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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.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Topological Effects Near Order–Disorder Transitions in Symmetric Diblock Copolymer Melts

The effects of polymer chain topology on the order–disorder transition of symmetric AB diblock copolymer melts are studied using coarse-grained molecular dynamics simulations. Specifically, we compared chain conformations near the lamellar-disordered transition in melts of symmetric (i.e., 50–50) AB diblock copolymers of linear chains, rings, and trefoil knots at the same chain lengths. The order (lamellar)–disorder transition temperature and the domain sizes both shifted to lower values with the introduction of topological constraints, leading to the following sequence: linear chains > rings > trefoil knots. Furthermore, investigation of the polymer chain conformations in terms of their radii of gyration, their writhe values (a measure for the degree of intertwining of a chain around itself), and their Jones polynomials (a method to measure entanglement of curves) showed that linear chains and rings remained stretched, while knots were stretched and tightened in disordered melts close to the lamellar-disorder transition. This work highlights chain topology as an important factor in affecting microphase separation in block copolymers.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Magnetic Breakdown and Topology in the Kagome Superconductor CsV 3 Sb 5 under High Magnetic Field

The recently discovered layered kagome metals of composition AV 3 Sb 5 (A = K, Rb, Cs) exhibit a complex interplay among superconductivity, charge density wave order, topologically nontrivial electronic band structure and geometrical frustration. Here, we probe the electronic band structure underlying these exotic correlated electronic states in CsV 3 Sb 5 with quantum oscillation measurements in pulsed fields up to 86 T. The high-field data reveal a sequence of magnetic breakdown orbits that allows the construction of a model for the folded Fermi surface of CsV 3 Sb 5 . The dominant features are large triangular Fermi surface sheets that cover almost half the folded Brillouin zone. These sheets have not yet been detected in angle resolved photoemission spectroscopy and display pronounced nesting. In conclusion, the Berry phases of the electron orbits have been deduced from Landau level fan diagrams near the quantum limit without the need for extrapolations, thereby unambiguously establishing the nontrivial topological character of several electron bands in this kagome lattice superconductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice

Abstract Quantum loop and dimer models are prototypical correlated systems with local constraints, which are not only intimately connected to lattice gauge theories and topological orders but are also widely applicable to the broad research areas of quantum materials and quantum simulation. Employing our sweeping cluster quantum Monte Carlo algorithm, we reveal the complete phase diagram of the triangular-lattice fully packed quantum loop model. Apart from the known lattice nematic (LN) solid and the even$${{\mathbb{Z}}}_{2}$$ Z 2 quantum spin liquid (QSL) phases, we discover a hidden vison plaquette (VP) phase, which had been overlooked and misinterpreted as a QSL for more than a decade. Moreover, the VP-to-QSL continuous transition belongs to the (2 + 1)D cubic * universality class, which offers a lattice realization of the (fractionalized) cubic fixed point that had long been considered as irrelevant towards the O(3) symmetry until corrected recently by conformal bootstrap calculations. Our results are therefore of relevance to recent developments in both experiments and theory, and facilitate further investigations of hidden phases and transitions.

Physics↗
DOE OSTI2020

A Unified View of Topological Phase Transition in Band Theory

We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Reevaluating the band evolution from an “atomic crystal” (a normal insulator (NI)) to a solid crystal, such as a semiconductor, we demonstrate that there exists ubiquitously an intermediate phase of topological insulator (TI), whose critical transition point displays a linear scaling between electron hopping potential and average bond length, underlined by deformation-potential theory. The validity of the scaling relation is verified in various two-dimensional (2D) lattices regardless of lattice symmetry, periodicity, and form of electron hoppings, based on a generic tight-binding model. Significantly, this linear scaling is shown to set an upper bound for the degree of structural disorder to destroy the topological order in a crystalline solid, as exemplified by formation of vacancies and thermal disorder. Our work formulates a simple framework for understanding the physical nature of TPTs with significant implications in practical applications of topological materials.

