In recent years,the study of Majorana signatures in quantum transport has become a central focus in condensed matter physics.Here,we present a rigorous and systematic derivation of the fermionic superoperator describi...In recent years,the study of Majorana signatures in quantum transport has become a central focus in condensed matter physics.Here,we present a rigorous and systematic derivation of the fermionic superoperator describing the open quantum dynamics of electron transport through Majorana zero modes,building on the techniques introduced in Phys.Rev.B 105,035121(2022).The numerical implementation of this superoperator is to construct its differential equivalence,the hierarchical equations of motion(HEOM).The HEOM approach describes the system-bath correlated dynamics.Furthermore,we also develop a functional derivative scheme that provides exact expressions for the transport observables in terms of the auxiliary density operators introduced in the HEOM formulation.The superoperator formalism establishes a solid theoretical foundation for analyzing key transport signatures that may uncover the unique characteristics of Majorana physics in mesoscopic systems.展开更多
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 e...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.展开更多
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 mecha...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.展开更多
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...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.展开更多
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 consi...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.展开更多
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 re...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.展开更多
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...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.展开更多
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)...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.展开更多
We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in （5＋1） dimensions. Using the generalized Abelian-Higgs model, we obtain the inner topological structure...We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in （5＋1） dimensions. Using the generalized Abelian-Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.展开更多
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 ...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.展开更多
In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two-dimensional compact manifold S2 as extra dimensions. The result is that there exist massless Dirac fermions which have normali...In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two-dimensional compact manifold S2 as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes under quite general assumptions about these backgrounds on the bulk. Several special cases of gauge background on the sphere axe discussed and some simple fermionic zero modes are obtained.展开更多
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 intera...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.展开更多
Majorana zero modes(MZMs),promising for topological quantum computation,are naturally hosted in vortices of two-dimensional topological superconductors(TSCs).However,precise control and braiding of these vortex-bound ...Majorana zero modes(MZMs),promising for topological quantum computation,are naturally hosted in vortices of two-dimensional topological superconductors(TSCs).However,precise control and braiding of these vortex-bound MZMs remain a significant challenge.This work proposes and numerically demonstrates a novel braiding scheme utilizing a programmable matrix of spintransfer torque(STT) devices(STT-matrix) integrated with a TSC layer.By selectively activating individual STT elements,their localized stray fields enable deterministic manipulation,including driving,braiding,and fusion,of superconducting vortices and their associated MZMs.We establish a comprehensive simulation framework combining finite element analysis for STT-induced vortex formation,time-dependent Ginzburg-Landau equations for vortex dynamics and time-dependent Bogoliubov-de Gennes equations for MZM evolution.Simulations confirm the STT-matrix's capability for high-fidelity vortex manipulation and demonstrate MZM braiding dynamics.We quantify the impact of vortex acceleration and finite MZM coupling on braiding fidelity,showing that it can be optimized by adjusting STT spacing and vortex separation.Furthermore,we demonstrate controlled MZM fusion and measure the resultant energy splitting.This STT-matrix-based approach offers a highly versatile,scalable,and potentially practical platform for operating MZMs within TSC vortices,advancing the development of fault-tolerant topological quantum computation.conductivity.展开更多
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 addit...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.展开更多
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 t...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 BiETe3 and an s-wave superconductor NbSe2. This paper will briefly review the experimental progresses based on the Bi2Te3/NbSe2 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 ofMajorana fermions in solid state physics and a starting point of MZM＇s application in topological quantum computation.展开更多
