Topological Behavior Research Articles

Topological Anderson Insulator in Cation-Disordered Cu2ZnSnS4.

We present the first candidate for the realization of a disorder-induced Topological Anderson Insulator in a real material system. High-energy reactive mechanical alloying produces a polymorph of Cu2ZnSnS4 with high cation disorder. Density functional theory calculations show an inverted ordering of bands at the Brillouin zone center for this polymorph, which is in contrast to its ordered phase. Adiabatic continuity arguments establish that this disordered Cu2ZnSnS4 can be connected to the closely related Cu2ZnSnSe4, which was previously predicted to be a 3D topological insulator, while band structure calculations with a slab geometry reveal the presence of robust surface states. This evidence makes a strong case in favor of a novel topological phase. As such, the study opens up a window to understanding and potentially exploiting topological behavior in a rich class of easily-synthesized multinary, disordered compounds.

Additive manufacturing of channeled acoustic topological insulators.

We propose and fabricate an acoustic topological insulator to channel sound along statically reconfigurable pathways. The proposed topological insulator exploits additive manufacturing to create unit cells with complex geometry designed to introduce topological behavior while reducing attenuation. We break spatial symmetry in a hexagonal honeycomb lattice structure composed of a unit cell with two rounded cylindrical chambers by altering the volume of each chamber, and thus, observe the quantum valley Hall effect when the Dirac cone at the K-point lifts to form a topologically protected bandgap. Moderately protected edge states arise at the boundary between two regions with opposite orientations. The resulting propagation of a topologically protected wave along the interface is predicted computationally and validated experimentally. This represents a first step towards creating reconfigurable, airborne topological insulators that can lead to promising applications, such as four-dimensional sound projection, acoustic filtering devices, or multiplexing in harsh environments.

Quasiparticle twist dynamics in non-symmorphic materials

Quasiparticle physics underlies our understanding of the microscopic dynamical behaviors of materials that govern a vast array of properties, including structural stability, excited states and interactions, dynamical structure factors, and electron and phonon conductivities. Thus, understanding band structures and quasiparticle interactions is foundational to the study of condensed matter. Here we advance a ‘twist’ dynamical description of quasiparticles (including phonons and Bloch electrons) in non-symmorphic chiral and achiral materials. Such materials often have structural complexity, strong thermal resistance, and efficient thermoelectric performance for waste heat capture and clean refrigeration technologies. The twist dynamics presented here provides a novel perspective of quasiparticle behaviors in such complex materials, in particular highlighting how non-symmorphic symmetries determine band crossings and anti-crossings, topological behaviors, quasiparticle interactions that govern transport, and observables in scattering experiments. We provide specific context via neutron scattering measurements and first-principles calculations of phonons and electrons in chiral tellurium dioxide. Building twist symmetries into the quasiparticle dynamics of non-symmorphic materials offers intuition into quasiparticle behaviors, materials properties, and guides improved experimental designs to probe them. More specifically, insights into the phonon and electron quasiparticle physics presented here will enable materials design strategies to control interactions and transport for enhanced thermoelectric and thermal management applications.

An Unsupervised Approach for Detecting Group Shilling Attacks in Recommender Systems Based on Topological Potential and Group Behaviour Features

To protect recommender systems against shilling attacks, a variety of detection methods have been proposed over the past decade. However, these methods focus mainly on individual features and rarely consider the lockstep behaviours among attack users, which suffer from low precision in detecting group shilling attacks. In this work, we propose a three-stage detection method based on strong lockstep behaviours among group members and group behaviour features for detecting group shilling attacks. First, we construct a weighted user relationship graph by combining direct and indirect collusive degrees between users. Second, we find all dense subgraphs in the user relationship graph to generate a set of suspicious groups by introducing a topological potential method. Finally, we use a clustering method to detect shilling groups by extracting group behaviour features. Extensive experiments on the Netflix and sampled Amazon review datasets show that the proposed approach is effective for detecting group shilling attacks in recommender systems, and the F1-measure on two datasets can reach over 99 percent and 76 percent, respectively.