42 ENGINEERING↗
DOE OSTI2020

Magic-angle semimetals with chiral symmetry

Here, we construct and solve a two-dimensional, chirally symmetric model of Dirac cones subjected to a quasiperiodic modulation. In real space, this is realized with a quasiperiodic hopping term. This hopping model, as we show, at the Dirac node energy has a rich phase diagram with a semimetal-to-metal phase transition at intermediate amplitude of the quasiperiodic modulation, and a transition to a phase with a diverging density of states (DOS) and subdiffusive transport when the quasiperiodic hopping is strongest. We further demonstrate that the semimetal-to-metal phase transition can be characterized by the multifractal structure of eigenstates in momentum space and can be considered as a unique “unfreezing” transition. This unfreezing transition in momentum space generates flat bands with a dramatically renormalized bandwidth in the metallic phase similar to the phenomena of the band structure of twisted bilayer graphene at the magic angle. We characterize the nature of this transition numerically as well as analytically in terms of the formation of a band of topological zero modes. For pure quasiperiodic hopping, we provide strong numerical evidence that the low-energy DOS develops a divergence and the eigenstates exhibit Chalker (quantum-critical) scaling despite the model not being random. At particular commensurate limits the model realizes higher-order topological insulating phases. We discuss how these systems can be realized in experiments on ultracold atoms and metamaterials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Robustness of topological insulating phase against vacancy, vacancy cluster, and grain boundary bulk defects

One distinguished property of the topological insulator (TI) is its robust quantized edge conductance against edge defect. However, this robustness, underlined by the topological principle of bulk-boundary correspondence, is conditioned by assuming a perfect bulk. Here, we investigate the robustness of the TI phase against bulk defects, including vacancy (VA), vacancy cluster (VC), and grain boundary (GB), instead of edge defect. In this work, based on a tight-binding model analysis, we show that a two-dimensional (2D) TI phase, as characterized by a nonzero spin Bott index, will vanish beyond a critical VA concentration ($n^\text{c}_\text{v}$). Generally, $n^\text{c}_\text{v}$ decreases monotonically with the decreasing topological gap induced by spin-orbit coupling. Interestingly, the $n^\text{c}_\text{v}$ to destroy the topological order, namely, the robustness of the TI phase, is shown to be increased by the presence of VCs but decreased by GBs. As a specific example of a large-gap 2D TI, we further show that the surface-supported monolayer Bi can sustain a nontrivial topology up to $n^\text{c}_\text{v}$ ~ 17%, based on a density-functional theory–Wannier-function calculation. Our findings should provide useful guidance for future experimental studies of effects of defects on TIs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Phase diagram of the three-dimensional subsystem toric code

Subsystem quantum error-correcting codes typically involve measuring a sequence of noncommuting parity check operators. They can sometimes exhibit greater fault tolerance than conventional codes, which use commuting checks. However, unlike subspace codes, it is unclear if subsystem codes—in particular their advantages—can be understood in terms of ground-state properties of a physical Hamiltonian. In this paper, we address this question for the three-dimensional subsystem toric code (3D STC), as recently constructed by Kubica and Vasmer [], which exhibits single-shot error correction. Motivated by a conjectured relation between single-shot properties and thermal stability, we study the zero- and finite-temperature phases of an associated noncommuting Hamiltonian. By mapping the Hamiltonian model to a pair of 3D Z 2 gauge theories coupled by a kinetic constraint, we find various phases at zero temperature, all separated by first-order transitions: There are 3D toric code-like phases with deconfined point-like excitations in the bulk, and there are phases with a confined bulk supporting a 2D toric code on the surface when appropriate boundary conditions are chosen. The latter is similar to the surface topological order present in 3D STC. However, the similarities between the single-shot correction in 3D STC and the confined phases are only partial: they share the same sets of degrees of freedom, but they are governed by different dynamical rules. Instead, we argue that the process of single-shot error correction can more suitably be associated with a path (rather than a point) in the zero-temperature phase diagram, a perspective, which inspires alternative measurement sequences enabling single-shot error correction. Moreover, since none of the above-mentioned phases survives at nonzero temperature, the single-shot error-correction property of the code does not imply thermal stability of the associated Hamiltonian phase. Published by the American Physical Society 2024

Li, Yaodong (ORCID:0000000337421944)↗
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↗
DOE OSTI2022

Microscopic diagnosis of universal geometric responses in fractional quantum Hall liquids

