Majorana zero modes induced by skyrmion lattice

One-dimensional s-wave superconductor with spin-orbit coupling is a platform for the realization of Majorana zero modes. The spin-exchange with the magnetic skyrmion lattice can induce spin-orbit coupling in a s-wave superconductor system and the effects are different from the constant spin–orbit coupling. The strength of the effective spin–orbit coupling as well as the rich topoloigcal phase diagram are directly connected to the radius of the skyrmion lattice R. We obtain the rich topological phase diagram of this system with different skyrmion lattice radii by numerically evaluating the spectrum of the system under the periodic boundary condition, and we also find the Majorana zero modes under the open boundary condition to verify the bulk–edge correspondence.

Explicit forms of zero modes in symmetric interacting Kitaev chain without and with dimerization

The fermionic and bosonic zero modes of the one-dimensional（1D） interacting Kitaev chain at the symmetric point are unveiled. The many-body structures of the Majorana zero modes in the topological region are given explicitly by carrying out a perturbation expansion up to infinite order. We also give the analytic expressions of the bosonic zero modes in the topologically trivial phase. Our results are generalized to the hybrid fermion system comprised of the interacting Kitaev model and the Su–Schrieffer–Heeger（SSH） model, in which we show that these two types of zero modes can coexist in a certain region of its phase diagram.

ZERO MODE NATURAL FREQUENCY AND NONLINEAR VIBRATION OF COUPLED LATERAL AND TORSION OF A LARGE TURBINE GENERATOR

Zero mode natural frequency (ZMNF) is found during experiments. The ZMNF andvibrations resulted by it are studied. First, calculating method of the ZMNF excited byelectromagnetic in vibrational system of coupled mechanics and electrics are given from the view ofmagnetic energy. Laws that the ZMNF varies with active power and exciting current are obtained andare verified by experiments. Then, coupled lateral and torsional vibration of rotor shaft system isstudied by considering rest eccentricity, rotating eccentricity and swing eccentricity. UsingLargrange-Maxwell equation when three phases are asymmetric derives differential equation of thecoupled vibration. With energy method of nonlinear vibration, amplitude-frequency characteristics ofresonance are studied when rotating speed of rotor equals to ZMNF. The results show that ZMNF willoccur in turbine generators by the action of electromagnetic. Because ZMNF varies withelectromagnetic parameters, resonance can occur when exciting frequency of the rotor speed is fixedwhereas exciting current change. And also find that a generator is in the state of large amplitudein rated exciting current.

Exploring Majorana zero modes in iron-based superconductors

Majorana zero modes(MZMs) are Majorana-fermion-like quasiparticles existing in crystals or hybrid platforms with topologically non-trivial electronic structures. They obey non-Abelian braiding statistics and are considered promising to realize topological quantum computing. Discovery of MZM in the vortices of the iron-based superconductors(IBSs)has recently fueled the Majorana research in a way which not only removes the material barrier requiring construction of complicated hybrid artificial structures, but also enables observation of pure MZMs under higher temperatures. So far,MZMs have been observed in iron-based superconductors including FeTe_(0.55)Se_(0.45),(Li_(0.84)Fe_(0.16))OHFe Se, Ca KFe_(4)As_(4),and Li Fe As. In this topical review, we present an overview of the recent STM studies on the MZMs in IBSs. We start with the observation of MZMs in the vortices in FeTe_(0.55)Se_(0.45)and discuss the pros and cons of FeTe_(0.55)Se_(0.45) compared with other platforms. We then review the following up discovery of MZMs in vortices of Ca KFe_(4)As_(4), impurity-assisted vortices of Li Fe As, and quantum anomalous vortices in FeTe_(0.55)Se_(0.45), illustrating the pathway of the developments of MZM research in IBSs. Finally, we give perspective on future experimental works in this field.

Majorana zero modes,unconventional real-complex transition,and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice

A one-dimensional non-Hermitian quasiperiodic p-wave superconductor without PT-symmetry is studied.By analyzing the spectrum,we discovered that there still exists real-complex energy transition even if the inexistence of PT-symmetry breaking.By the inverse participation ratio,we constructed such a correspondence that pure real energies correspond to the extended states and complex energies correspond to the localized states,and this correspondence is precise and effective to detect the mobility edges.After investigating the topological properties,we arrived at a fact that the Majorana zero modes in this system are immune to the non-Hermiticity.

