Search NASA⌕ Search

SEARCH · Search NASA

Results for “topological order”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
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 OSTI2022

Evidence of a room-temperature quantum spin Hall edge state in a higher-order topological insulator

Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics. The quantum spin Hall phase is a topological quantum phase that features a two-dimensional insulating bulk and a helical edge state. Here we use vector magnetic field and variable temperature based scanning tunnelling microscopy to provide micro-spectroscopic evidence for a room-temperature quantum spin Hall edge state on the surface of the higher-order topological insulator Bi 4 Br 4 . Here, we find that the atomically resolved lattice exhibits a large insulating gap of over 200 meV, and an atomically sharp monolayer step edge hosts an in-gap gapless state, suggesting topological bulk–boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent in the underlying band topology. We further identify the geometrical hybridization of such edge states, which not only supports the Z 2 topology of the quantum spin Hall state but also visualizes the building blocks of the higher-order topological insulator phase. Our results further encourage the exploration of high-temperature transport quantization of the putative topological phase reported here.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
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 OSTI2024

Higher-order topological corner and bond-localized modes in magnonic insulators

We theoretically investigate a two-dimensional decorated honeycomb lattice framework to realize a second-order topological magnon insulator (SOTMI) phase featuring distinct corner-localized modes. Here, our study emphasizes the pivotal role of spin-magnon mapping in characterizing bosonic topological properties, which exhibit differences from their fermionic counterparts. We employ a symmetry indicator topological invariant to identify and characterize this SOTMI phase, particularly for systems respecting time-reversal and rotational symmetry. Using a spin model defined on a honeycomb lattice geometry, we demonstrate that introducing “kekulé” type distortions yields a topological phase. In contrast, “antikekulé” distortions result in a nontopological magnonic phase. The presence of kekulé distortions manifests in two distinct topologically protected bosonic corner modes—an intrinsic and a pseudo, based on the specific edge terminations. On the other hand, antikekulé distortions give rise to Tamm/Shockley type bond-localized boundary modes, which are nontopological and reliant on particular edge termination. We further investigate the effects of random out-of-plane exchange anisotropy disorder on the robustness of these bosonic corner modes. The distinction between SOTMIs and their fermionic counterparts arises due to the system-specific magnonic onsite energies, a crucial feature often overlooked in prior literature. Our study unveils exciting prospects for engineering higher-order topological phases in magnon systems and enhances our understanding of their unique behavior within decorated honeycomb lattices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Higher-order topological superconductivity in twisted bilayer graphene

In this work, we show that introducing spin-singlet or spin-triplet superconductivity into twisted bilayer graphene induces higher-order topological superconductivity. Multiple copies of C 2z ⁢T-protected Majorana Kramers pairs appear at corners on pairing domain walls. The topology originates from the anomaly analyzed in Song et al.—the absence of a lattice support—of the single-valley band structure of twisted bilayer graphene, which is protected by C 2z ⁢T and approximate particle-hole symmetry $\mathcal{P}$. We prove that any pairing (spin-singlet or spin-triplet) term preserving valley-U(1), spin-SU(2), time-reversal, C 2z ⁢T, and $\mathcal{P}$ must drive the system into a higher-order topological superconductor. Here spin-SU(2) is the global spin-SU(2) for the singlet pairing and is broken to U(1) for the triplet pairing. Using a Dirac Hamiltonian, we derive the corner modes and confirm with numerics. These corner states are stable even if $\mathcal{P}$ is weakly broken, which is true in experimental setups. Finally, we suggest experimental detection via the fractional Josephson effect in a TBG-TSC Josephson junction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking

Recent experimental progress in controlling open quantum systems enables the pursuit of mixed-state nonequilibrium quantum phases. We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. Focusing on the decohered cluster state – a mixed-state symmetry-protected topological state protected by a combined strong and weak symmetry – we construct a parent Lindbladian that hosts it as a steady state. This Lindbladian can be mapped onto exactly solvable reaction-diffusion dynamics, even in the presence of certain perturbations, allowing us to solve the parent Lindbladian in detail and reveal previously-unknown steady states. Using both analytical and numerical methods, we find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. However, when perturbations introduce only weak symmetry defects, the steady-state mixed-state symmetry-protected topological order remains stable. Additionally, we construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.

