an abrupt change in magnetic coupling. Overall, the results reveal that ErAsS is an experimentally available TCI candidate and provide a unique platform to understand the formation of hourglass fermion surface state and explore magnetic-tuned topological phase transitions.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity]

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.

42 ENGINEERING↗
DOE OSTI2018

Time reversal, SU(N) Yang–Mills and cobordisms: Interacting topological superconductors/insulators and quantum spin liquids in 3+1D

We introduce a web of strongly correlated interacting 3+1D topological superconductors/insulators of 10 particular global symmetry groups of Cartan classes, realizable in electronic condensed matter systems, and their new SU(N) generalizations. The symmetries include SU(N), SU(2), U(1), fermion parity, time reversal and relate to each other through symmetry embeddings. We overview the lattice Hamiltonian formalism. We complete the list of field theories of bulk symmetry-protected topological invariants (SPT invariants/partition functions that exhibit boundary ’t Hooft anomalies) via cobordism calculations, matching their full classification. We also present explicit 4-manifolds that detect these SPTs. On the other hand, once we dynamically gauge part of their global symmetries, we arrive in various new phases of SU(N) Yang–Mills (YM) gauge theories, analogous to quantum spin liquids with emergent gauge fields. We discuss how coupling YM theories to time reversal-SPTs affects the strongly coupled theories at low energy. For example, we point out a possibility of having two deconfined gapless time-reversal symmetric SU(2) YM theories at θ=π as two distinct conformal field theories, which although are secretly indistinguishable by correlators of local operators on orientable spacetimes nor by gapped SPT states, can be distinguished on non-orientable spacetimes or potentially by correlators of extended operators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures

The quantum anomalous Hall (QAH) effect is a consequence of non-zero Berry curvature in momentum space. The QAH insulator harbours dissipation-free chiral edge states in the absence of an external magnetic field. Yet, the topological Hall (TH) effect, a hallmark of chiral spin textures, is a consequence of real-space Berry curvature. Herein, by inserting a topological insulator (TI) layer between two magnetic TI layers, we realized the concurrence of the TH effect and the QAH effect through electric-field gating. The TH effect is probed by bulk carriers, whereas the QAH effect is characterized by chiral edge states. The appearance of the TH effect in the QAH insulating regime is a consequence of chiral magnetic domain walls that result from the gate-induced Dzyaloshinskii–Moriya interaction and occurs during the magnetization reversal process in the magnetic TI sandwich samples. The coexistence of chiral edge states and chiral spin textures provides a platform for proof-of-concept dis- sipationless spin-textured spintronic applications.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Effects of two-dimensional magnetic uncertainties and three-dimensional error and perturbation fields on the Small Angle Slot divertor geometry and topology [Effects of two- and three-dimensional magnetic fields on the Small Angle Slot divertor magnetic topology]

The Small Angle Slot (SAS) was recently installed on DIII-D as an advanced divertor, promising easier plasma detachment and lower temperatures across the whole target. A twofold study of the SAS magnetic topology is presented in this paper. On one hand, a twodimensional uncertainty quantification analysis is carried out through a Monte Carlo approach in order to understand the level of accuracy of two-dimensional equilibrium computations in reconstructing the strike point and angle onto the divertor. Under typical experimental conditions, the uncertainties are found to be roughly 6.8 mm and 0.56 deg, respectively. On the other hand, a three-dimensional “vacuum” analysis is carried out to understand the effects of typical external perturbation fields on the scrape-off layer topology. When the threedimensional I-coils are switched on, poloidally-localized lobes are found to appear, grow, and hit the SAS target, although barely, even for 5 kA; at the same time, the strike point modulation is found to be roughly 1.8 mm and thus negligible for most purposes. Furthermore, such results complement previous two-dimensional analyses in characterizing typical SAS equilibria and provide useful background information for planning and interpreting SAS experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Shot noise and differential conductance as signatures of putative topological superconductivity in FeSe 0.45 ⁢Te 0.55

We present a theory for the differential shot noise, dS/dV, as measured via shot-noise scanning tunneling spectroscopy, and the differential conductance, dI/dV, for tunneling into Majorana zero modes (MZMs) in the putative topological superconductor FeSe 0.45 Te 0.55 . We demonstrate that for tunneling into chiral Majorana edge modes near domain walls, as well as MZMs localized in vortex cores and at the end of defect lines, dS/dV vanishes whenever dI/dV reaches a quantized value proportional to the quantum of conductance. Furthermore, these results are independent of the particular orbital tunneling path, thus establishing a vanishing dS/dV concomitant with a quantized dI/dV, as universal signatures for Majorana modes in two-dimensional topological superconductors, irrespective of the material’s specific complex electronic band structure.

