Despite extensive research,the achievement of tunable Chern numbers in quantum anomalous Hall(QAH)systems remains a challenge in the field of condensed matter physics.Here,we theoretically proposed that Ti_(2)X_(2)(X=...Despite extensive research,the achievement of tunable Chern numbers in quantum anomalous Hall(QAH)systems remains a challenge in the field of condensed matter physics.Here,we theoretically proposed that Ti_(2)X_(2)(X=P,As,Sb,Bi)can realize tunable Chern numbers QAH effect by adjusting their magnetization orientations.In the case of Ti_(2)P_(2) and Ti_(2)As_(2),if the magnetization lies in the x-y plane,and all C_(2) symmetries are broken,a low-Chern-number phase with C=1 will manifest.Conversely,if the magnetization is aligned to the z-axis,the systems enter a high-Chern number phase with C=3.As for Ti_(2)Sb_(2) and Ti_(2)Bi_(2),by manipulating the inplane magnetization orientation,these systems can periodically enter topological phases(C=±1)over a 60°interval.Adjusting the magnetization orientation from+z to-z will result in the systems’Chern number alternating between±1.The non-trivial gap in monolayer Ti_(2)X_(2)(X=P,As,Sb,Bi)can reach values of 23.4,54.4,60.8,and 88.2 meV,respectively.All of these values are close to the room-temperature energy scale.Furthermore,our research has revealed that the application of biaxial strain can effectively modify the magnetocrystalline anisotropic energy,which is advantageous in the manipulation of magnetization orientation.This work provides a family of large-gap QAH insulators with tunable Chern numbers,demonstrating promising prospects for future electronic applications.展开更多
This paper mainly deals with the question of equivalence between equivariant cohomology Chern numbers and equivariant K-theoretic Chern numbers when the transformation group is a torus. By using the equivariant Rieman...This paper mainly deals with the question of equivalence between equivariant cohomology Chern numbers and equivariant K-theoretic Chern numbers when the transformation group is a torus. By using the equivariant Riemann-Roch relation of AtiyahHirzebruch type, it is proved that the vanishing of equivariant cohomology Chern numbers is equivalent to the vanishing of equivariant K-theoretic Chern numbers.展开更多
In this paper a gauge theory is proposed for the two-band model of Chern insulators.Based on the so-calle't Hooft monopole model,a U(1)Maxwell electromagnetic sub-field is constructed from an SU(2)gauge field,from...In this paper a gauge theory is proposed for the two-band model of Chern insulators.Based on the so-calle't Hooft monopole model,a U(1)Maxwell electromagnetic sub-field is constructed from an SU(2)gauge field,from which arise two types of topological defects,monopoles and e2 merons.We focus on the topological number in the Hall conductance σ_(xy)=e^(2)/hC,where C is the Chern number.It is discovered that in the monopole case C is indeterminate,while in the meron case C takes different values,due to a varying on-site energy m.As a typical example,we apply this method to the square lattice and compute the winding numbers(topological charges)of the defects;the C-evaluations we obtain reproduce the results of the usual literature.Furthermore,based on the gauge theory we propose a new model to obtain the high Chern numbers|C|=2,4.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
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
The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite...The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.展开更多
We employ the Dirac cone model to explore the high Chern number(C)phases that are realized in the magnetic-doped topological insulator(TI)multilayer structures by Zhao et al.[Nature 588419(2020)].The Chern number is c...We employ the Dirac cone model to explore the high Chern number(C)phases that are realized in the magnetic-doped topological insulator(TI)multilayer structures by Zhao et al.[Nature 588419(2020)].The Chern number is calculated by capturing the evolution of the phase boundaries with the parameters,then the Chern number phase diagrams of the TI multilayer structures are obtained.The high-C behavior is attributed to the band inversion of the renormalized Dirac cones,along with which the spin polarization at theΓpoint will get increased.Moreover,another two TI multilayer structures as well as the TI superlattice structures are studied.展开更多
