Trivial State Research Articles

Facet Engineering to Regulate Surface States of Topological Crystalline Insulator Bismuth Rhombic Dodecahedrons for Highly Energy Efficient Electrochemical CO2 Reduction

Bismuth (Bi) is a topological crystalline insulator (TCI), which has gapless topological surface states (TSSs) protected by a specific crystalline symmetry that strongly depends on the facet. Bi is also a promising electrochemical CO2 reduction reaction (ECO2 RR) electrocatalyst for formate production. In this study, single-crystalline Bi rhombic dodecahedrons (RDs) exposed with (104) and (110) facets are developed. The Bi RDs demonstrate a very low overpotential and high selectivity for formate production (Faradic efficiency >92.2%)in a wide partial current density range from 9.8 to 290.1mAcm-2 , leading to a remarkably high full-cell energy efficiency (69.5%) for ECO2 RR. The significantly reduced overpotential is caused by the enhanced *OCHO adsorption on the Bi RDs. The high selectivity of formate can be ascribed to the TSSs and the trivial surface states opening small gaps in the bulk gap on Bi RDs, which strengthens and stabilizes the preferentially adsorbed *OCHO and mitigates the competing adsorption of *H during ECO2 RR. This study describes a promising application of Bi RDs for high-rate formate production and high-efficiency energy storage of intermittent renewable electricity. Optimizing the geometry of TCIs is also proposed as an effective strategy to tune the TSSs of topological catalysts.

Interaction-Stabilized Topological Magnon Insulator in Ferromagnets

Condensed matter systems admit topological collective excitations above a trivial ground state, an example being Chern insulators formed by Dirac bosons with a gap at finite energies. However, in contrast to electrons, there is no particle-number conservation law for collective excitations. This gives rise to particle number-nonconserving many-body interactions whose influence on single-particle topology is an open issue of fundamental interest in the field of topological quantum materials. Taking magnons in ferromagnets as an example, we uncover topological magnon insulators that are stabilized by interactions through opening Chern-insulating gaps in the magnon spectrum. This can be traced back to the fact that the particle-number nonconserving interactions break the effective time-reversal symmetry of the harmonic theory. Hence, magnon-magnon interactions are a source of topology that can introduce chiral edge states, whose chirality depends on the magnetization direction. Importantly, interactions do not necessarily cause detrimental damping but can give rise to topological magnons with exceptionally long lifetimes. We identify two mechanisms of interaction-induced topological phase transitions---one driven by an external field, the other by temperature---and show that they cause unconventional sign reversals of transverse transport signals, in particular of the thermal Hall conductivity. We identify candidate materials where this many-body mechanism is expected to occur, such as the metal-organic kagome-lattice magnet Cu(1,3-benzenedicarboxylate), the van der Waals honeycomb-lattice magnet CrI$_3$, and the multiferroic kamiokite (Fe$_2$Mo$_3$O$_8$). Our results demonstrate that interactions can play an important role in generating nontrivial topology.

Selective Substrate-Orbital-Filtering Effect to Realize the Large-Gap Quantum Spin Hall Effect.

Although Pb harbors a strong spin-orbit coupling effect, pristine plumbene (the last group-IV cousin of graphene) hosts topologically trivial states. Based on first-principles calculations, we demonstrate that epitaxial growth of plumbene on the BaTe(111) surface converts the trivial Pb lattice into a quantum spin Hall (QSH) phase with a large gap of ∼0.3 eV via a selective substrate-orbital-filtering effect. Tight-binding model analyses show the pz orbital in half of the Pb overlayer is selectively removed by the BaTe substrate, leaving behind a pz-px,y band inversion. Based on the same working principle, the gap can be further increased to ∼0.5-0.6 eV by surface adsorption of H or halogen atoms that filters out the other half of the Pb pz orbitals. The mechanism of selective substrate-orbital-filtering is general, opening an avenue to explore large-gap QSH insulators in heavy-metal-based materials. It is worth noting that plumbene has already been widely grown on various substrates experimentally.

