Topological Origin Research Articles

Topological Gaseous Plasmon Polariton in Realistic Plasma.

Nontrivial topology in bulk matter has been linked with the existence of topologically protected interfacial states. We show that a gaseous plasmon polariton (GPP), an electromagnetic surface wave existing at the boundary of magnetized plasma and vacuum, has a topological origin that arises from the nontrivial topology of magnetized plasma. Because a gaseous plasma cannot sustain a sharp interface with discontinuous density, one must consider a gradual density falloff with scale length comparable to or longer than the wavelength of the wave. We show that the GPP may be found within a gapped spectrum in present-day laboratory devices, suggesting that platforms are currently available for experimental investigation of topological wave physics in plasmas.

One-Dimensional Edge Transport in Few-Layer WTe2.

WTe2 is a layered transitional-metal dichalcogenide (TMD) with a number of intriguing topological properties. Recently, WTe2 has been predicted to be a higher-order topological insulator (HOTI) with topologically protected hinge states along the edges. The gapless nature of WTe2 complicates the observation of one-dimensional (1D) topological states in transport due to their small contribution relative to the bulk. Here, we study the behavior of the Josephson effect in magnetic field to distinguish edge from bulk transport. The Josephson effect in few-layer WTe2 reveals 1D states residing on the edges and steps. Moreover, our data demonstrates a combination of Josephson transport properties observed solely in another HOTI—bismuth, including Josephson transport over micrometer distances, extreme robustness in a magnetic field, and nonsinusoidal current-phase relation (CPR). Our observations strongly suggest the topological origin of the 1D states and that few-layer WTe2 is a HOTI.

Is the cosmological constant of topological origin?

The observed value of the cosmological constant poses large theoretical problems. We find that topology of the Universe provides a natural source for it. Restricting dynamically an Einstein-Cartan gravity to General Relativity in our observed Universe allows topological invariants to induce an effective cosmological constant from dynamical quintessence-like topological fields. Its evaluation through the boundary of black holes yields a range compatible with the observed value, with uncertainty of three orders of magnitude. In turns, it provides a measurement of the Universe's isoperimetric constant.

Quadrupolar flows around spots in internal shear flows

Turbulent spots occur in shear flows confined between two walls and are surrounded by robust quadrupolar flows. Although the far-field decay of such large-scale flows has been reported to be exponential, we predict a different algebraic decay for the case of plane Couette flow. We address this problem theoretically, by modelling an isolated spot as an obstacle in a linear plane shear flow with free-slip boundary conditions at the walls. By seeking invariant solutions in a co-moving Lagrangian frame and using geometric scale separation, a set of differential equations governing large-scale flows is derived from the Navier–Stokes equations and solved analytically. The wall-normal velocity turns out to be exponentially localised in the plane, while the quadrupolar in-plane velocity field, after wall-normal averaging, features a superposition of algebraic and exponential decays. The algebraic decay exponent is . The quadrupolar angular dependence stems from (i) the shearing of the streamwise velocity and (ii) the breaking of the spanwise homogeneity. Near the spot, exponentially decaying solutions can generate reversed quadrupolar flows. Eventually, by noting that the algebraically decaying in-plane flow is two-dimensional and harmonic, we suggest a topological origin to the quadrupolar large-scale flow.

Field-free platform for Majorana-like zero mode in superconductors with a topological surface state

Superconducting materials exhibiting topological properties are emerging as an exciting platform to realize fundamentally new excitations from topological quantum states of matter. In this work, we explore the possibility of a field-free platform for generating Majorana zero energy excitations by depositing magnetic Fe impurities on the surface of candidate topological superconductors, LiFeAs and PbTaSe$_2$. We use scanning tunneling microscopy to probe localized states induced at the Fe adatoms on the atomic scale and at sub-Kelvin temperatures. We find that each Fe adatom generates a striking zero-energy bound state inside the superconducting gap, which do not split in magnetic fields up to 8T, underlining a nontrivial topological origin. Our findings point to magnetic Fe adatoms evaporated on bulk superconductors with topological surface states as a new platform for exploring Majorana zero modes and quantum information science under field-free conditions.