Due to the topology, insulators become non-trivial, particularly those with large Chern numbers which support multiple edge channels, catching our attention. In the framework of the tight binding approximation, we stu...Due to the topology, insulators become non-trivial, particularly those with large Chern numbers which support multiple edge channels, catching our attention. In the framework of the tight binding approximation, we study a non-interacting Chern insulator model on the three-component dice lattice with real nearest-neighbor and complex next-nearest-neighbor hopping subjected to Λ-or V-type sublattice potentials. By analyzing the dispersions of corresponding energy bands, we find that the system undergoes a metal–insulator transition which can be modulated not only by the Fermi energy but also the tunable extra parameters. Furthermore, rich topological phases, including the ones with high Hall plateau, are uncovered by calculating the associated band’s Chern number. Besides, we also analyze the edge-state spectra and discuss the correspondence between Chern numbers and the edge states by the principle of bulk-edge correspondence. In general, our results suggest that there are large Chern number phases with C = ±3 and the work enriches the research about large Chern numbers in multiband systems.展开更多
The well-known Yau＇s uniformization conjecture states that any complete noncompact Kahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal ...The well-known Yau＇s uniformization conjecture states that any complete noncompact Kahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal volume growth has been recently confirmed, by G. Liu in [23]. In the first part, we will give a survey on thc progress. In the second part, we will consider Yau＇s conjecture for manifolds with non-maximal volume growth. We will show that the finiteness of the first Chern number Cn1 is an essential condition to solve Yau＇s conjecture by using algebraic embedding method. Moreover, we prove that, under bounded curvature conditions, Cn1 is automatically finite provided that there exists a positive line bundle with finite Chern number. In particular, we obtain a partial answer to Yau＇s uniformization conjecture on Kahler manifolds with minimal volume growth.展开更多
We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expression...We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.展开更多
In a quantum Hall effect,flat Landau levels may be broadened by disorder.However,it has been found that in the thermodynamic limit,all extended(or current carrying)states shrink to one single energy value within each ...In a quantum Hall effect,flat Landau levels may be broadened by disorder.However,it has been found that in the thermodynamic limit,all extended(or current carrying)states shrink to one single energy value within each Landau level.On the other hand,a quantum anomalous Hall effect consists of dispersive bands with finite widths.We numerically investigate the picture of current carrying states in this case.With size scaling,the spectrum width of these states in each bulk band still shrinks to a single energy value in the thermodynamic limit,in a power law way.The magnitude of the scaling exponent at the intermediate disorder is close to that in the quantum Hall effects.The number of current carrying states obeys similar scaling rules,so that the density of states of current carrying states is finite.Other states in the bulk band are localized and may contribute to the formation of a topological Anderson insulator.展开更多
We proposed a model with non reciprocal coupling coefficients, in which the imaginary parts γ indicate the phase delay or exceed term. The distributions of band structure and the group velocity are both characterized...We proposed a model with non reciprocal coupling coefficients, in which the imaginary parts γ indicate the phase delay or exceed term. The distributions of band structure and the group velocity are both characterized as a function of the coupling. we studied the system’s topological states and group velocity control. The results show that the movement and breaking of Dirac points exist in the energy band of the system. By changing the coupling coefficients, the conversion between any topological states corresponds to different Chern number. Topological edge states exist in topological nontrivial systems that correspond to the two different Chern numbers. Besides, it is also found that both the coupling coefficient and the wave vector can cause the oscillation of the pulse group velocity. At the same time, the topological state can suppress the amplitude of the group velocity profiles. Our findings enrich the theory of light wave manipulation in high-dimensional photonic lattices and provide a novel view for realizing linear localization and group velocity regulation of light waves,which has potential application in high-speed optical communication and quantum information fields.展开更多