Topological quantum liquids contain internal degrees of freedom that are coupled to geometric response. Yet, an explicit and microscopic identification of the geometric response remains difficult. Here, taking notable fractional quantum Hall (FQH) states as typical examples, we systematically investigate a promising protocol—the Dehn-twist deformation on the torus geometry—to probe the geometric response of correlated topological states and establish the relation between such response and universal properties of pertinent states. Based on analytical derivations and numerical simulations, we find that the geometry-induced Berry phase encodes features for a broad class of FQH states at the Laughlin, hierarchy, Halperin and non-Abelian Moore-Read fillings. Our findings conclusively demonstrate that the adiabatic Dehn-twist deformation can faithfully capture rich geometric and topological information, including the Hall viscosity and topological spin of the pertinent FQH state and the chiral central charge of the underlying edge conformal field theory. Our approach provides a powerful way to reveal topological orders of generic FQH states and address previously open questions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model

Here we consider a paradigmatic solvable model of topological order in two dimensions, Kitaev's honeycomb Hamiltonian, and turn it into a measurement-only dynamics consisting of stochastic measurements of two-qubit bond operators. We find an entanglement phase diagram that resembles that of the Hamiltonian problem in some ways, while being qualitatively different in others. When one type of bond is dominantly measured, we find area-law entangled phases that protect two topological qubits (on a torus) for a time exponential in system size. This generalizes the recently proposed idea of Floquet codes, where logical qubits are dynamically generated by a time-periodic measurement schedule, to a stochastic setting. When all types of bonds are measured with comparable frequency, we find a critical phase with a logarithmic violation of the area law, which sharply distinguishes it from its Hamiltonian counterpart. The critical phase has the same set of topological qubits, as diagnosed by the tripartite mutual information, but protects them only for a time polynomial in system size. Furthermore, we observe an unusual behavior for the dynamical purification of mixed states, characterized at late times by the dynamical exponent z = $\frac{1}{2}$ a superballistic dynamics made possible by measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Quantum materials for nanosensing and fault-tolerant quantum computing

New concepts of symmetry related to topological order emerged from the discovery of the fractional quantum Hall effect and high-temperature superconductivity in strongly correlated electron systems. This led to the study of quantum materials-- materials exhibiting emergent quantum phenomena with no classical analogues. While these materials have engendered exciting basic materials science and physics, realizing novel devices is a key challenge in the field. The goal of this proposal is to harness the unique properties of topological materials for quantum computing and quantum sensing applications. In this project, we investigated a variety of topological superconducting platforms and identified three technologies that can benefit from their quantum properties: quantum memory, single-photon detection, and non reciprocal electronics. The platforms developed in this work will be broadly useful to National Security and Basic Science.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Tuning Electronic Properties of 2D Materials Using Metal Adsorbates: Cu at WTe 2 Edges

Two-dimensional materials exhibit properties promising for novel applications. Topologically protected states at their edges can be harnessed for use in quantum devices. We use ab initio simulations to examine properties of edges in 1T'-WTe 2 monolayers, known to exhibit topological order, and their interactions with Cu atoms. Comparison of (010)-oriented edges that have the same composition but different terminations shows that, as the number of Cu atoms increases, their thermodynamically-preferred arrangement depends on the details of the edge structure. Cu atoms aggregate into a cluster at the most stable edge; while the cluster is non-magnetic, it spin-polarizes the W atoms along the edge, which removes the topological protection. At the metastable edge, Cu atoms form a chain incorporated into the WTe 2 lattice; the topological state is preserved in spite of the dramatic edge restructuring. This suggests that exploiting interactions of metal species with metastable edge terminations can provide a path towards non-invasive interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Codimension-2 defects and higher symmetries in (3+1)D topological phases

(3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error-correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of \mathbb{Z}_2 ℤ 2 gauge theory with fermionic charges, in \mathbb{Z}_2 \times \mathbb{Z}_2 ℤ 2 × ℤ 2 gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral ( D_n D n ) and alternating ( A_6 A 6 ) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H^4 H 4 cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of the interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D A_6 A 6 gauge theory.