Iron-based superconductors↗
DOE OSTI2023

Possible topological superconductivity in the topological crystalline insulator $\mathrm{(Pb_{1-x} Sn_x)_{1-y}In_yTe}$

Superconductivity in topological insulators is expected to show very unconventional features such as a $p+ip$ order parameter, Majorana fermions, etc. However, intrinsic superconductivity has been observed in a very limited number of materials in which the pairing symmetry is still a matter of debate. Here, we study the topological crystalline insulator (TCI) $\mathrm{(Pb_{1-x} Sn_x)_{1-y}In_yTe}$, for which a peculiar insulator to superconductor transition was previously reported near the gap inversion transition, where the system is nearly a three-dimensional Dirac semimetal. Both the existence of superconductivity near the three-dimensional Dirac semimetal and the occurrence of an insulator to superconductor transition in an isotropic material are highly unusual. We suggest that the observed phenomena are related to the intrinsic instability of a three-dimensional Dirac semimetal state in $\mathrm{(Pb_{1-x} Sn_x)_{1-y}In_yTe}$ and “flattening” of the bulk valence and conduction bands as they acquire a Mexican-hat-like dispersion on the inverted side of the phase diagram. Importantly, this favors the pairing instability if the chemical potential is pinned to these flat regions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

First-Principles Prediction of New Electrides with Nontrivial Band Topology Based on One-Dimensional Building Blocks

In this work, we introduce a new class of electrides with nontrivial band topology by coupling materials database searches and first-principles-calculations-based analysis. Cs 3 O and Ba 3 N are for the first time identified as a new class of electrides, consisting of one-dimensional (1D) nanorod building blocks. Their crystal structures mimic β-TiCl 3 with the position of anions and cations exchanged. Unlike the weakly coupled nanorods of β-TiCl 3 , Cs 3 O and Ba 3 N retain 1D anionic electrons along the hollow interrod sites; additionally, a strong interrod interaction in C 3 O and Ba 3 N induces band inversion in a 2D superatomic triangular lattice, resulting in Dirac-node lines. The new class of electrides can serve as a prototype for new electrides with a large cavity space that can be utilized for various applications such as gas storage, ion transport, and metal intercalation.

36 MATERIALS SCIENCE↗
DOE OSTI2017

THE TOPOLOGY OF CANONICAL FLUX TUBES IN FLARED JET GEOMETRY

Magnetized plasma jets are generally modeled as magnetic flux tubes filled with flowing plasma governed by magnetohydrodynamics (MHD). We outline here a more fundamental approach based on flux tubes of canonical vorticity, where canonical vorticity is defined as the circulation of the species’ canonical momentum. This approach extends the concept of magnetic flux tube evolution to include the effects of finite particle momentum and enables visualization of the topology of plasma jets in regimes beyond MHD. A flared, current-carrying magnetic flux tube in an ion-electron plasma with finite ion momentum is thus equivalent to either a pair of electron and ion flow flux tubes, a pair of electron and ion canonical momentum flux tubes, or a pair of electron and ion canonical vorticity flux tubes. We examine the morphology of all these flux tubes for increasing electrical currents, different radial current profiles, different electron Mach numbers, and a fixed, flared, axisymmetric magnetic geometry. Calculations of gauge-invariant relative canonical helicities track the evolution of magnetic, cross, and kinetic helicities in the system, and show that ion flow fields can unwind to compensate for an increasing magnetic twist. The results demonstrate that including a species’ finite momentum can result in a very long collimated canonical vorticity flux tube even if the magnetic flux tube is flared. With finite momentum, particle density gradients must be normal to canonical vorticities, not to magnetic fields, so observations of collimated astrophysical jets could be images of canonical vorticity flux tubes instead of magnetic flux tubes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Prediction of intrinsic topological superconductivity in Mn-doped GeTe monolayer from first-principles

The recent discovery of topological superconductors (TSCs) has sparked enormous interest. The realization of TSC requires a delicate tuning of multiple microscopic parameters, which remains a great challenge. Here, we develop a first-principles approach to quantify realistic conditions of TSC by solving self-consistently Bogoliubov-de Gennes equation based on a Wannier function construction of band structure, in presence of Rashba spin-orbit coupling, Zeeman splitting and electron-phonon coupling. We further demonstrate the power of this method by predicting the Mn-doped GeTe (Ge 1- x Mn x Te) monolayer—a well-known dilute magnetic semiconductor showing superconductivity under hole doping—to be a Class D TSC with Chern number of -1 and chiral Majorana edge modes. By constructing a first-principles phase diagram in the parameter space of temperature and Mn concentration, we propose the TSC phase can be induced at a lower-limit transition temperature of ~40 mK and the Mn concentration of x ~0.015%. Our approach can be generally applied to TSCs with a phonon-mediated pairing, providing useful guidance for future experiments.

Chemistry↗
DOE OSTI2017

Proximity-effect-induced Superconducting Gap in Topological Surface States – A Point Contact Spectroscopy Study of NbSe 2 /Bi 2 Se 3 Superconductor-Topological Insulator Heterostructures

Proximity-effect-induced superconductivity was studied in epitaxial topological insulator Bi 2 Se 3 thin films grown on superconducting NbSe 2 single crystals. A point contact spectroscopy (PCS) method was used at low temperatures down to 40 mK. An induced superconducting gap in Bi 2 Se 3 was observed in the spectra, which decreased with increasing Bi 2 Se 3 layer thickness, consistent with the proximity effect in the bulk states of Bi 2 Se 3 induced by NbSe 2 . At very low temperatures, an extra point contact feature which may correspond to a second energy gap appeared in the spectrum. For a 16 quintuple layer Bi 2 Se 3 on NbSe 2 sample, the bulk state gap value near the top surface is ~159 μeV, while the second gap value is ~120 μeV at 40 mK. The second gap value decreased with increasing Bi 2 Se 3 layer thickness, but the ratio between the second gap and the bulk state gap remained about the same for different Bi 2 Se 3 thicknesses. It is plausible that this is due to superconductivity in Bi 2 Se 3 topological surface states induced through the bulk states. In conclusion, the two induced gaps in the PCS measurement are consistent with the three-dimensional bulk state and the two-dimensional surface state superconducting gaps observed in the angle-resolved photoemission spectroscopy (ARPES) measurement.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