Universal momentum-to-real-space mapping of topological singularities

Topological properties of materials are typically presented in momentum space. Here, we demonstrate a universal mapping of topological singularities from momentum to real space. By exciting Dirac-like cones in photonic honeycomb (pseudospin-1/2) and Lieb (pseudospin-1) lattices with vortex beams of topological charge l, optimally aligned with a given pseudospin state s, we directly observe topological charge conversion that follows the rule l → l + 2s. Although the mapping is observed in photonic lattices where pseudospin-orbit interaction takes place, we generalize the theory to show it is the nontrivial Berry phase winding that accounts for the conversion which persists even in systems where angular momentum is not conserved, unveiling its topological origin. Our results have direct impact on other branches of physics and material sciences beyond the 2D photonic platform: equivalent mapping occurs for 3D topological singularities such as Dirac-Weyl synthetic monopoles, achievable in mechanical, acoustic, or ultracold atomic systems, and even with electron beams.

Topologically induced prescrambling and dynamical detection of topological phase transitions at infinite temperature

We report a numerical observation where the infinite-temperature out-of-time-order correlators (OTOCs) directly probe quantum phase transitions at zero temperature, in contrast to common intuition where low energy quantum effects are washed away by strong thermal fluctuations at high temperature. By comparing numerical simulations with exact analytic results, we determine that this phenomenon has a topological origin and is highly generic, as long as the underlying system can be mapped to a 1D Majorana chain. Using the Majorana basis, we show that the infinite-temperature OTOCs probe zero-temperature quantum phases via detecting the presence of Majorana zero modes at the ends of the chain that is associated with 1D $Z_2$ topological order. Hence, we show that strong zero modes also affect OTOCs and scrambling dynamics. Our results demonstrate an intriguing interplay between information scrambling and topological order, which leads to a new phenomenon in the scrambling of generic nonintegrable models: topological order induced prescrambling, paralleling the notion of prethermalization of two-time correlators, that defines a time-scale for the restricted scrambling of topologically-protected quantum information.

Spontaneous Hall effect enhanced by local Ir moments in epitaxial Pr2Ir2O7 thin films

Rare earth pyrochlore Iridates (RE2Ir2O7) consist of two interpenetrating cation sublattices, the RE with highly-frustrated magnetic moments, and the Iridium with extended conduction orbitals significantly mixed by spin-orbit interactions. The coexistence and coupling of these two sublattices create a landscape for discovery and manipulation of quantum phenomena such as the topological Hall effect, massless conduction bands, and quantum criticality. Thin films allow extended control of the material system via symmetry-lowering effects such as strain. While bulk Pr2Ir2O7 shows a spontaneous hysteretic Hall effect below 1.5K, we observe the effect at elevated temperatures up to 15K in epitaxial thin films on (111) YSZ substrates synthesized via solid phase epitaxy. Similar to the bulk, the lack of observable long-range magnetic order in the thin films points to a topological origin. We use synchrotron-based element-specific x-ray diffraction (XRD) and x-ray magnetic circular dichroism (XMCD) to compare powders and thin films to attribute the spontaneous Hall effect in the films to localization of the Ir moments. We link the thin film Ir local moments to lattice distortions absent in the bulk-like powders. We conclude that the elevated-temperature spontaneous Hall effect is caused by the topological effect originating either from the Ir or Pr sublattice, with interaction strength enhanced by the Ir local moments. This spontaneous Hall effect with weak net moment highlights the effect of vanishingly small lattice distortions as a means to discover topological phenomena in metallic frustrated magnetic materials.

Topological Origin of Non-Hermitian Skin Effects.

A unique feature of non-Hermitian systems is the skin effect, which is the extreme sensitivity to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non-Hermitian topology. Such a topological origin not merely explains the universal feature of the known skin effect, but also leads to new types of the skin effects-symmetry-protected skin effects. In particular, we discover the Z_{2} skin effect protected by time-reversal symmetry. On the basis of topological classification, we also discuss possible other skin effects in arbitrary dimensions. Our work provides a unified understanding about the bulk-boundary correspondence and the skin effects in non-Hermitian systems.

Evolving complexity: how tinkering shapes cells, software and ecological networks.