Barkeshli, Maissam↗
DOE OSTI2021

Freestanding Ferroelectric Bubble Domains

Bubble-like domains, typically a precursor to the electrical skyrmions, arise in ultrathin complex oxide ferroelectric-dielectric-ferroelectric heterostructures epitaxially clamped with flat substrates. Here, it is reported that these specially ordered electric dipoles can also be retained in a freestanding state despite the presence of inhomogeneously distributed structural ripples. By probing local piezo and capacitive responses and using atomistic simulations, this study analyzes these ripples, sheds light on how the bubbles are stabilized in the modified electromechanical energy landscape, and discusses the difference in morphology between bubbles in freestanding and as-grown states. Furthermore, these results are anticipated to be the starting point of a new paradigm for the exploration of electric skyrmions with arbitrary boundaries and physically flexible topological orders in ferroelectric curvilinear space.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Triangular lattice quantum dimer model with variable dimer density

Abstract Quantum dimer models are known to host topological quantum spin liquid phases, and it has recently become possible to simulate such models with Rydberg atoms trapped in arrays of optical tweezers. Here, we present large-scale quantum Monte Carlo simulation results on an extension of the triangular lattice quantum dimer model with terms in the Hamiltonian annihilating and creating single dimers. We find distinct odd and even $${{\mathbb{Z}}}_{2}$$ Z 2 spin liquids, along with several phases with no topological order: a staggered crystal, a nematic phase, and a trivial symmetric phase with no obvious broken symmetry. We also present dynamic spectra of the phases, and note implications for experiments on Rydberg atoms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Higher-rank tensor field theory of non-abelian fracton and embeddon

We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our theory describes a mixed unitary phase interplaying between gapless and gapped topological order phases (which can live with or without Euclidean, Poincaré, or anisotropic symmetry, at least in ultraviolet high or intermediate energy field theory, but not yet to a lattice cutoff scale). The “gauge structure” can be compact, continuous, abelian or non-abelian. Our theory sits outside the paradigm of Maxwell electromagnetic theory in 1865 and Yang–Mills isospin/color theory in 1954. We discuss its local gauge transformation in terms of the ungauged vector-like or tensor-like higher-moment global symmetry. The non-abelian gauge structure is caused by gauging the non-commutative symmetries: a higher-moment symmetry and a charge conjugation (particle–hole) symmetry. Vector global symmetries along time direction may exhibit time crystals. We explore the relation of these long-range entangled matters to a non-abelian generalization of Fracton order in condensed matter, a field theory formulation of foliation, the spacetime embedding and Embeddon that we newly introduce, and possible fundamental physics applications to dark matter or dark energy.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Subterahertz collective dynamics of polar vortices

The collective dynamics of topological structures are of interest from both fundamental and applied perspectives. For example, studies of dynamical properties of magnetic vortices and skyrmions have not only deepened our understanding of many-body physics but also offered potential applications in data processing and storage. Topological structures constructed from electrical polarization, rather than electron spin, have recently been realized in ferroelectric superlattices, and these are promising for ultrafast electric-field control of topological orders. However, little is known about the dynamics underlying the functionality of such complex extended nanostructures. In this study, using terahertz-field excitation and femtosecond X-ray diffraction measurements, we observe ultrafast collective polarization dynamics that are unique to polar vortices, with orders-of-magnitude higher frequencies and smaller lateral size than those of experimentally realized magnetic vortices. A previously unseen tunable mode, hereafter referred to as a vortexon, emerges in the form of transient arrays of nanoscale circular patterns of atomic displacements, which reverse their vorticity on picosecond timescales. Its frequency is considerably reduced (softened) at a critical strain, indicating a condensation (freezing) of structural dynamics. We use first-principles-based atomistic calculations and phase-field modelling to reveal the microscopic atomic arrangements and corroborate the frequencies of the vortex modes. The discovery of subterahertz collective dynamics in polar vortices opens opportunities for electric-field-driven data processing in topological structures with ultrahigh speed and density.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A quantum liquid of magnetic octupoles on the pyrochlore lattice

Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles. Theories define such states using gauge fields and deconfined quasiparticle excitations that emerge from a local constraint governing the ground state of a frustrated magnet. For example, the ‘2-in–2-out’ ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice in rare-earth pyrochlores. However, $f$-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and ‘hidden’ orders. In this paper we show that the correlated ground state of a Ce 3+ -based pyrochlore, Ce 2 Sn 2 O 7 , is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with a fluid-like state where degrees of freedom have a more complex magnetization density than that of magnetic dipoles. The nature and strength of the octupole–octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a ‘2-plus–2-minus’ rule. Our work identifies Ce 2 Sn 2 O 7 as a unique example of frustrated multipoles forming a ‘hidden’ topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.

36 MATERIALS SCIENCE↗