We investigate the localization and topological properties of the Haldane model under the influence of random flux and Anderson disorder. Our localization analysis reveals that random flux induces a transition from in...We investigate the localization and topological properties of the Haldane model under the influence of random flux and Anderson disorder. Our localization analysis reveals that random flux induces a transition from insulating to metallic states, while Anderson localization only arises under the modulation of Anderson disorder. By employing real-space topological invariant methods, we demonstrates that the system undergoes topological phase transitions under different disorder manipulations, whereas random flux modulation uniquely induces topological Anderson insulator phases, with the potential to generate states with opposite Chern numbers. These findings highlight the distinct roles of disorder in shaping the interplay between topology and localization, providing insights into stabilizing topological states and designing robust topological quantum materials.展开更多
In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue...In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue integration, in some equations concerning various sectors of Chern-Simons theory and Yang-Mills gauge theory, precisely the two dimensional quantum Yang-Mills theory. In conclusion, in Section 3, we have described also the possible mathematical connections with some sectors of String Theory and Number Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings.展开更多
High-performance quantum anomalous Hall(QAH)systems are crucial materials for exploring emerging quantum physics and magnetic topological phenomena.Inspired by layered FeSe materials with excellent superconducting pro...High-performance quantum anomalous Hall(QAH)systems are crucial materials for exploring emerging quantum physics and magnetic topological phenomena.Inspired by layered FeSe materials with excellent superconducting properties,the Janus monolayers Fe_(2)SSeX_(2)(X=Ga,In and Tl)are built by the decoration of Ga,In and T1 atoms in monolayer Fe_(2)SSe.In first-principles calculations,Fe_(2)SSeX_(2)have stable structures and prefer ferromagnetic(FM)ordering,and can be considered as Weyl semimetals without spin-orbit coupling.For out-of-plane(OOP)magnetic anisotropy,large nontrivial gaps are opened and the Fe_(2)SSeX_(2)are predicted to be large-gap QAH insulators with a high Chern number C=2,proved by two chiral edge states and Berry curvature.When the magnetization is flipped,the two chiral edge states can be simultaneously changed and C=-2 can be obtained,revealing the fascinating behavior of chiral spin-edge state locking.It is found that the QAH properties of Fe_(2)SSeX_(2)are robust against strain.In particular,nontrivial topological quantum states can spontaneously appear for Fe_(2)SSeGa_(2)and Fe_(2)SSeIn_(2)because the orientations of the easy magnetic axis are adjusted from in-plane to OOP by the biaxial strain.Our studies provide excellent candidate systems to realize QAH properties with a high Chern number,and suggest more experimental explorations combining superconductivity and topology.展开更多
Recently,Chern insulators in an antiferromagnetic(AFM)phase have been suggested theoretically and predicted in a few materials.However,the experimental observation of two-dimensional(2D)AFM quantum anomalous Hall effe...Recently,Chern insulators in an antiferromagnetic(AFM)phase have been suggested theoretically and predicted in a few materials.However,the experimental observation of two-dimensional(2D)AFM quantum anomalous Hall effect is still a challenge to date.In this work,we propose that an AFM Chern insulator can be realized in a 2D monolayer of NiOsCl_(6)modulated by a compressive strain.Strain modulation is accessible experimentally and used widely in predicting and tuning topological nontrivial phases.With first-principles calculations,we have investigated the structural,magnetic,and electronic properties of NiOsCl_(6).Its stability has been confirmed through molecular dynamical simulations,elasticity constant,and phonon spectrum.It has a collinear AFM order,with opposite magnetic moments of 1.3μBon each Ni/Os atom,respectively,and the Neel temperature is estimated to be 93 K.In the absence of strain,it functions as an AFM insulator with a direct gap with spin-orbital coupling included.Compressive strain will induce a transition from a normal insulator to a Chern insulator characterized by a Chern number C=1,with a band gap of about 30 meV.This transition is accompanied by a structural distortion.Remarkably,the Chern insulator phase persists within the 3%-10%compressive strain range,offering an alternative platform for the utilization of AFM materials in spintronic devices.展开更多