Despite the rapid progress in the study of planar Hall effect(PHE)in recent years,all the previous works only showed that the PHE is connected to local geometric quantities,such as Berry curvature.Here,for the first t...Despite the rapid progress in the study of planar Hall effect(PHE)in recent years,all the previous works only showed that the PHE is connected to local geometric quantities,such as Berry curvature.Here,for the first time,we point out that the PHE in magnetic Weyl semimetals is directly related to a global quantity,namely,the Chern number of the Weyl point.This leads to a remarkable consequence that the PHE observation predicted here is robust against many system details,including the Fermi energy.The main difference between non-magnetic and magnetic Weyl points is that the latter breaks time-reversal symmetry T,thus generally possessing an energy tilt.Via semiclassical Boltzmann theory,we investigate the PHE in generic magnetic Weyl models with energy tilt and arbitrary Chern number.We find that by aligning the magnetic and electric fields in the same direction,the trace of the PHE conductivity contributed by Berry curvature and orbital moment is proportional to the Chern number and the energy tilt of the Weyl points,resulting in a previously undiscovered quantized PHE plateau by varying the Fermi energy.We further confirm the existence of PHE plateaus in a more realistic lattice model without T symmetry.By proposing a new quantized physical quantity,our work not only provides a new tool for extracting the topological character of the Weyl points but also suggests that the interplay between topology and magnetism can give rise to intriguing physics.展开更多
In this paper,we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S.Cheung,Bun Wong and Stephen S.T.Yau concerning a local rigidity problem of the tangent bundle over...In this paper,we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S.Cheung,Bun Wong and Stephen S.T.Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.展开更多
We theoretically study the band structures and the valley Chern numbers of the AB-AB and AB-BA stacked twisted double bilayer graphene under heterostrain effect.In the absence of heterostrain,due to the constrains by ...We theoretically study the band structures and the valley Chern numbers of the AB-AB and AB-BA stacked twisted double bilayer graphene under heterostrain effect.In the absence of heterostrain,due to the constrains by the spatial symmetries,the central two flat bands of the AB-AB are topological trivial bands,while in the AB-BA they have a finite Chern number.The heterostrain breaks all the point group symmetries and the constrains are lifted,hence the topological properties of the two arrangements can be tuned by different strain magnitudesεand directionsφ.The heterostrain has dissimilar impacts on the Chern numbers of the AB-AB and AB-BA,owing to their different band gaps,and these gaps can be modified by a vertical electric field.Our results show that the topological transitions for both arrangements occur in theεrange of 0.1%-0.4%,which can be realized in the graphene-based sample.展开更多
Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local–global correspondenc...Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local–global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states.We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation.We demonstrate this approach by the non-Hermitian Chern insulator model.We give the consistent topological phases obtained from the Chern number and vorticity.We also find some novel topological invariants embedded in the topological phases of the Chern insulator model,which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity.We also propose a generalized vorticity and its flipping index to understand physics behind this novel local–global correspondence and discuss the relationships between the local–global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane.These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states,which is expected to be applicable in more generic non-Hermitian systems.展开更多
The author shows that if a locally conformal K?hler metric is Hermitian YangMills with respect to itself with Einstein constant c≤0,then it is a Kahler-Einstein metric.In the case of c>0,some identities on torsion...The author shows that if a locally conformal K?hler metric is Hermitian YangMills with respect to itself with Einstein constant c≤0,then it is a Kahler-Einstein metric.In the case of c>0,some identities on torsions and an inequality on the second Chern number are derived.展开更多