Field-free topological behavior in the magnetic domain wall of ferrimagnetic GdFeCo

Exploring and controlling topological textures such as merons and skyrmions has attracted enormous interests from the perspective of fundamental research and spintronic applications. It has been predicted theoretically and proved experimentally that the lattice form of topological meron-skyrmion transformation can be realized with the requirement of external magnetic fields in chiral ferromagnets. However, such topological transition behavior has yet to be verified in other materials. Here, we report real-space observation of magnetic topology transformation between meron pairs and skyrmions in the localized domain wall of ferrimagnetic GdFeCo films without the need of magnetic fields. The topological transformation in the domain wall of ferrimagnet is introduced by temperature-induced spin reorientation transition (SRT) and the underlying mechanism is revealed by micromagnetic simulations. The convenient electric-controlling topology transformation and driving motion along the confined domain wall is further anticipated, which will enable advanced application in magnetic devices.

Unraveling peculiar magnetism and band topology in Mn3Sb

Magnetic, pseudogap, topological, magnetostructural, and elastic behaviors of Mn3Sb have been unraveled. The ferrimagnetism (FIM) is described by localized and delocalized electron magnetism resulting in different magnetic moments on Mn atoms, confirming the neutron diffraction data. The identified magnetostructural properties are due to the non-equivalent Mn atoms in its lowest symmetry structure. The electronic structure is also unique due to variable valance states of Mn atoms. The magnetic moment (4.10 μB) of non-equivalent Mn1 atom is antiparallely aligned with the magnetic moments (2.34 μB) of Mn2 and Mn3 atoms. The estimated Curie temperature, TC, is higher than the room temperature, which may have above the room temperature applications in spintronic devices. The band structure and density of states (DOS) show the characteristics of band topology (opening of a gap in Dirac-like band features) and pseudo-gap, respectively, around the Fermi level. While expanding the unit cell, the tetragonal FIM ground state transforms to the cubic primitive FIM phase, however, the contraction transforms it to the L12 ferromagnetic (FM) phase. The estimated elastic constants, bulk to shear modulus ratio, and elastic anisotropy factor indicate that Mn3Sb exhibits mechanically stable, ductile, and anisotropic behaviors, respectively.

Characterization and topological behavior of homomorphism tree-shifts

The purpose of this article is twofold. On one hand, we reveal the equivalence of shift of finite type between a one-sided shift X and its associated hom tree-shift TX, as well as the equivalence in the sofic shift. On the other hand, we investigate the interrelationship among the comparable mixing properties on tree-shifts as those on multidimensional shift spaces. They include irreducibility, topologically mixing, block gluing, and strong irreducibility, all of which are defined in the spirit of classical multidimensional shift, complete prefix code (CPC), and uniform CPC. In summary, the mixing properties defined in all three manners coincide for TX. Furthermore, an equivalence between irreducibility on TA and irreducibility on XA are seen, and so is one between topologically mixing on TA and mixing property on XA, where XA is the one-sided shift space induced by the matrix A and TA is the associated tree-shift. These equivalences are consistent with the mixing properties on X or XA when viewed as a degenerate tree-shift.

Cryogenic Electron Microscopy on Strongly Correlated Quantum Materials.