Shah, Jeet [University of Maryland, College Park, ↗
DOE OSTI2020

Temperature-dependent electronic structure in a higher-order topological insulator candidate EuIn 2 As 2

Higher-order topological insulators (HOTIs) have enticed enormous research interests owing to their novelty in supporting gapless states along the hinges of a crystal. Despite several theoretical predictions, enough experimental confirmation of the HOTI state in crystalline solids is still lacking. Here, it is shown that interplay between topology and magnetism can give rise to various magnetic topological states, including HOTI and axion insulator states. Here, using high-resolution angle-resolved photoemission spectroscopy combined with the first-principles calculations, we report a systematic study of the electronic structure and its evolution across the magnetic phase transition in EuIn 2 As 2 which possesses an antiferromagnetic ground state below 16 K. Antiferromagnetic EuIn 2 As 2 has been predicted to host both the axion insulator and the HOTI states.We directly observe the linearly dispersing holelike bands crossing the Fermi level and the change in their dispersion across the magnetic phase transition. Our paper points to EuIn 2 As 2 as being a promising material for the exploration of interplay between topology and magnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Higher-order topological and nodal superconducting transition-metal sulfides M S ( M = Nb and Ta )

Intrinsic topological superconducting materials are exotic and vital to develop the next-generation topological superconducting devices, topological quantum calculations, and quantum information technologies. Here, we predict the topological and nodal superconductivity of NiAs-type M ⁢S ( M = Nb and Ta) transition-metal sulfides. We reveal their higher-order topology nature with an index of Z 4 = 2. These materials have a higher T c than the Nb or Ta metal superconductors due to their flat band and strong electron-phonon coupling nature. Electron doping and lighter isotopes can effectively enhance the T c . In conclusion, our findings show that the M ⁢S ( M = Nb and Ta) systems can be platforms to study exotic physics in the higher-order topological superconductors, and provide a theoretical support to utilize them as the topological superconducting devices in the field of advanced topological quantum calculations and information technologies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Engineering a non-Hermitian second-order topological insulator state in quasicrystals

Non-Hermitian topological phases have gained immense attention due to their potential to unlock novel features beyond Hermitian bounds. PT -symmetric (parity time-reversal symmetric) non-Hermitian models have been studied extensively over the past decade. In recent years, the topological properties of general non-Hermitian models, regardless of the balance between gains and losses, have also attracted vast attention. Here, we propose a non-Hermitian second-order topological (SOT) insulator that hosts gapless corner states on a two-dimensional quasicrystalline lattice (QL). We first construct a non-Hermitian extension of the Bernevig-Hughes-Zhang model on a QL generated by the Amman-Beenker tiling. This model has real spectra and supports helical edge states. Corner states emerge by adding a proper Wilson-mass term that gaps out the edge states. We propose two variations of the mass term that result in fascinating characteristics. In the first variation, we obtain a purely real spectra for the second-order topological phase. In the latter, we get a complex spectra with corner states localized at only two corners due to the higher-order non-Hermitian skin effect of the edge modes. Furthermore, our findings pave a path to engineering exotic SOT phases where corner states can be localized at designated corners.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Evidence for a higher-order topological insulator in a three-dimensional material built from van der Waals stacking of bismuth-halide chains

Low-dimensional van der Waals materials have been extensively studied as a platform with which to generate quantum effects. Advancing this research, topological quantum materials with van der Waals structures are currently receiving a great deal of attention. Here, we use the concept of designing topological materials by the van der Waals stacking of quantum spin Hall insulators. Most interestingly, we find that a slight shift of inversion centre in the unit cell caused by a modification of stacking induces a transition from a trivial insulator to a higher-order topological insulator. Based on this, we present angle-resolved photoemission spectroscopy results showing that the real three-dimensional material Bi4Br4 is a higher-order topological insulator. Our demonstration that various topological states can be selected by stacking chains differently, combined with the advantages of van der Waals materials, offers a playground for engineering topologically non-trivial edge states towards future spintronics applications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Buckled honeycomb antimony: Higher order topological insulator and its relation to the Kekulé lattice

Higher order topological tnsulators are d-spatial dimensional systems featuring topologically protected gapless states at their (d-n)-dimensional boundaries. With the help of ab initio calculations and tight-binding models along with symmetry considerations, we show that monolayer buckled honeycomb structures of group-V elements (Sb, As), which have already been synthesized, belong in this category and have a spinless charge fractionalization of $\frac{e}{2}$ at the corner states as well as weak topological edge states, protected by the S 6 symmetry operation, which classify this system as a quadrupole topological insulator. The robustness of these edge and corner states to perturbations is explicitly demonstrated.