Floquet π mode engineering in non-Hermitian waveguide lattices

Floquet topological systems exhibit rich physics associated with quasienergy band structures and new topological states; nevertheless, they are usually explored in Hermitian systems. Recent studies have shown the capability of non-Hermiticity in engineering topological states, while the interplay of Floquet topological phases and non-Hermiticity remains unclear. Here, we reveal that the non-Hermitian modulation can induce the phase transitions between trivial and nontrivial topological Floquet states. Our study theoretically predicts that the non-Hermitian modulation can create a Floquet π mode in an originally topological trivial system according to the reopening of quasienergy band gap (i.e., the π gap), which is well confirmed experimentally in the silicon waveguide platform. Our approach shows the powerful capability of non-Hermitian modulation in engineering topological modes in Floquet photonics systems and would inspire different possibilities in optical field manipulation in open systems.1 MoreReceived 8 February 2021Revised 31 March 2021Accepted 28 April 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023211Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEdge statesTopological phase transitionPhysical SystemsWaveguide arraysPropertiesPT-symmetryCondensed Matter, Materials & Applied Physics

Minimal Zeeman field requirement for a topological transition in superconductors

Platforms for creating Majorana quasiparticles rely on superconductivity and breaking of time-reversal symmetry. By studying continuous deformations to known trivial states, we find that the relationship between superconducting pairing and time reversal breaking imposes rigorous bounds on the topology of the system. Applying these bounds to s-wave systems with a Zeeman field, we conclude that a topological phase transition requires that the Zeeman energy at least locally exceed the superconducting pairing by the energy gap of the full Hamiltonian. Our results are independent of the geometry and dimensionality of the system.

Topological quantum criticality in superfluids and superconductors: Surface criticality, thermal properties, and Lifshitz Majorana fields

Time reversal invariant (TRI) topological superfluids (TSFs) and topological superconductors (TSCs) are robust symmetry protected gapped topological states. In this article, we study the evolution of these topological states in the presence of time reversal symmetry breaking (TRB) fields and/or sufficiently large TRI fields. Physically, one of the realizations of TRB fields can be internal spin exchange fields due to background magnetic ordering. We find that the fully gapped TSFs and TSCs are generically separated from other nodal states by various zero temperature quantum critical points that are characterized by generalized quantum Lifshitz fields with distinct scaling properties. These emergent Lifshitz fields also define finite temperature properties in quantum critical regimes. Moreover, for a certain subset of TRB fields, there exist a precursor to bulk transitions, where surface states can also exhibit quantum critical behavior near zero fields. The possibility for a fully gapped TSF/TSC to smoothly crossover into a topologically trivial state without a phase transition is also examined.

Nonlinear Vibration Analysis of a Hinged–Clamped Beam Moving with Pulsating Speed and Subjected to Internal Resonance

This work focuses on the revelation of nonlinear characteristics of a hinged–clamped beam moving with pulsating speed. Cubic geometric nonlinearity, viscous damping due to intervening medium, and viscoelastic material damping are considered in the governing equation of motion. Parametric excitation is induced in the system due to pulsating speed amid 3:1 internal resonance between the first two modes. A perturbation technique-direct method of multiple scales is applied to solve the problem. Nonlinear features like various stability and bifurcation phenomena are extracted by applying a continuation algorithm. Trivial state stability plot and the impacts of viscous and material damping have been studied. The consequence of alterations of the amplitude of pulsating speed constituent, internal frequency detuning parameter, axial stiffness, and parametric detuning parameter on the vibration responses have been analyzed in detail. The analytic-numeric approach reveals rich and interesting nonlinear phenomena under united parametric and internal resonances in the study of the hinged–clamped beam that are not available in the existing literature.

Linear and nonlinear analysis of traditional and non-traditional piezoelectric vibration absorber with time delay feedback for simultaneous resonance conditions

In the present work, vibration suppression of a single degree of freedom nonlinear spring-mass primary (main) system subjected to simultaneous external harmonic and parametric excitation by using traditional and non-traditional active nonlinear vibration absorber (ANVA) is carried out. The traditional and non-traditional ANVA consists of a PZT (lead zirconate titanate) stack actuator in series with a nonlinear spring and a damper. In the traditional ANVA, the damper is connected to the main system whereas, in non-traditional ANVA, the damper is connected to the base of the main system. The governing nonlinear equations of motion for the system have been derived using weighted modal matrix approach considering novel actuation force by time delay in displacement, velocity and acceleration feedback of the main system by the PZT stack actuator and the nonlinear spring in series combination. The method of multiple scales (MMS) is used to obtain the reduced equations which are solved using Newton’s method. The responses of the system for the primary, principal parametric and simultaneous primary and principal parametric resonance conditions have been studied. The results are compared with those obtained by using the harmonic balance method (HBM), numerical method and with previous literature. From these results, two resonating peaks in the frequency response of the main system are shown by using the reduced equation of the MMS which was not reported in earlier literature. It is shown that for the active case the vibration of the undamped main system is completely reduced at the specified operating frequency for both the linear and nonlinear systems. Also, for a wider range of operating frequencies, the vibration of the main system is reduced by actively tuning the absorber for various mass ratios. Further, the efficacy of the active force is observed in reducing the instability regions and improving the critical value of excitations in the trivial state.