ConspectusQuantum materials refers to a class of materials with exotic properties that arise from the quantum mechanical nature of their constituent electrons, exhibiting, for example, high-temperature superconductivity, colossal magnetoresistivity, multiferroicity, and topological behavior. Quantum materials often have incompletely filled d- or f-electron shells with narrow energy bands, and the conduct of their electrons is strongly correlated. One distinct characteristic of the materials is that their electronic states are often spatially inhomogeneous and thus well suited for study using a spatially resolved electron beam with its great scattering power and sensitivity to atomic ionicity. Furthermore, most of these exotic properties only manifest at very low temperatures, posing a challenge to modern electron microscopy. It requires extraordinarily instrument stabilities at cryogenic temperatures with critical spatial, temporal, and energy resolutions in both static and dynamic manner to probe these materials. On the other hand, the ability to directly visualize the atomic, electronic and spin structures and inhomogeneities of quantum materials and correlate them to their functionalities creates enormous opportunities. At the most elementary levels of condensed matter physics, understanding the competing order of electron, spin, orbital, and lattice and their degrees of freedom, the impacts of defects and interfaces, and the site-specific quantum phenomena and phase transitions that give rise to the emergent behaviors allows us to discover and control novel materials for quantum information science and technologies.In this Account, several of our research examples are selected to highlight the use of cryogenic electron microscopy (cryo-EM) to study strongly correlated quantum materials. We focus on the critical roles of heterogeneity, interfaces, defects, and disorder in crystal structure, magnetic structure, and electronic structure to understand the physical properties of the materials that cryo-EM enables. We show how electron crystallography coupled with Bragg diffraction and diffuse scattering analysis empowers us to reveal the nature of structural modulations, lattice distortion, and phonons and how quantitative electron diffraction can be used to map the distributions of the valence electrons that bond atoms together. We exploit transformative advances in imaging capabilities including the use of femtosecond laser and ultrafast electron diffraction to probe electron-lattice interactions and photoinduced transitions beyond equilibrium of matter. We review our Lorentz phase microscopy studies to illustrate the intriguing transformations among various topological chiral spin states under applied magnetic field at various cryogenic temperatures. Finally, we show that atomically resolved imaging and electron energy-loss spectroscopy at 10 K can be used to understand interface-enhanced superconductivity. The wide range of research and progress on quantum materials at low temperature reported here may inspire and attract more researchers in this ever-expanding field of cryo-EM.

EMI Mitigation of a Ćuk-Based Power-Electronic System Using Switching-Sequence-Based Control

Switching-sequence-based control (SBC) laws when designed based on topological switching behavior can have positive effects on slow- and fast-scale dynamics of a power-electronic system (PES). The slow-scale control can encompass fast PES state regulation and tracking, based on predefined objective, while fast-scale control can address differential-mode (DM) and common-mode (CM) spectral-peak energy associated with PES switching operation. Such control laws may offer enhanced programmability to conventional PES design where bulky electromagnetic interference (EMI) filters have been traditionally used to reduce EMI of switching power converters to meet EMI regulatory standards. An EMI filter is always a less programmable solution since it is usually designed for the worst-case EMI mitigation and usually overkill for a PES operating under reduced load condition. The control scheme outlined in this article offers EMI mitigation across wide operating regions without compromising PES regulation. Moreover, it does so by use of switching sequences that guarantee the reachability of the PES dynamics using an advanced Lyapunov-function-based approach. SBC is a powerful tool to generate control actions for a PES based on multivariate PES state constraints. Hence, contemporary EMI regulatory standards are used as constraints in the SBC formulation to operate the PES under wide operating regime while autonomously mitigating the EMI levels. The work may be of paramount importance for operating the ultra-fast-transition recent wide-bandgap semiconductor devices like GaN-FET and SiC MOSFET under higher power with increasing switching frequencies, which is usually desirable for increased power density and reduced switching losses. Here, a hardware Ćuk-PES operated with GaN-FETs is fabricated and is used for case illustration. It is shown by experimental results how SBC mitigate DM and CM EMI noise of the PES while maintaining regulation even for the higher order nonminimum phase PES, while reducing sensor requirements using state observer derived from the switching model of the PES.