A common trait of complex systems is that they can be represented by means of a network of interacting parts. It is, in fact, the network organization (more than the parts) that largely conditions most higher-level properties, which are not reducible to the properties of the individual parts. Can the topological organization of these webs provide some insight into their evolutionary origins? Both biological and artificial networks share some common architectural traits. They are often heterogeneous and sparse, and most exhibit different types of correlations, such as nestedness, modularity or hierarchical patterns. These properties have often been attributed to the selection of functionally meaningful traits. However, a proper formulation of generative network models suggests a rather different picture. Against the standard selection-optimization argument, some networks reveal the inevitable generation of complex patterns resulting from reuse and can be modelled using duplication-rewiring rules lacking functionality. These give rise to the observed heterogeneous, scale-free and modular architectures. Here, we examine the evidence for tinkering in cellular, technological and ecological webs and its impact in shaping their architecture. Our analysis suggests a serious consideration of the role played by selection as the origin of network topology. Instead, we suggest that the amplification processes associated with reuse might shape these graphs at the topological level. In biological systems, selection forces would take advantage of emergent patterns. This article is part of the theme issue 'Unifying the essential concepts of biological networks: biological insights and philosophical foundations'.

Tunable charged domain wall from topological confinement in nodal-line semimetals

We study theoretically the electronic structure of topological nodal-line semimetals. We show that, in the presence of a gap-opening spatially dependent mass term that forms a domain wall, an in-gap charged localized mode emerges at the domain wall. It turns out that such a domain wall is realized by head-to-head (or tail-to-tail) bulk electric polarizations. The localized mode has a topological origin, i.e., a topological confinement is realized, which is understood by a semiclassical topological number defined in the semiclassical momentum-real space. In contrast to previous studies, our study demonstrates a topological confinement at the interface between two insulators without bulk topological numbers. Moreover, the dispersion of the localized mode evolves from gapless to gapped as the bulk bandgap increases, which means that its conductivity is externally tunable. We discuss a possible experimental realization of the stable, electrically-tunable charged domain wall.

Intrinsic Anomalous Hall Effect in Ni-Substituted Magnetic Weyl Semimetal Co3Sn2S2.

Topological Weyl semimetals have recently attracted considerable attention among materials scientists as their properties are predicted to be protected against perturbations such as lattice distortion and chemical substitution. However, any experimental proof of such robustness is still lacking. In this study, we experimentally demonstrate that the topological properties of the ferromagnetic kagomé compound Co3Sn2S2 are preserved upon Ni substitution. We systematically vary the Ni content in Co3Sn2S2 single crystals and study their magnetic and anomalous transport properties. For the intermediate Ni substitution, we observe a remarkable increase in the coercive field while still maintaining significant anomalous Hall conductivity. The large anomalous Hall conductivity of these compounds is intrinsic, consistent with first-principles calculations, which proves its topological origin. Our results can guide further studies on the chemical tuning of topological materials for better understanding.

Magnetic properties of layered chiral topological magnetic material Cr<sub>1/3</sub>NbS<sub>2</sub>

With the discovery and development of topological materials, topological physics has attracted enormous research interest in the fields of contemporary condensed matter physics. Topological property, which describes such a property that physical quantity remains invariant under continuous transformation (such as Chern number), has been revealed in a variety of materials, including topological insulators, topological semimetals (such as Weyl or Dirac semimetals), topological magnetic materials, etc. One-dimensional chiral magnetic soliton, similar to magnetic skyrmion, is a type of magnetic configuration with topological origin and quasi-particle property, which has shown tremendous physical properties and device functionalities. In this review, we mainly focus on a chiral helimagnet, called Cr<sub>1/3</sub>NbS<sub>2</sub>, which possesses chiral magnetic soliton lattice and other more spin configurations under different conditions. We systematically summarize the work on Cr<sub>1/3</sub>NbS<sub>2</sub>, discussing its crystal symmetry, band structure, magnetic interactions, rich magnetic phases, and the physics of associated phase transitions. In particular, the layered crystal structure of Cr<sub>1/3</sub>NbS<sub>2</sub> enables us to control the soliton number through tuning the layer number or crystal thickness. Our review provides a comprehensive summary of Cr<sub>1/3</sub>NbS<sub>2</sub> in order to draw more attention to this interesting material. Moreover, we envision that our work could offer useful guidance to the researchers working on topological and chiral magnetic materials, and thus introducing topological or chiral magnetism into two-dimensional layered materials and promoting the development of modern magnetism and spintronics. Therefore, this review mainly focuses on a magnet, called Cr<sub>1/3</sub>NbS<sub>2</sub>. We systematically summarize the work on Cr<sub>1/3</sub>NbS<sub>2</sub>, discussing its crystal symmetry, band structure, magnetic interaction, rich magnetic phases and the interesting physical phenomena occurring at each phase transition. In addition, the layered crystal structure of Cr<sub>1/3</sub>NbS<sub>2</sub> also enables us to use the layer number or crystal thickness to modulate and control its rich magnetic phases. We believe that our review provides a comprehensive summary of Cr<sub>1/3</sub>NbS<sub>2</sub>, which can make people have a better understanding of a typical topological magnetic material, thereby enriching the material types of magnets and low-dimensional material family and promoting the development of magnetism and spintronics applications, such as in magnetic memory devices, spintronic devices, and quantum information devices.