Suppression of a nonplanar motion in an externally excited string by the addition of viscosity based on velocity feedback control

This study concerns the out-of-plane motion of a vertically disposed string with one end fixed and the other subjected to a harmonic excitation. Excited in its primary resonance, the string can vibrate in the direction orthogonal to the excitation direction through nonlinear coupling effects and has out-of-plane motion. To suppress this out-of-plane motion, we propose a boundary control method that modifies the boundary condition of the fixed upper end, i.e., we move the fixed upper end in the direction orthogonal to the external excitation. The unstable range for trivial steady state motion in this direction, which exists in the neighborhood of the primary resonance condition, changes to a stable range under suitable feedback gain. The out-of-plane motion is then suppressed for any excitation frequency. Experiments conducted using a simple apparatus confirmed the validity of the proposed method adopting boundary control.

Large Fermi-Energy Shift and Suppression of Trivial Surface States in NbP Weyl Semimetal Thin Films.

Weyl semimetals, a class of 3D topological materials, exhibit a unique electronic structure featuring linear band crossings and disjoint surface states (Fermi-arcs). While first demonstrations of topologically driven phenomena have been realized in bulk crystals, efficient routes to control the electronic structure have remained largely unexplored. Here, a dramatic modification of the electronic structure in epitaxially grown NbP Weyl semimetal thin films is reported, using in situ surface engineering and chemical doping strategies that do not alter the NbP lattice structure and symmetry, retaining its topological nature. Through the preparation of a dangling-bond-free, P-terminated surface which manifests in a surface reconstruction, all the well-known trivial surface states of NbP are fully suppressed, resulting in a purely topological Fermi-arc dispersion. In addition, a substantial Fermi-energy shift from -0.2to 0.3 eVacross the Weyl points is achieved bysurfacechemical doping, unlocking access to the hitherto unexplored n-type region of the Weyl spectrum. These findings constitute a milestone toward surface-state and Fermi-level engineering of topological bands in Weyl semimetals, and, whilethere are still challenges in minimizing doping-driven disorder and grain boundary density in the films,they do represent a major advance to realize device heterostructures based on Weyl physics.

Temporal-spatial analysis of an age-space structured foot-and-mouth disease model with Dirichlet boundary condition.

Foot-and-mouth disease is a highly contagious and economically devastating disease of cloven-hoofed animals. The historic occurrences of foot-and-mouth diseases led to huge economic losses and seriously threatened the livestock food security. In this paper, a novel age-space diffusive foot-and-mouth disease model with a Dirichlet boundary condition, coupling the virus-to-animals and animals-to-animals transmission routes, has been proposed. The basic reproduction number R0 is defined as the spectral radius of a next generation operator K, which is calculated in an explicit form, and it serves as a vital value determining whether or not the disease persists. The existence of a unique trivial nonconstant steady state and at least one nonconstant endemic steady state of the system is established by a smart Lyapunov functional and the Kronoselskii fixed point theorem. An application to a foot-and-mouth outbreak in China is presented. The findings suggest that increasing the movements and disinfection of the environment for animals apparently reduce the risk of a foot-and-mouth infection.

Evaluation of behavior components in the elevated plus maze after the action of external and internal factors

To optimize the treatment of diseases which are accompanied by disorders of the psycho-emotional sphere, it is necessary to identify differences and expose the pathogenesis of these changes appearance depending on the primary pathology. During the study, changes in the components of behavior in the elevated plus maze were studied in rats with a developed explosion-induced neurotrauma (EINT), hyper- and hypothyroidism. The experiment conduc­ted on 33 Wistar rats, of which 12 sexually mature rats were divided into control and expe­rimental (with an established EINT) group, 21 young rats were divided into 3 groups – with hyperthyroidism, hypothyroidism and a control group. All animals were kept in standard conditions of the vivarium of the DSMU, the studies were carried out in accordance with the requirements of bioethics. Analysis of the results showed that under the action of various pathological factors, different behavioral profiles are formed, which indicate the development of a trivial state during stress-like reactions after neurotrauma or with an altered hormonal state. The behavioral profile of rats after reproduction of the EINT in comparison with the control group indicates the development of stress-like conditions (statistically significant (p≤0.05) increase in upright stands by 62%, an increase in the number of bowel movements by 50%. Hyperthyroidism is characterized by sympathetic nervous system activation, as evidenced by a significant (p≤0.05) increase in both the number of measures in the open sleeves by 70% and a significant (p≤0.05) increase in the time spent in light sleeves by 51%. In hypothyroidism, there is a suppression of the emotional component of the rats behavior, as evidenced by a significant (p≤0.05) reduction of measures by 63% and time spent in light sleeves by 86%, grooming duration by 71%, hanging from the edges of open sleeves by 80% and the number of bolus defecation by 100%. Keywords: thyroid gland, antigen, staphylococcal toxoid, mast cells, experiment, rats.