Quantum anomalous Hall(QAH) insulators have excellent properties driven by fancy topological physics, but their practical application is greatly hindered by the observed temperature of liquid nitrogen, and the QAH ins...Quantum anomalous Hall(QAH) insulators have excellent properties driven by fancy topological physics, but their practical application is greatly hindered by the observed temperature of liquid nitrogen, and the QAH insulator with high Chern number is conducive to spintronic devices with lower energy consumption. Here, we find that monolayer Fe SIn is a good candidate for realizing the QAH phase;it exhibits a high magnetic transition temperature of 221 K and tunable C = ±2 with respect to magnetization orientation in the y–z plane. After the application of biaxial strain, the magnetic axis shifts from the x–y plane to the z direction, and the effect of the high C and ferromagnetic ground state on the stress is robust. Also, the effect of correlation U on C has been examined. These properties are rooted in the large size of the Fe atom that contributes to ferromagnetic kinetic exchange with neighboring Fe atoms. These findings demonstrate monolayer Fe SIn to be a major template for probing novel QAH devices at higher temperatures.展开更多
Unraveling the mechanism underlying topological phases, notably the Chern insulators(Ch Is) in strong correlated systems at the microscopy scale, has captivated significant research interest. Nonetheless, Ch Is harbor...Unraveling the mechanism underlying topological phases, notably the Chern insulators(Ch Is) in strong correlated systems at the microscopy scale, has captivated significant research interest. Nonetheless, Ch Is harboring topological information have not always manifested themselves, owing to the constraints imposed by displacement fields in certain experimental configurations. In this study, we employ density-tuned scanning tunneling microscopy(DT-STM) to investigate the Ch Is in twisted monolayer–bilayer graphene(t MBG). At zero magnetic field, we observe correlated metallic states.While under a magnetic field, a metal–insulator transition happens and an integer Ch I is formed emanating from the filling index s = 3 with a Chern number C = 1. Our results underscore the pivotal role of magnetic fields as a powerful probe for elucidating topological phases in twisted Van der Waals heterostructures.展开更多
The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattic...The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.展开更多
We review a 3d quantum gravity model, which incorporates massive spinning fields into the Euclidean path integral in a Chern-Simons formulation. Fundamental matter as defined in our previous preon model is recapped. B...We review a 3d quantum gravity model, which incorporates massive spinning fields into the Euclidean path integral in a Chern-Simons formulation. Fundamental matter as defined in our previous preon model is recapped. Both quantum gravity and the particle model are shown to be derivable from the supersymmetric 3d Chern-Simons action. Forces-Matter unification is achieved.展开更多
基金Project supported by the National Key Research and Development Program of China (Grant Nos. 2021YFA1400900, 2021YFA0718300, and 2021YFA1402100)the National Natural Science Foundation of China (Grant Nos. 12174461, 12234012, 12334012, and 52327808)。
文摘We investigate the localization and topological properties of the Haldane model under the influence of random flux and Anderson disorder. Our localization analysis reveals that random flux induces a transition from insulating to metallic states, while Anderson localization only arises under the modulation of Anderson disorder. By employing real-space topological invariant methods, we demonstrates that the system undergoes topological phase transitions under different disorder manipulations, whereas random flux modulation uniquely induces topological Anderson insulator phases, with the potential to generate states with opposite Chern numbers. These findings highlight the distinct roles of disorder in shaping the interplay between topology and localization, providing insights into stabilizing topological states and designing robust topological quantum materials.
文摘In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue integration, in some equations concerning various sectors of Chern-Simons theory and Yang-Mills gauge theory, precisely the two dimensional quantum Yang-Mills theory. In conclusion, in Section 3, we have described also the possible mathematical connections with some sectors of String Theory and Number Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52173283 and 62071200)Taishan Scholar Program of Shandong Province(Grant No.ts20190939)Independent Cultivation Program of Innovation Team of Jinan City(Grant No.2021GXRC043)。
文摘High-performance quantum anomalous Hall(QAH)systems are crucial materials for exploring emerging quantum physics and magnetic topological phenomena.Inspired by layered FeSe materials with excellent superconducting properties,the Janus monolayers Fe_(2)SSeX_(2)(X=Ga,In and Tl)are built by the decoration of Ga,In and T1 atoms in monolayer Fe_(2)SSe.In first-principles calculations,Fe_(2)SSeX_(2)have stable structures and prefer ferromagnetic(FM)ordering,and can be considered as Weyl semimetals without spin-orbit coupling.For out-of-plane(OOP)magnetic anisotropy,large nontrivial gaps are opened and the Fe_(2)SSeX_(2)are predicted to be large-gap QAH insulators with a high Chern number C=2,proved by two chiral edge states and Berry curvature.When the magnetization is flipped,the two chiral edge states can be simultaneously changed and C=-2 can be obtained,revealing the fascinating behavior of chiral spin-edge state locking.It is found that the QAH properties of Fe_(2)SSeX_(2)are robust against strain.In particular,nontrivial topological quantum states can spontaneously appear for Fe_(2)SSeGa_(2)and Fe_(2)SSeIn_(2)because the orientations of the easy magnetic axis are adjusted from in-plane to OOP by the biaxial strain.Our studies provide excellent candidate systems to realize QAH properties with a high Chern number,and suggest more experimental explorations combining superconductivity and topology.