The magnetic Weyl semimetal(WSM)is important for fundamental physics and potential applications due to its spontaneous magnetism,robust band topology,and enhanced Berry curvature.It possesses many unique quantum effec...The magnetic Weyl semimetal(WSM)is important for fundamental physics and potential applications due to its spontaneous magnetism,robust band topology,and enhanced Berry curvature.It possesses many unique quantum effects,including a large intrinsic anomalous Hall effect,Fermi arcs,and chiral anomaly.In this work,using ab initio calculations,we propose that Nidoped pyrochlore Tl2Nb2O7is a magnetic WSM caused by the exchange field splitting on bands around its quadratic band crossing point.The exchange field tuned by Ni 3d on-site Coulomb interaction parameter U drives the evolution of Weyl nodes and the resulting topological phase transition.As Weyl nodes can exist at generic points in the Brillouin zone and are hard to identify exactly,their creation and annihilation,i.e.,the change in their number,chirality,and distribution,have been consistently confirmed with a combined theoretical approach,which employs parity criterion,symmetry indicator analysis,and the Wilson loop of the Wannier center.We find that Weyl nodes remain in a large range of U and are close to the Fermi level,which makes the experimental observation very possible.We think that this method and our proposal of magnetic WSM will be useful in finding more WSMs and add to the understanding of the topological phase transition.展开更多
Higher-order topological insulators(HOTIs)can support boundary states at least two dimensions lower than the bulk,attracting intensive attention from both fundamental science and application sides.Lattice-based tight-...Higher-order topological insulators(HOTIs)can support boundary states at least two dimensions lower than the bulk,attracting intensive attention from both fundamental science and application sides.Lattice-based tight-binding models such as Benalcazar-Bernevig-Hughes model have driven significant advancements in realizing HOTIs across various physical systems.Here,beyond lattice model,we demonstrate that a cylinder with an arbitrary cross section,composed of a homogeneous electromagnetic medium featuring nontrivial second Chern numbers c_(2)=±1 in a synthetic five-dimensional space,can exhibit topologically protected HOTI-type hinge states in three-dimensional laboratory space.Interestingly,this hinge state is essentially a chiral zero mode arising from the interaction between Weyl arc surface states,guaranteed by a nontrivial c_(2),and an effective magnetic field induced by the curvature of the cylinder surface.Compared to conventional schemes to generate HOTIs,our approach is more robust,as it is an intrinsic topological phase and therefore does not rely on additional symmetry protections such as time-reversal,parity,or chiral symmetry.We experimentally realize such a cylinder using a photonic metamaterial and confirm the existence of hinge states via microwave near-field measurements.Our work introduces the concept of boundary gauge fields and establishes the link between synthetic-space c_(2) and real-space HOTI states,thereby generalizing HOTIs to cornerless systems.展开更多
基金the support by the National Natural Science Foundation of China(Grant Nos.30930852,62371397,and 62374134)the start-up funds from Northwestern Polytechnical University.
文摘Despite extensive research,the achievement of tunable Chern numbers in quantum anomalous Hall(QAH)systems remains a challenge in the field of condensed matter physics.Here,we theoretically proposed that Ti_(2)X_(2)(X=P,As,Sb,Bi)can realize tunable Chern numbers QAH effect by adjusting their magnetization orientations.In the case of Ti_(2)P_(2) and Ti_(2)As_(2),if the magnetization lies in the x-y plane,and all C_(2) symmetries are broken,a low-Chern-number phase with C=1 will manifest.Conversely,if the magnetization is aligned to the z-axis,the systems enter a high-Chern number phase with C=3.As for Ti_(2)Sb_(2) and Ti_(2)Bi_(2),by manipulating the inplane magnetization orientation,these systems can periodically enter topological phases(C=±1)over a 60°interval.Adjusting the magnetization orientation from+z to-z will result in the systems’Chern number alternating between±1.The non-trivial gap in monolayer Ti_(2)X_(2)(X=P,As,Sb,Bi)can reach values of 23.4,54.4,60.8,and 88.2 meV,respectively.All of these values are close to the room-temperature energy scale.Furthermore,our research has revealed that the application of biaxial strain can effectively modify the magnetocrystalline anisotropic energy,which is advantageous in the manipulation of magnetization orientation.This work provides a family of large-gap QAH insulators with tunable Chern numbers,demonstrating promising prospects for future electronic applications.
基金supported by the National Natural Science Foundation of China(No.11301335)
文摘This paper mainly deals with the question of equivalence between equivariant cohomology Chern numbers and equivariant K-theoretic Chern numbers when the transformation group is a torus. By using the equivariant Riemann-Roch relation of AtiyahHirzebruch type, it is proved that the vanishing of equivariant cohomology Chern numbers is equivalent to the vanishing of equivariant K-theoretic Chern numbers.
基金The authors XL and ZC acknowledge the financial support from the Natural Science Foundation of Beijing Grant No.Z180007the National Science Foundation of China Grant No.11572005WH acknowledges the support from the National Science Foundation of China Grant No.11874003 and Grant No.51672018.