Exploration of Majorana bound states in topological superconductors

Majorana bound states are considered useful for realizing topological quantum computation since they obey the non-Abelian quantum statistics. Recent experiments have provided evidences for their existence in some superconducting systems, triggering significant interests from scientists in the field of condensed matter physics and related materials science. In this article, we briefly review the basic concepts and recent developments in the study of Majorana bound states. We first discuss about the origin of the nontrivial topology in superconducting systems within the Bogoliubov-de Gennes mean-field scheme. Then we show the construction of Majorana quasiparticle excitations from an electronic state, and the realization of non-Abelian statistics based on position exchanges of the Majorana bound states hosted in superconductivity vortices. Afterwards we talk about specific one-dimensional and two-dimensional topological superconductors, and propose possible experimental methods for detecting Majorana bound states and operating the Majorana qubits. In particular, a quantum device for Majorana braiding without moving vortices is introduced. Finally, perspectives of the study on Majorana bound states are provided.

General nature of the step-induced frustration at ferromagnetic/antiferromagnetic interfaces: topological origin and quantitative understanding

We present a study of the magnetic configuration due to step-induced magnetic frustration at ferromagnetic/antiferromagnetic (FM/AFM) interfaces. At a substrate monatomic step edge, a 180° domain wall emerges. A physically appealing form for the thickness dependence of the domain wall width is obtained. It follows a universal behaviour in the whole thickness range, from ultrathin film to bulk and in both cases of an AFM domain wall on top of the FM layer and a FM domain wall on top of an AFM substrate. In the ultrathin limit of the capping layer, the domain wall grows linearly with the slope depending only on the ratio of the inter-layer and intra-layer Heisenberg exchange constants, regardless of the presence of magneto-crystalline anisotropy. These findings are in good agreement with previous experimental observations. As the thickness grows beyond the ultrathin regime, the corresponding thickness dependence departs from linearity and tends to its bulk value. The analytical insights are supported by conclusive numerical simulations of two independent varieties, namely, the Monte Carlo method which also includes the growth kinetics and the object oriented micromagnetic framework based micromagnetic simulations. While the quantitative details of the study are naturally dependent on the specific material parameters of the complex magnetic system, the global features of the spin texture in the capping layer are dictated by the topological step-edge defect. The latter in itself is quantifiable by a winding number of

Topological phase transition and tunable electronic properties of hydrogenated bismuthene: from single-layer to double-layer

Planar bismuthene grown on SiC substrate provides a promising candidate to engineer van der Waals double-layer (DL) made of two dimensional (2D) topological insulators. We perform systematical calculations in DL hydrogenated bismuthene (H-Bi) that can be used to simulate the experimentally grown planar bismuthene to explore realizable 2D topological insulator van der Waals DL. Two possible geometry configurations of AA- and AB-stacked DL H-Bi are investigated. Due to pseudo Jahn-Teller effect, AB-stacked DL H-Bi has a strong interlayer coupling interaction and shows buckled lattice. Particularly, both AA- and AB-stacked DL H-Bi are topologically trivial rather than topologically nontrivial. The physical origin of the trivial topology is clarified by analyzing orbital composition. We discuss how the electronic properties are modified by interlayer coupling, external strain, and metal atom intercalation. It is also found that, for AB-stacked DL H-Bi, metal atom intercalation gives rise to novel multiple Rashba splitting near the valence band top, which is expected to manipulate the same spin in different planar bismuthene layers. Our results present various and tunable electronic properties of van der Waals DL H-Bi and allow for probing into multiple Rashba effect in 2D inversion-asymmetric topological insulators.