Piezoelectric Machines: Achieving Non-Standard Actuation and Sensing Properties in Poled Ceramics

Summary In the framework of linear piezoelectric ceramics, we study the deformations of a circular infinite hollow cylinder, subjected to a potential difference between the inner and outer surfaces. When the poling direction is perfectly aligned with the cylinder axis, the solution to this problem is a trivial axisymmetric anti-plane state. However, when the poling direction has an offset angle with respect to the cylinder axis, the corresponding behavior becomes more complex, with the anti-plane state coupled to an in-plane, potentially non axisymmetric, deformation. In this work, we show that this structural coupling, due to the poling direction, can be fruitfully exploited to achieve non-standard actuation and sensing properties, like the possibility to generate a torque under axially symmetric electromechanical controls.

Majorana entropy revival via tunneling phases

Measuring the Majorana entropy ${S}_{M}={k}_{B}log({2}^{\frac{1}{2}})$ (where $log$ is the natural logarithm) may uniquely reveal whether an initial equilibrium state of a nanoscale device has a Majorana nature, and subsequent operations deal with an essentially nonlocal pair of non-Abelian Majorana bound states and not with trivial or other accidental non-Abelian states. However, in realistic setups both Majorana modes are inevitably involved in tunneling processes. We show that even when the tunneling amplitude of one Majorana mode is significantly suppressed, the Majorana entropy is ruined, and straightforward experiments will, in general, detect entropy $S\ensuremath{\ll}{S}_{M}$. To avoid this general problem we present a mechanism of the Majorana entropy revival via the tunneling phases of the Majorana modes and demonstrate that to successfully observe the universal Majorana plateau $S={S}_{M}$ one should intelligently tune the tunneling phases instead of leaving them uncontrolled. Practical feasibility of appropriate Majorana entropy measurements is supported by an example with parameters well achievable in modern labs.

Unwinding fermionic symmetry-protected topological phases: Supersymmetry extension

We show how $1+1$-dimensional fermionic symmetry-protected topological states (SPTs, i.e., nontrivial short-range entangled gapped phases of quantum matter whose boundary exhibits 't Hooft anomaly and whose bulk cannot be deformed into a trivial tensor product state under finite-depth local unitary transformations only in the presence of global symmetries), indeed can be unwound to a trivial state by enlarging the Hilbert space via adding extra degrees of freedom and suitably extending the global symmetries. The extended projective global symmetry on the boundary can become supersymmetric in a specific sense, i.e., it contains group elements that do not commute with the fermion number parity ${(\ensuremath{-}1)}^{F}$, while the antiunitary time-reversal symmetry becomes fractionalized. This also means we can uplift and remove certain exotic fermionic anomalies (e.g., ``parity'' anomaly in time-reversal or reflection symmetry) via appropriate supersymmetry extensions in terms of group extensions. We work out explicit examples for multilayers of $1+1\mathrm{d}$ Majorana fermion chains, then comment on models with Sachdev-Ye-Kitaev (SYK) interactions, intrinsic fermionic gapless SPTs protected by supersymmetry, and generalizations to higher space-time dimensions via a cobordism theory.

Global dynamics and zero-diffusion limit of a parabolic–elliptic–parabolic system for ion transport networks

This paper is concerned with a parabolic–elliptic–parabolic system arising from ion transport networks. It shows that for any properly regular initial data, the corresponding initial–boundary value problem associated with Neumann–Dirichlet boundary conditions possesses a global classical solution in one-dimensional setting, which is uniformly bounded and converges to a trivial steady state, either in infinite time with a time-decay rate or in finite time. Moreover, by taking the zero-diffusion limit of the third equation of the problem, the global weak solution of its partially diffusive counterpart is established and the explicit convergence rate of the solution of the fully diffusive problem toward the solution of the partially diffusive counterpart, as the diffusivity tends to zero, is obtained.