We present a theoretical investigation of Majorana zero mode(MZM)assisted spin pumping which consists of a quantum dot(QD)and two normal leads.When the coupling between the MZM and the QD is absent,d.c.pure spin curre...We present a theoretical investigation of Majorana zero mode(MZM)assisted spin pumping which consists of a quantum dot(QD)and two normal leads.When the coupling between the MZM and the QD is absent,d.c.pure spin current can be excited by a rotating magnetic field where low energy spin down electrons are flipped to high energy spin up electrons by absorbing photons.However,when the coupling is turned on,the d.c.pure spin current vanishes,and an a.c.charge current emerges with its magnitude independent of the coupling strength.We reveal that this change is due to the formation of a highly localized MZM assisted topological Andreev state at the Fermi level,which allows only the injection of electron pairs with opposite spin into the QD.By absorbing or emitting photons,the electron pairs are separated to opposite spin electrons,and then return back to the lead again,generating an a.c.charge current without spin polarization.We demonstrate the switching from d.c.pure spin current to a.c.charge current based on both Kitaev model and a more realistic topological superconductor nanowire.Although this switching can also be induced by partially separated Andreev bound state(ps-ABS)in the topological trivial phase,it is extremely unstable and highly sensitive to the Zeeman field,which is different from the switching induced by MZM.Our result suggests that quantum spin pumping may be a feasible local transport method for detecting the presence of MZMs at the ends of a superconducting nanowire.展开更多
Topological crystalline insulators are known to support multiple Majorana zero modes(MZMs)at a single vortex,their hybridization is forbidden by a magnetic mirror symmetry MT.Due to the limited energy resolution of sc...Topological crystalline insulators are known to support multiple Majorana zero modes(MZMs)at a single vortex,their hybridization is forbidden by a magnetic mirror symmetry MT.Due to the limited energy resolution of scanning tunneling microscopes and the very small energy spacing of trivial bound states,it remains challenging to directly probe and demonstrate the existence of multiple MZMs.In this work,we propose to demonstrate the existence of MZMs by studying the hybridization of multiple MZMs in a symmetry breaking field.The different responses of trivial bound states and MZMs can be inferred from their spatial distribution in a vortex.However,the theoretical simulations are very demanding since it requires an extremely large system in real space.By utilizing the kernel polynomial method,we can efficiently simulate large lattices with over 108 orbitals to compute the local density of states which bridges the gap between theoretical studies based on minimal models and experimental measurements.We show that the spatial distribution of MZMs and trivial vortex bound states differs drastically in tilted magnetic fields.The zero-bias peak elongates when the magnetic field preserves MT,while it splits when MT is broken,giving rise to an anisotropic magnetic response.Since the bulk of SnTe are metallic,we also study the robustness of MZMs against the bulk states,and clarify when can the MZMs produce a pronounced anisotropic magnetic response.展开更多
In this paper,we study the ρ-meson electromagnetic form factors(EMFFs)within the framework of the light-front quark model.The physical form factors G_(C,M,Q)(Q^(2))of the ρ-meson,as well as the charged square radius...In this paper,we study the ρ-meson electromagnetic form factors(EMFFs)within the framework of the light-front quark model.The physical form factors G_(C,M,Q)(Q^(2))of the ρ-meson,as well as the charged square radius<r^(2)>,the magnetic moment μ,and the quadrupole moment Q,are calculated,which describe the behaviors of EMFFs at zero momentum transfer.Using the type-Ⅱ replacement,we find that the zero-mode does contribute zero to the matrix element S_(00)^(+).It is found that the“M→M_(0)”replacement improves the angular condition remarkably,which permits different prescriptions of ρ-meson EMFFs to give the consistent results.The residual tiny violation of angular condition needs other explanations beyond the zero-mode contributions.Our results indicate that the relativistic effects or interaction internal structure are weaken in the zero-binding limit.This work is also applicable to other spin-1 particles.展开更多
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 orthogonalizati...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.展开更多
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 ...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.展开更多
基金supported by the National Natural Science Foundation of China(Nos.224B2305,22373091)the Innovation Program for Quantum Science and Technology(No.2021ZD0303301)。
文摘In recent years,the study of Majorana signatures in quantum transport has become a central focus in condensed matter physics.Here,we present a rigorous and systematic derivation of the fermionic superoperator describing the open quantum dynamics of electron transport through Majorana zero modes,building on the techniques introduced in Phys.Rev.B 105,035121(2022).The numerical implementation of this superoperator is to construct its differential equivalence,the hierarchical equations of motion(HEOM).The HEOM approach describes the system-bath correlated dynamics.Furthermore,we also develop a functional derivative scheme that provides exact expressions for the transport observables in terms of the auxiliary density operators introduced in the HEOM formulation.The superoperator formalism establishes a solid theoretical foundation for analyzing key transport signatures that may uncover the unique characteristics of Majorana physics in mesoscopic systems.
基金supported by the National Natural Science Foundation of China(Grant No.11274379)the Research Funds of Renmin University of China(Grant No.14XNLQ07)
文摘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.