Chiral phonons in the honeycomb sublattice of layered CoSn-like compounds

Honeycomb and kagome lattices exhibit extraordinary electronic properties. It is a natural consequence of additional discrete degree of freedom associated with a valley or the occurrence of electronic flat bands. The combination of both types of lattices, observed in CoSn-like compounds, leads not only to the topological electronic behavior, but also to the emergence of chiral phonon modes. We study CoSn-like compounds and show that chiral phonons are realized here. Previous theoretical studies demonstrated that the chiral phonons can be found in ideal two-dimensional honeycomb or kagome lattices. Recent experimental results support such a prediction as the chiral phonons were observed in the transition metal dichalcogenide ${\mathrm{WSe}}_{2}$. It turns out that in the case of CoSn-like systems with the $P6/mmm$ symmetry, the kagome lattice formed by $d$-block element is decorated by the additional $p$-block atom. As a result one finds a two-dimensional triangular lattice of atoms with nonequal masses and the absence of chiral phonons in the kagome plane. Contrary to this, the interlayer honeycomb lattice of $p$-block atoms is preserved and allows for the realization of chiral phonons. In this paper we discuss the properties of such chiral phonons in seven CoSn-like compounds and demonstrate that they do not depend on the atomic mass ratio or the presence of intrinsic magnetic order. The chiral phonons of $d$-block atoms can be restored by removing the inversion symmetry. The latter is possible in the crystal structure of CoGe and RhPb with the reduced symmetry ($P\overline{6}2m$) and in distorted-kagome-like lattice.

Compatibility of transport effects in non-Hermitian nonreciprocal systems

Based on a general transport theory for nonreciprocal non-Hermitian systems and a topological model that encompasses a wide range of previously studied examples, we (i) provide conditions for effects such as reflectionless and transparent transport, lasing, and coherent perfect absorption, (ii) identify which effects are compatible and linked with each other, and (iii) determine by which levers they can be tuned independently. For instance, the directed amplification inherent in the non-Hermitian skin effect does not enter the spectral conditions for reflectionless transport, lasing, or coherent perfect absorption, but allows to adjust the transparency of the system. In addition, in the topological model the conditions for reflectionless transport depend on the topological phase, but those for coherent perfect absorption do not. This then allows us to establish a number of distinct transport signatures of non-Hermitian, nonreciprocal, and topological behavior, in particular (1) reflectionless transport in a direction that depends on the topological phase, (2) invisibility coinciding with the skin-effect phase transition of topological edge states, and (3) coherent perfect absorption in a system that is transparent when probed from one side.

Intrinsic anharmonicity and thermal properties of ultralow thermal conductivity Ba6Sn6Se13

Ultralow thermal conductivity materials continue to be of great interest for technologically important applications such as thermal insulators and thermoelectrics. Often, such materials possess constituents with extensive dynamic disorder, or ``rattlers,'' or structural disorder such as metallic glasses. Nevertheless, targeted crystalline bonding order and anharmonicity can provide effective means for the scattering of the phonons in certain materials. Our combined experimental and theoretical investigation of ${\mathrm{Ba}}_{6}{\mathrm{Sn}}_{6}{\mathrm{Se}}_{13}$ reveals such a material, with ultralow thermal conductivity measured over a large temperature range. Optic phonon modes hybridize with acoustic modes at relatively low energies resulting in strong acoustic-optic scattering and limited phonon lifetimes. Moreover, our investigations reveal various avoided crossings at low energies that contribute to phonon scattering. These are derived from chiral phase symmetries and may result in nontrivial topological behaviors for phonon band crossings in this chiral material. This work contributes to the ongoing research on low thermal conductivity materials and the underlying mechanisms that affect their thermal behaviors. Manipulation of these effects may provide pathways for enhancement of material properties for targeted thermal applications using similar materials.

Quantized nonlinear Thouless pumping.