Topological phase diagrams and Majorana zero modes of the Kitaev ladder and tube

In this paper,we study two quasi-one-dimensional（1 D） Kitaev models with ladder-like and tube-like spatial structures,respectively.Our results provide the phase diagrams and explicit expressions of the Majorana zero modes.The topological phase diagrams are obtained by decomposing the topological invariants and the topological conditions for topologically nontrivial phases are given precisely.For systems which belongs to topological class BDI,we obtain the regions in the phase diagrams where the topological numbers show even-odd effect.For the Kitaev tube model a phase factor induced by the magnetic flux in the axial direction of the tube is introduced to alter the classification of the tube Hamiltonian from class BDI to D.The Kitaev tube of class D is characterized by the Z2 index when the number of chains is odd while 0,1,2 when the number of chains is even.The phase diagrams show periodic behaviors with respect to the magnetic flux.The bulk-boundary correspondence is demonstrated by the observations that the topological conditions for the bulk topological invariant to take nontrivial values are precisely those for the existence of the Majorana zero modes.

Cross correlation mediated by distant Majorana zero modes with no overlap

Existing studies via shot noise calculation conclude that the cross correlation between the currents in the two leads connected by a pair of Majorana zero modes(MZMs)vanishes when their coupling energy𝜖∈_(M)→0.Motivated by the intrinsic nature of nonlocality of the MZMs,we revisit this important problem and propose an experimental scheme to demonstrate the nonvanishing cross correlation even at the limit𝜖∈_(M)→0.The proposed scheme employs the Andreevprocess-associated branch circuit currents,which are theoretically obtained by applying a decomposition analysis for the total currents while are accessible directly in practical measurement.For different bias voltage setup,we find intriguing results of both negative and positive correlations and carry out simple physical understanding using a quantum jump technique.Importantly,combining together with the evidence of the zero-bias-peak of conductance,the nonlocal cross correlation predicted in this work can help to confirm the existence of the nonlocal MZMs.

Effect of Interaction on the Majorana Zero Modes in the Kitaev Chain at Half Filling

The one-dimensional interacting Kitaev chain at half filling is studied. The symmetry of the Hamiltonian is examined by dual transformations, and various physical quantities as a function of the fermion-fermion interaction U are calculated systematically using the density matrix renormalization group method. A special value of interaction Up is revealed in the topological region of the phase diagram. We show that at Up the ground states are strictly two-fold degenerate even though the chain length is finite and the zero-energy peak due to the Majorana zero modes is maximally enhanced and exactly localized at the end sites. Here Up may be attractive or repulsive depending on other system parameters. We also give a qualitative understanding of the effect of interaction under the self-consistent mean field framework.

Fermionic Zero Modes in Gauge and Gravity Backgrounds on a Sphere

在这封信，我们学习 fermionic 在拿一个二维的协议的计量器和严肃背景的零个模式歧管 S 2 作为额外的尺寸。结果在那里是那存在有 normalizable 的集体更少迪拉克费米子在关于体积上的这些背景的相当一般的假设下面的零个模式。范围上的计量器背景的几种特殊情况被讨论并且某简单 fermionic 零个模式被获得。

Topological phase transitions and Majorana zero modes induced by the periodic potential in an antiferromagnetic chain

We investigate the topological properties of an antiferromagnetic(AFM)chain with an on-site periodic potential,considering the intrinsic spin–orbit coupling and an external Zeeman field along with the nanowire.Our results indicate that Majorana zero modes(MZMs)can be observed by adjusting the strength of the periodic potential.We have calculated the energy spectrum,the wave-function and transport properties,and all these results support the existence of MZMs in the AFM chain.Additionally,multiple topological phase transitions occur as the strength of the periodic potential changes,and several regions support MZMs.

Recent progress on non-Abelian anyons:from Majorana zero modes to topological Dirac fermionic modes

Majorana zero modes(MZMs)have been intensively studied in recent decades theoretically and experimentally as the most promising candidate for non-Abelian anyons supporting topological quantum computation(TQC).In addition to the Majorana scheme,some non-Majorana quasiparticles obeying non-Abelian statistics,including topological Dirac fermionic modes,have also been proposed and therefore become new candidates for TQC.In this review,we overview the non-Abelian braiding properties as well as the corresponding braiding schemes for both the MZMs and the topological Dirac fermionic modes,emphasizing the recent progress on topological Dirac fermionic modes.A topological Dirac fermionic mode can be regarded as a pair of MZMs related by unitary symmetry,which can be realized in a number of platforms,including the one-dimensional topological insulator,higher-order topological insulator,and spin superconductor.This topological Dirac fermionic mode possesses several advantages compared with its Majorana cousin,such as superconductivity-free and larger gaps.Therefore,it provides a new avenue for investigating non-Abelian physics and possible TQC.

Majorana noise model and its influence on the power spectrum

Majorana quantum computation offers a potential approach to securely manipulating and storing quantum data in a topological manner that may effectively resist the decoherence induced by local noise. However, actual Majorana qubit setups are susceptible to noise. In this study, from a quantum dynamics perspective, we develop a noise model for Majorana qubits that accounts for quasi-particle poisoning and Majorana overlapping with fluctuation. Furthermore, we focus on Majorana parity readout methodologies, specifically those leveraging an ancillary quantum dot, and carry out an indepth exploration of continuous measurement techniques founded on the quantum jump model of a quantum point contact.Utilizing these methodologies, we proceed to analyze the influence of noise on the afore-mentioned noise model, employing numerical computation to evaluate the power spectrum and frequency curve. In the culmination of our study, we put forward a strategy to benchmark the presence and detailed properties of noise in Majorana qubits.