Higher-Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures.

We show, theoretically, that a heterostructure of monolayer FeTe_{1-x}Se_{x}-a superconducting quantum spin Hall material-with a monolayer of FeTe-a bicollinear antiferromagnet-realizes a higher order topological superconductor phase characterized by emergent Majorana zero modes pinned to the sample corners. We provide a minimal effective model for this system, analyze the origin of higher order topology, and fully characterize the topological phase diagram. Despite the conventional s-wave pairing, we find a rather surprising emergence of a novel topological nodal superconductor in the phase diagram. Featured by edge-dependent Majorana flat bands, the topological nodal phase is protected by an antiferromagnetic chiral symmetry. We also discuss the experimental feasibility, the estimation of realistic model parameters, and the robustness of the Majorana corner modes against magnetic and potential disorder. Our work provides a new experimentally feasible high-temperature platform for both higher order topology and non-Abelian Majorana physics.

A new strategy to microscopic modeling of topological entanglement in polymers based on field theory

In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of the so-called numerical topological invariants. For each invariant it is possible to derive a field theory that describes the statistical behavior of knotted and linked polymer rings following a straightforward algorithm. The treatment is not limited to the partition function of the system, but it allows also to express the expectation values of general observables as field theory amplitudes.Our strategy is illustrated taking as examples the Gauss linking number and a topological invariant belonging to a class of invariants due to Massey. The consistency of the new method developed here is checked by reproducing a previous field theoretical model of two linked polymer rings. After the passage to field theory, the original topological constraints imposed on the fluctuating paths of the polymers become constraints over the configurations of the topological fields that mediate the interactions of topological origin between the monomers. These constraints involve quantities like the cross-helicity which are of interest in other disciplines, like for instance in modeling the solar magnetic field.While the calculation of the expectation values of generic observables remains still challenging due to the complexity of the problem of topological entanglement in polymer systems, we succeed here to reduce the evaluation of the moments of the Gauss linking number for two linked polymer rings to the computation of the amplitudes of a free field theory.

Klein-Gordon Representation of Acoustic Waves and Topological Origin of Surface Acoustic Modes.

Recently, it was shown that surface electromagnetic waves at interfaces between continuous homogeneous media (e.g., surface plasmon-polaritons at metal-dielectric interfaces) have a topological origin [K. Y. Bliokh etal., Nat. Commun. 10, 580 (2019)NCAOBW2041-172310.1038/s41467-019-08397-6]. This is explained by the nontrivial topology of the non-Hermitian photon helicity operator in the Weyl-like representation of Maxwell equations. Here we analyze another type of classical waves: longitudinal acoustic waves corresponding to spinless phonons. We show that surface acoustic waves, which appear at interfaces between media with opposite-sign densities, can be explained by similar topological features and the bulk-boundary correspondence. However, in contrast to photons, the topological properties of sound waves originate from the non-Hermitian four-momentum operator in the Klein-Gordon representation of acoustic fields.

Topological Origins of the Mixed Alkali Effect in Glass

The mixed alkali effect, the deviation from expected linear property changes when alkali ions are mixed in a glass, remains a point of contention in the glass community. While several earlier models have been proposed to explain mixed alkali effects on ionic motion, models based on or containing discussion of structural aspects of mixed-alkali glasses remain rare by comparison. However, the transition-range viscosity depression effect is many orders in magnitude for mixed-alkali glasses, and the original observation of the effect (then known as the Thermometer Effect) concerned the highly anomalous temperature dependence of stress and structural relaxation time constants. With this in mind, a new structural model based on topological constraint theory is proposed herein which elucidates the origin of the mixed alkali effect as a consequence of network strain due to differing cation radii. Discussion of literature models and data alongside new molecular dynamics simulations and experimental data are presented in support of the model, with good agreement.