The topological protection of wave transport, originally observed in the context of the quantum Hall effect in two-dimensional electron gases1, has been shown to apply broadly to a range of physical platforms, including photonics2-5, ultracold atoms in optical lattices6-8 and others9-12. That said, the behaviour of such systems can be very different from the electronic case, particularly when interparticle interactions or nonlinearity play a major role13-22. A Thouless pump23 is a one-dimensional model that captures the topological quantization of transport in the quantum Hall effect using the notion of dimensional reduction: an adiabatically, time-varying potential mathematically maps onto a momentum coordinate in a conceptual second dimension24-34. Importantly, quantization assumes uniformly filled electron bands below a Fermi energy, or an equivalent occupation for non-equilibrium bosonic systems. Here we theoretically propose and experimentally demonstrate quantized nonlinear Thouless pumping of photons with a band that is decidedly not uniformly occupied. In our system, nonlinearity acts to quantize transport via soliton formation and spontaneous symmetry-breaking bifurcations. Quantization follows from the fact that the instantaneous soliton solutions centred upon a given unit cell are identical after each pump cycle, up to translation invariance; this is an entirely different mechanism from traditional Thouless pumping. This result shows that nonlinearity and interparticle interactions can induce quantized transport and topological behaviour without a linear counterpart.

Intersecting topological nodal ring and nodal wall states in superhard superconductor FeB4

Novel materials with both topological nontrivial states and superconductivity have attracted considerable attention in recent years. Single-crystal FeB4 was recently synthesized and demonstrated to exhibit superconductivity at temperatures lower than 2.9 K, and its nanoindentation hardness was measured to be 65 GPa. In this study, based on first-principles calculation and the low-energy kp effective Hamiltonian, we found that this Pnnm-type superhard FeB4 superconductor hosts topological behaviors with intersecting nodal rings (INRs) in the k_x=0 and k_z=0 planes and nodal wall states in the k_y= {\pi} and k_z= {\pi} planes. The observed surface drum-head-like (D-H-L) states on the [100] and [001] surfaces confirmed the presence of INR states in this system. According to our investigation results, FeB4, with its superconductivity, superior mechanical behaviors, one-dimensional (1D) and two-dimensional topological elements, and D-H-L surface states, is an existing single-phase target material that can be used to realize the topological superconducting state in the near future.

Gauge-dependent topology in non-reciprocal hopping systems with pseudo-Hermitian symmetry

Energy conservation is not valid in non-Hermitian systems with gain/loss or non-reciprocity, which leads to various extraordinary resonant characteristics. Compared with Hermitian systems, the intersection of non-Hermitian physics and topology generates new phases that have not been observed in condensed-matter systems before. Here, utilizing the designed two-dimensional periodical model with non-reciprocal hopping terms, we show how to obtain both the ellipse-like or hyperbolic-like spectral degeneracy, the topological boundary modes and the bulk-boundary correspondence by the protection of time-reversal symmetry and pseudo-Hermitian symmetry. Notably, the boundary modes and bulk-boundary correspondence can simultaneously appear only for specific selection of the primitive cell, and we explored the analytical solution to verify such gauge-dependent topological behaviors. Our topolectrical circuit simulation provides a flexible approach to confirm the designed properties and clarify the crucial role of pseudo-Hermiticity on the stability of a practical system. In a broader view, our findings can be compared to other platforms such as meta-surface or photonic crystals, for the purpose on the control of resonant frequency and localization properties.

Electronic, elastic, and topological behavior of MgH2, MgTiH4, and TiH2 under pressure