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12104183,52173283,and 62071200)the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2021MA040 and ZR2023MA091)+2 种基金the Taishan Scholar Program of Shandong Province,China(Grant No.ts20190939)the Independent Cultivation Program of Innovation Team of Jinan City(Grant No.2021GXRC043)supported by high-performance computing platform at University of Jinan。
文摘Recently,Chern insulators in an antiferromagnetic(AFM)phase have been suggested theoretically and predicted in a few materials.However,the experimental observation of two-dimensional(2D)AFM quantum anomalous Hall effect is still a challenge to date.In this work,we propose that an AFM Chern insulator can be realized in a 2D monolayer of NiOsCl_(6)modulated by a compressive strain.Strain modulation is accessible experimentally and used widely in predicting and tuning topological nontrivial phases.With first-principles calculations,we have investigated the structural,magnetic,and electronic properties of NiOsCl_(6).Its stability has been confirmed through molecular dynamical simulations,elasticity constant,and phonon spectrum.It has a collinear AFM order,with opposite magnetic moments of 1.3μBon each Ni/Os atom,respectively,and the Neel temperature is estimated to be 93 K.In the absence of strain,it functions as an AFM insulator with a direct gap with spin-orbital coupling included.Compressive strain will induce a transition from a normal insulator to a Chern insulator characterized by a Chern number C=1,with a band gap of about 30 meV.This transition is accompanied by a structural distortion.Remarkably,the Chern insulator phase persists within the 3%-10%compressive strain range,offering an alternative platform for the utilization of AFM materials in spintronic devices.
基金Project supported by the National Natural Science Foundation of China (Grant No. 52173283)the Taishan Scholar Program of Shandong Province,China (Grant No. ts20190939)the Independent Cultivation Program of Innovation Team of Jinan City (Grant No. 2021GXRC043)。
文摘Quantum anomalous Hall(QAH) insulators have excellent properties driven by fancy topological physics, but their practical application is greatly hindered by the observed temperature of liquid nitrogen, and the QAH insulator with high Chern number is conducive to spintronic devices with lower energy consumption. Here, we find that monolayer Fe SIn is a good candidate for realizing the QAH phase;it exhibits a high magnetic transition temperature of 221 K and tunable C = ±2 with respect to magnetization orientation in the y–z plane. After the application of biaxial strain, the magnetic axis shifts from the x–y plane to the z direction, and the effect of the high C and ferromagnetic ground state on the stress is robust. Also, the effect of correlation U on C has been examined. These properties are rooted in the large size of the Fe atom that contributes to ferromagnetic kinetic exchange with neighboring Fe atoms. These findings demonstrate monolayer Fe SIn to be a major template for probing novel QAH devices at higher temperatures.
文摘Unraveling the mechanism underlying topological phases, notably the Chern insulators(Ch Is) in strong correlated systems at the microscopy scale, has captivated significant research interest. Nonetheless, Ch Is harboring topological information have not always manifested themselves, owing to the constraints imposed by displacement fields in certain experimental configurations. In this study, we employ density-tuned scanning tunneling microscopy(DT-STM) to investigate the Ch Is in twisted monolayer–bilayer graphene(t MBG). At zero magnetic field, we observe correlated metallic states.While under a magnetic field, a metal–insulator transition happens and an integer Ch I is formed emanating from the filling index s = 3 with a Chern number C = 1. Our results underscore the pivotal role of magnetic fields as a powerful probe for elucidating topological phases in twisted Van der Waals heterostructures.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12074101 and 11604081)sponsored by the Natural Science Foundation of Henan Province, China (Grant No. 212300410040)。
文摘The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.
文摘We review a 3d quantum gravity model, which incorporates massive spinning fields into the Euclidean path integral in a Chern-Simons formulation. Fundamental matter as defined in our previous preon model is recapped. Both quantum gravity and the particle model are shown to be derivable from the supersymmetric 3d Chern-Simons action. Forces-Matter unification is achieved.