Majorana zero mode in the vortex of an artificial topological superconductor

Majorana fermion(MF),an exotic particle that is identical to its own antiparticle,was recently found in solid matter as a quasiparticle excitation,the Majorana zero mode(MZM),in the vortex of an artificial topological superconductor(TSC).This artificial TSC,first proposed by Fu and Kane in 2008,is a heterostructure made of a topological insulator Bi_2Te_3 and an s-wave superconductor NbSe_2.This paper will briefly review the experimental progresses based on the Bi_2Te_3/NbSe_2 heterostructure.All evidences are self-consistent and reveal that the MZM exists in the center of vortex.Those experimental results are also supported by theory.This finding is a milestone in the research of Majorana fermions in solid state physics and a starting point of MZM's application in topological quantum computation.

Hexagonal warping effect on Majorana zero modes at the ends of superconducting vortex lines in doped strong 3D topological insulators

In a superconducting topological insulator, a superconducting vortex line can trap a one-dimensional topological band with localized Majorana zero modes at the ends. Here, we study the effect of hexagonal warping and its corresponding symmetry-breaking effect on vortex phase transition. We perform both analytical calculations based on a semiclassical formula and numerical calculations based on full quantum mechanics using the Bogoliubov-de Gennes equation. We find that the hexagonal warping term extends the topological region of the vortex line as the chemical potential changes and leads to MZMs, even in the absence of topological surface states.

Orthogonal basic deformation mode method for zero-energy mode suppression of hybrid stress elements

A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The result- ing orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. More- over, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.

Mode Interaction at a Triple Zero Point of O(2) symmetric Nonlinear Systems with Two Parameters

We consider a triple zero point of nonlinear equations with O(2 symmetry, where the Jacobian has a zero eigenvalue of geometric multiplicity one and algebraic multiplicity three. We show that this triple zero point exhibits a new bifurcation phenomenon, that is, a mode interaction of the following three paths: bifurcation points from steady states, steady states and rotating waves to standing waves, rotating waves and modulated rotating waves respectively.

基于电流模分量特性的多端柔性直流配电网线路纵联保护

多端柔性直流配电网因在供电可靠性方面极具优势而受到广泛的关注,然而对于直流线路保护中故障的快速、可靠识别成为其急速发展所需解决的关键问题之一。因此,设计了一种利用电流模分量特性的直流线路纵联保护方法。该方法利用故障时正极电流线模分量方向来判别区内外故障,以不同故障条件下故障点正极电流零模分量平均值的差异来构造保护判据,从而判别故障类型,形成保护策略。最后,在PSCAD/EMTDC4.5上搭建了多端柔性直流配电网模型,对保护判据及关键影响要素进行了仿真分析。结果表明,该保护方法能够有选择性地快速、可靠识别区内外故障及故障类型,且具有较好的耐过渡电阻与抗噪声能力。

基于拐点密集区凹凸波动特性的直流配网故障检测方法

基于模块化多电平换流器(modular multilevel converter,MMC)的柔性直流配电网具有不存在换相失败等优点。但换流器存在低惯性、弱阻尼等特性,导致故障电流上升速度快且峰值高,对系统危害极大。针对直流配电网发生单极接地故障难以准确选择故障馈线的问题,提出了一种基于拐点密集区凹凸波动特性的直流配网故障检测方法。首先,利用变分模态分解算法对各馈线零模电流进行分解,选取特征分量。然后,计算特征分量的二阶导数,选择拐点密集区并进行归一化处理,得到各馈线的凹凸波动性。最后,判定凹凸波动性与其他馈线相异的线路为故障线路。仿真结果表明,所提方法能够快速识别故障馈线,且受过渡电阻、采样频率、数据窗和噪声等因素影响小。

永磁同步电机模型预测转矩控制共模电压抑制研究

针对永磁同步电机模型预测转矩控制共模电压较大的问题,对比分析了磁链、转矩和共模电压共同控制、直接去除零电压矢量和虚拟零电压矢量三种抑制共模电压的方法。仿真结果表明,三种方法均可有效抑制共模电压。前两种方法均未采用零电压矢量,导致磁链脉动和转矩脉动增大;虚拟零电压矢量方法既保留了零电压矢量,又有效抑制了共模电压,但开关频率有所增大;动态虚拟零电压矢量选择开关次数最小的零电压矢量生成方式,可在控制性能基本相当的前提下,有效减小开关频率,综合性能最优。