Characterizing spin-one Kitaev quantum spin liquids

Material realizations of the bond-dependent Kitaev interactions with $S$=1/2 local moments have vitalized the research in quantum spin liquids. Recently, it has been proposed that higher-spin analogues of the Kitaev interactions may also occur in a number of materials with strong spin-orbit coupling. In contrast to the celebrated $S$=1/2 Kitaev model on the honeycomb lattice, the higher-spin Kitaev models are not exactly solvable. Hence, the existence of quantum spin liquids in these systems remains an outstanding question. In this work, we use the density matrix renormalization group (DMRG) methods to numerically investigate the $S$=1 Kitaev model with both ferromagnetic (FM) and antiferromagnetic (AFM) interactions. Using results on a cylindrical geometry with various circumferences, we conclude that the ground state of the $S$=1 Kitaev model is a quantum spin liquid with a $\mathbb{Z}_2$ gauge structure. We also put a bound on the excitation gap, which turns out to be quite small. The magnetic field responses for the FM and AFM models are similar to those of the $S$=1/2 counterparts. In particular, in the AFM $S$=1 model, a gapless quantum liquid state emerges in an intermediate window of magnetic field strength, before the system enters a trivial polarized state.

Two types of corner states in two-dimensional photonic topological insulators

Higher-order topological insulators, which go beyond the conventional bulk-boundary correspondence, have become a hot research topic in recent years. In this paper, we propose a two dimensional second-order topological photonic crystal based on a C4 symmetric lattice. By tuning the distance between the dielectric cylinders, the topological phase transition of the structure is realized, one edge state and two types of corner states (one topological and one trivial corner state) are found. Our findings provide an evolution of bulk–corner–edge–corner–bulk in a hierarchy of dimensions, which enriches the study of corner states in photonic systems. Besides, we distinguish two corner states by discussing robustness and mode area, and we verify the topological corner state can be embedded in the bulk states, forming a bound state in continuum by simulation.

Transitional Faraday and Kerr effect in hybridized topological insulator thin films

We theoretically investigate quantum phase transitions from topologically non-trivial to trivial states in three-dimensional hybridized topological insulator (TI) ultra-thin films. The interplay between the hybridization of the top and bottom surface states (SSs) and Zeeman energy gives rise to topological and normal insulating phases. By tuning the Zeeman energy, we can drive phase transition between these two phases by closing and reopening the band gap. Furthermore, we impinge a Gaussian beam on the surface of the 3D TI to study the Faraday rotation (FR) and magneto-optical Kerr effect (MOKE) in the presence of an external magnetic field, while explicitly taking into account the hybridization between the top and bottom Dirac SSs of the TI film. The FR and MOKE change sign when the polarization is changed from s to p. We demonstrate that giant FR and MOKE can be achieved by tuning the external magnetic field. Furthermore, the MOKE signal takes a sharp anti-phase peak at the charge neutrality point as the system goes from the quantum spin Hall insulator (QSHI) to the semimetallic state. Lastly, the MOKE and FR in the bottom and top SSs can be independently tuned for intra-band and inter-band transitions via n-type and p-type doping respectively.

Three-terminal nonlocal conductance in Majorana nanowires: Distinguishing topological and trivial in realistic systems with disorder and inhomogeneous potential

We develop a theory for the three-terminal nonlocal conductance in Majorana nanowires as existing in the superconductor-semiconductor hybrid structures in the presence of superconducting proximity, spin-orbit coupling, and Zeeman splitting. The key question addressed is whether such nonlocal conductance can decisively distinguish between trivial and topological Majorana scenarios in the presence of chemical potential inhomogeneity and random impurity disorder. We calculate the local electrical as well as nonlocal electrical and thermal conductance of the pristine nanowire (good zero-bias conductance peaks), the nanowire in the presence of quantum dots and inhomogeneous potential (bad zero-bias conductance peaks), and the nanowire in the presence of large disorder (ugly zero-bias conductance peaks). The local conductance by itself is incapable of distinguishing the trivial states from the topological states since zero-bias conductance peaks are generic in the presence of disorder and inhomogeneous potential. The nonlocal conductance, which in principle is capable of providing the bulk gap closing and reopening information at the topological quantum phase transition, is found to be far too weak in magnitude to be particularly useful in the presence of disorder and inhomogeneous potential. Therefore, we focus on the question of whether the combination of the local, nonlocal electrical, and thermal conductance can separate the good, bad, and ugly zero-bias conductance peaks in finite-length wires. Our paper aims to provide a guide to future experiments, and we conclude that a combination of all three measurements would be necessary for a decisive demonstration of topological Majorana zero modes in nanowires---positive signals corresponding to just one kind of measurements are likely to be false positives arising from disorder and inhomogeneous potential.