36 MATERIALS SCIENCE↗
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↗
DOE OSTI2023

Higher order topological superconductivity in magnet-superconductor hybrid systems

Abstract Quantum engineering of topological superconductors and of the ensuing Majorana zero modes might hold the key for realizing topological quantum computing and topology-based devices. Magnet-superconductor hybrid (MSH) systems have proven to be experimentally versatile platforms for the creation of topological superconductivity by custom-designing the complex structure of their magnetic layer. Here, we demonstrate that higher order topological superconductivity (HOTSC) can be realized in two-dimensional MSH systems by using stacked magnetic structures. We show that the sensitivity of the HOTSC to the particular magnetic stacking opens an intriguing ability to tune the system between trivial and topological phases using atomic manipulation techniques. We propose that the realization of HOTSC in MSH systems, and in particular the existence of the characteristic Majorana corner modes, allows for the implementation of a measurement-based protocols for topological quantum computing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Structural Amorphization-Induced Topological Order

Electronic properties of crystals are inherently pertained to crystalline symmetry, so that amorphization that lowers and breaks symmetry is detrimental. One important crystalline property is electron band topology which is known to be weakened and destroyed by structural disorder. Here, we report a counterintuitive theoretical discovery that atomic structural disorder by amorphization can in fact induce electronic order of topology in an otherwise topologically trivial crystal. The resulting nontrivial topology is characterized by a nonzero spin Bott index, associated with robust topological edge states and quantized conductance. Further, the underlying topological phase transition (TPT) from a trivial crystal to a topological amorphous is analyzed by mapping out a phase diagram in the degree of structural disorder using an effective medium theory. The atomic disorder is revealed to induce topological order by renormalizing the spectral gap toward nontriviality near the phase boundary. As a concrete example, we further show such TPT in amorphous stanane by first-principles calculations. Our findings point to possible observation of an electronic ordering transition accompanied by a structural disorder transition.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Topological order and entanglement dynamics in the measurement-only XZZX quantum code

We examine the dynamics of a ( 1 + 1 ) -dimensional measurement-only circuit defined by the stabilizers of the [[5,1,3]] quantum error correcting code interrupted by single-qubit Pauli measurements. The code corrects arbitrary single-qubit errors and it stabilizes an area law entangled state with a D 2 = Z 2 × Z 2 symmetry protected topological (SPT) order, as well as a symmetry breaking (SB) order from a twofold bulk degeneracy. The Pauli measurements break the topological order and induce a phase transition into a trivial area law phase. Allowing more than one type of Pauli measurement increases the measurement-induced frustration and the SPT and SB order can be broken either simultaneously or separately at nonzero measurement rate. This yields a rich phase diagram and unanticipated critical behavior at the phase transitions. Although the correlation length exponent ν = 4 3 and the dynamical critical exponent z = 1 are consistent with bond percolation, the prefactor of the logarithmic entanglement growth may take noninteger multiples of the percolation value. Remarkably, we identify a robust transient scaling regime for the purification dynamics of L qubits. It reveals a modified dynamical critical exponent z * ≠ z , which is observable up to times t ~ L z * and is reminiscent of the relaxation of critical systems into a prethermal state.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands

Here, we study networks of Coulomb-blockaded integer quantum Hall islands with even fillings ν = 2 k ( k being an integer), including cases with 2 k layers each of ν = 1 fillings. Allowing only spin-current interactions between the islands (i.e., without any charge transfer), we obtain solvable models leading to a rich set of insulating S U ( 2 ) k topologically ordered phases. The case with k = 1 is dual to the Kalmeyer-Laughlin phase, k = 2 to Kitaev's chiral spin liquid and the Moore-Read state, and k = 3 contains a Fibonacci anyon that may be utilized for universal topological quantum computation. Additionally, we show how the S U ( 2 ) k topological phases may be obtained also in an array of islands with ν = 2 k integer quantum Hall states and critical spin chains in a checkerboard pattern. The array and checkerboard constructions gap out the charge mode and additional “flavor” modes by virtue of their geometry. Furthermore, we find that a fine tuning of the system parameter is not needed in the checkerboard configuration and the ν = 2 case. We also discuss their bulk excitations, and show that their thermal Hall conductance is universal, reflecting the central charge c = 3 k / ( k + 2 ) of the chiral edge modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Topological order of the Rys F-model and its breakdown in realistic square spin ice: Topological sectors of Faraday loops

Both the Rys F-model and antiferromagnetic square ice possess the same ordered, antiferromagnetic ground state, but the ordering transition is of second order in the latter, and of infinite order in the former. To tie this difference to topological properties and their breakdown, we introduce a Faraday lines representation where loops carry the energy and magnetization of the system. Because the F-model does not admit monopoles, its Faraday loops have distinct topological properties, absent in square ice, and which allow for a natural partition of its phase space into topological sectors. Then, the Néel temperature corresponds to a transition from topologically trivial to non-trivial Faraday loops. Because magnetization is a homotopy invariant of the Faraday loops, and it is zero for topologically trivial ones, the susceptibility is zero below a critical field. In square spin ice, instead, monopoles destroy the homotopy invariance and the parity distinction among loops, thus erasing this rich topological structure. Consequently, even trivial loops can be magnetized in square ice, and their susceptibility is never zero.

36 MATERIALS SCIENCE↗