基金This project is supported by National Natural Science Foundation of China (No.50375049).
文摘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.
基金the National Natural Science Foundation of China(Grant Nos.11835011 and 12174346).
文摘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.
基金supported by the Ministry of Science and Technology of China (Grant No. 2019YFA0308500)the Chinese Academy of Sciences (Grant Nos. XDB28000000 and YSBR-003)。
文摘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.
基金supported by the Hunan Provincial Natural Science Foundation of China(Nos.2020JJ4240,2018JJ2078)the Scientific Research Fund of Hunan Provincial Education Department(No.19A106,18C0699)the Postgraduate University-Level Research Programme of Jishou University(No.Jdy22043)。
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.11274379)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.14XNLQ07)
文摘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.
基金the National Key Research and Development Program of China(Grant No.2017YFA0303304)the National Natural Science Foundation of China(Grant Nos.11675016,11974011,and 61905174).
文摘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.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10275030 and 10475034 and the Fundamental Research Fund for Physics and Mathematics of Lanzhou University （No. lzu0702）
文摘We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in （5＋1） dimensions. Using the generalized Abelian-Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.
基金Project supported by the National Key R&D Program of China (Grant Nos.2021YFA1400900,2021YFA0718300,and 2021YFA1400243)the National Natural Science Foundation of China (Grant No.61835013)。
文摘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.
基金National Natural Science Foundation of China under Grant Nos.10475034 and 10705013the Fundamental Research Fund for Physics and Mathematics of Lanzhou University under Grant No.Lzu07002
文摘In this letter we study fermionic zero modes in gauge and gravity backgrounds taking a two-dimensional compact manifold S2 as extra dimensions. The result is that there exist massless Dirac fermions which have normalizable zero modes under quite general assumptions about these backgrounds on the bulk. Several special cases of gauge background on the sphere axe discussed and some simple fermionic zero modes are obtained.
基金Supported by the National Natural Science Foundation of China under Grant No 11274379the Research Funds of Renmin University of China under Grant No 14XNLQ07
文摘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.
基金supported by the Innovation Program for Quantum Science and Technology (Grant No.2021ZD0302401)the Hunan Provincial Science Foundation for Distinguished Young Scholars (Grant No.2021JJ10043)+1 种基金the Open Research Fund from State Key Laboratory of High Performance Computing of China (HPCL)(Grant Nos.201901-092023-KJWHPCL-07)。
文摘Majorana zero modes(MZMs),promising for topological quantum computation,are naturally hosted in vortices of two-dimensional topological superconductors(TSCs).However,precise control and braiding of these vortex-bound MZMs remain a significant challenge.This work proposes and numerically demonstrates a novel braiding scheme utilizing a programmable matrix of spintransfer torque(STT) devices(STT-matrix) integrated with a TSC layer.By selectively activating individual STT elements,their localized stray fields enable deterministic manipulation,including driving,braiding,and fusion,of superconducting vortices and their associated MZMs.We establish a comprehensive simulation framework combining finite element analysis for STT-induced vortex formation,time-dependent Ginzburg-Landau equations for vortex dynamics and time-dependent Bogoliubov-de Gennes equations for MZM evolution.Simulations confirm the STT-matrix's capability for high-fidelity vortex manipulation and demonstrate MZM braiding dynamics.We quantify the impact of vortex acceleration and finite MZM coupling on braiding fidelity,showing that it can be optimized by adjusting STT spacing and vortex separation.Furthermore,we demonstrate controlled MZM fusion and measure the resultant energy splitting.This STT-matrix-based approach offers a highly versatile,scalable,and potentially practical platform for operating MZMs within TSC vortices,advancing the development of fault-tolerant topological quantum computation.conductivity.
基金financially supported by the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302400)the National Natural Science Foundation of China(Grant No.11974271)+2 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB28000000)the National Basic Research Program of China(Grant No.2015CB921102)the China Postdoctoral Science Foundation(Grant No.2021M690233)。
文摘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.
文摘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 BiETe3 and an s-wave superconductor NbSe2. This paper will briefly review the experimental progresses based on the Bi2Te3/NbSe2 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 ofMajorana fermions in solid state physics and a starting point of MZM＇s application in topological quantum computation.