This paper studies the elastic, structural, electronic, and topological behaviors of α-MgH2, β-MgH2, MgTiH4, and TiH2 under pressure by resorting to DFT-GGA’s first principle via FPLAPW-WIEN2K, ElaStic1.0, and Critic2 software. Pressure effects are studied from strain vectors generating a linear volume variation with strain. Important structural changes by the effect of pressure are evidenced. The highest strength at hydrostatic deformation was reached by TiH2; and the lowest, by α-MgH2. The elastic constants and moduli for each hydride studied showed agreement with the results reported in the literature. The TiH2 cubic lattice is shown to be structurally unstable. Hydrides showed more stability than pure crystals. The tetragonal structure of MgH2 was confirmed as more stable than its respective cubic structure; and the cubic structure of TiH2, even more so than that of the Mg hydrides, independently of their crystalline structure. Hydrides with a cubic structure showed a ductile condition, whereas those with a tetragonal structure showed a fragile one. α-MgH2 revealed an insulating character. Other hydrides studied showed a conductive character. The topology of charge density and potential energy density establishes a marked difference between the topological classes and the number of critical points (CPs) for both cubic (β-MgH2, TiH2) and tetragonal structures (α-MgH2, MgTiH4), the multiplicity of these being markedly superior in the former. The bonding character in general is covalent in the CP nucleus and both closed-layered and hydrogen-bonded in the other CPs, except in the Ti-H CP bond of the compressed structures, which bears an ionic character, unlike that of expanded structures. The incorporation of Ti to MgH2 weakens the Mg-H bond, which in turn favors the kinetics of dehydrogenation in MgTiH4.

On M-theory on real toric fibrations

Borrowing ideas from elliptic complex geometry, we approach M-theory compactifications on real fibrations. Precisely, we explore real toric equations rather than complex ones exploited in F-theory and related dual models. These geometries have been built by moving real toric manifolds over real bases. Using topological changing behaviors, we unveil certain data associated with gauge sectors relying on affine lie symmetries.

The traveling wave mode for nonlinear Biswas–Milovic equation in magneto-optical wave guide coupling system with Kudryashov’s law of refractive index

This paper studies the traveling wave modes for nonlinear Biswas–Milovic equation in magneto-optical wave guide coupling system with Kudryashov’s law of refractive index. By the complete discrimination system for polynomial and trial equation method, we derive a series of traveling wave solutions of the coupling system. These results show the abundant propagation patterns. In particular, by analyzing the topological stability and dynamic behavior we get four stable modes of this system. Under some special parameters, we give the concrete representations of solutions.

A Generalization of Caristi’s Fixed Point Theorem in the Variable Exponent Weighted Formal Power Series Space

Suppose p n be sequence of positive reals. By H w p n , we represent the space of all formal power series ∑ n = 0 ∞ a n z n equipped with ∑ n = 0 ∞ λ a n / n + 1 p n < ∞ , for some λ > 0 . Various topological and geometric behavior of H w p n and the prequasi ideal constructs by s -numbers and H w p n have been considered. The upper bounds for s -numbers of infinite series of the weighted n -th power forward shift operator on H w p n with applications to some entire functions are granted. Moreover, we investigate an extrapolation of Caristi’s fixed point theorem in H w p n .

Anomalous Conductance in Trans-Polyacetylene Chains with Even–Odd Parity

This work presents an analytical study of electronic transport in dimerized trans-polyacetylene (Trans PA) oligomers containing even (n = 4, 6, 8, 10 sites) and odd (n = 3, 5, 7, 9 sites) chains where the site C1 is sandwiched by two metallic electrodes (Left and Right). These devices exhibit T-shaped geometry and are investigated by Su-Schrieffer-Heeger (SSH) model via Heisenberg equation of motion combined with the Keldysh formalism. We introduced disorder into the system through the dimerization force (δ) demonstrating that the dimerization in the chain can effectively lead to a linear (low δ) or zigzag (high δ) behavior, besides also suffering increase or decrease in conductance peak [dI/dV]max. The odd chains exhibit trivial topological behavior to which the conductance peaks are suppressed as dimerization disorder is considered-creates barriers for tunneling. On the other hand, we have an opposite behavior for conductance peaks in the even chains. For example, the chain with weak dimerization (low δ) has a perfect transmission for even chains. In addition, we note for odd chains the formation of a plateau in the I–V curve for bias voltages and for even chains that show a linear current. This procedure shows an analytical study through the tunneling of the parameters on the device, such parameters as the tunneling amplitude (ГL/R) can be accessible experimentally.