基金supported by the National Natural Science Foundation of China(Grant No.12034014)the Shenzhen Natural Science Foundation(Grant No.20231120172734001)。
文摘We present a theoretical investigation of Majorana zero mode(MZM)assisted spin pumping which consists of a quantum dot(QD)and two normal leads.When the coupling between the MZM and the QD is absent,d.c.pure spin current can be excited by a rotating magnetic field where low energy spin down electrons are flipped to high energy spin up electrons by absorbing photons.However,when the coupling is turned on,the d.c.pure spin current vanishes,and an a.c.charge current emerges with its magnitude independent of the coupling strength.We reveal that this change is due to the formation of a highly localized MZM assisted topological Andreev state at the Fermi level,which allows only the injection of electron pairs with opposite spin into the QD.By absorbing or emitting photons,the electron pairs are separated to opposite spin electrons,and then return back to the lead again,generating an a.c.charge current without spin polarization.We demonstrate the switching from d.c.pure spin current to a.c.charge current based on both Kitaev model and a more realistic topological superconductor nanowire.Although this switching can also be induced by partially separated Andreev bound state(ps-ABS)in the topological trivial phase,it is extremely unstable and highly sensitive to the Zeeman field,which is different from the switching induced by MZM.Our result suggests that quantum spin pumping may be a feasible local transport method for detecting the presence of MZMs at the ends of a superconducting nanowire.
基金support from the National Key R&D Program of China(Grants No.2021YFA1401500)the Hong Kong Research Grants Council(Project No.16306220).
文摘Topological crystalline insulators are known to support multiple Majorana zero modes(MZMs)at a single vortex,their hybridization is forbidden by a magnetic mirror symmetry MT.Due to the limited energy resolution of scanning tunneling microscopes and the very small energy spacing of trivial bound states,it remains challenging to directly probe and demonstrate the existence of multiple MZMs.In this work,we propose to demonstrate the existence of MZMs by studying the hybridization of multiple MZMs in a symmetry breaking field.The different responses of trivial bound states and MZMs can be inferred from their spatial distribution in a vortex.However,the theoretical simulations are very demanding since it requires an extremely large system in real space.By utilizing the kernel polynomial method,we can efficiently simulate large lattices with over 108 orbitals to compute the local density of states which bridges the gap between theoretical studies based on minimal models and experimental measurements.We show that the spatial distribution of MZMs and trivial vortex bound states differs drastically in tilted magnetic fields.The zero-bias peak elongates when the magnetic field preserves MT,while it splits when MT is broken,giving rise to an anisotropic magnetic response.Since the bulk of SnTe are metallic,we also study the robustness of MZMs against the bulk states,and clarify when can the MZMs produce a pronounced anisotropic magnetic response.
基金supported by the National Natural Science Foundation of China(Grant Nos.11875122,12175025,and 12147102)Tongling University Talent Program(Grant No.R23100)。
文摘In this paper,we study the ρ-meson electromagnetic form factors(EMFFs)within the framework of the light-front quark model.The physical form factors G_(C,M,Q)(Q^(2))of the ρ-meson,as well as the charged square radius<r^(2)>,the magnetic moment μ,and the quadrupole moment Q,are calculated,which describe the behaviors of EMFFs at zero momentum transfer.Using the type-Ⅱ replacement,we find that the zero-mode does contribute zero to the matrix element S_(00)^(+).It is found that the“M→M_(0)”replacement improves the angular condition remarkably,which permits different prescriptions of ρ-meson EMFFs to give the consistent results.The residual tiny violation of angular condition needs other explanations beyond the zero-mode contributions.Our results indicate that the relativistic effects or interaction internal structure are weaken in the zero-binding limit.This work is also applicable to other spin-1 particles.
基金Project supported by the National Natural Science Foundation of China(No.10972188)the Fundamental Research Funds for the Central Universities of China(No.2010121073)the Scientific Program of Fujian Province of China(No.2007F3096)
文摘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.
基金supported by the Air Force Office of Scientific Research(AFOSR)(Grant No.FA9550-14-1-0168)supported by the National Natural Science Foundation of China(Grant No.11674278)+1 种基金the National Basic Research Program of China(Grant No.2014CB921203)the CAS Center for Excellence in Topological Quantum Computation,and the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB28000000)
文摘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.