文摘In this paper a gauge theory is proposed for the two-band model of Chern insulators.Based on the so-calle't Hooft monopole model,a U(1)Maxwell electromagnetic sub-field is constructed from an SU(2)gauge field,from which arise two types of topological defects,monopoles and e2 merons.We focus on the topological number in the Hall conductance σ_(xy)=e^(2)/hC,where C is the Chern number.It is discovered that in the monopole case C is indeterminate,while in the meron case C takes different values,due to a varying on-site energy m.As a typical example,we apply this method to the square lattice and compute the winding numbers(topological charges)of the defects;the C-evaluations we obtain reproduce the results of the usual literature.Furthermore,based on the gauge theory we propose a new model to obtain the high Chern numbers|C|=2,4.
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 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.
基金Project supported by the National Basic Research Program of China(Grant Nos.2009CB929504,2011CB922103,and 2010CB923400)the National Natural Science Foundation of China(Grant Nos.11225420,11074110,11174125,11074109,11074111,and 91021003)+3 种基金the Priority Academic Program Development of Jiangsu Higher Education Institutions,Chinathe Natural Science Foundation of Jiangsu Province,China(Grant No.BK2010364)the US NSF(Grant Nos.DMR-0906816 and DMR-1205734)he Princeton MRSEC(Grant No.DMR-0819860)
文摘The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11804122 and 11905054)the China Postdoctoral Science Foundation(Grant No.2021M690970)the Fundamental Research Funds for the Central Universities of China.
文摘We employ the Dirac cone model to explore the high Chern number(C)phases that are realized in the magnetic-doped topological insulator(TI)multilayer structures by Zhao et al.[Nature 588419(2020)].The Chern number is calculated by capturing the evolution of the phase boundaries with the parameters,then the Chern number phase diagrams of the TI multilayer structures are obtained.The high-C behavior is attributed to the band inversion of the renormalized Dirac cones,along with which the spin polarization at theΓpoint will get increased.Moreover,another two TI multilayer structures as well as the TI superlattice structures are studied.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11835011 and 11774316)。
文摘Due to the topology, insulators become non-trivial, particularly those with large Chern numbers which support multiple edge channels, catching our attention. In the framework of the tight binding approximation, we study a non-interacting Chern insulator model on the three-component dice lattice with real nearest-neighbor and complex next-nearest-neighbor hopping subjected to Λ-or V-type sublattice potentials. By analyzing the dispersions of corresponding energy bands, we find that the system undergoes a metal–insulator transition which can be modulated not only by the Fermi energy but also the tunable extra parameters. Furthermore, rich topological phases, including the ones with high Hall plateau, are uncovered by calculating the associated band’s Chern number. Besides, we also analyze the edge-state spectra and discuss the correspondence between Chern numbers and the edge states by the principle of bulk-edge correspondence. In general, our results suggest that there are large Chern number phases with C = ±3 and the work enriches the research about large Chern numbers in multiband systems.
文摘The well-known Yau＇s uniformization conjecture states that any complete noncompact Kahler manifold with positive bisectional curvature is bi-holomorphic to the Euclidean space. The conjecture for the case of maximal volume growth has been recently confirmed, by G. Liu in [23]. In the first part, we will give a survey on thc progress. In the second part, we will consider Yau＇s conjecture for manifolds with non-maximal volume growth. We will show that the finiteness of the first Chern number Cn1 is an essential condition to solve Yau＇s conjecture by using algebraic embedding method. Moreover, we prove that, under bounded curvature conditions, Cn1 is automatically finite provided that there exists a positive line bundle with finite Chern number. In particular, we obtain a partial answer to Yau＇s uniformization conjecture on Kahler manifolds with minimal volume growth.
基金Project supported by the Beijing Natural Science Foundation(Grant No.1232026)the Qinxin Talents Program of BISTU(Grant No.QXTCP C201711)+2 种基金the R&D Program of Beijing Municipal Education Commission(Grant No.KM202011232017)the National Natural Science Foundation of China(Grant No.12304190)the Research fund of BISTU(Grant No.2022XJJ32).
文摘We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11774336,12104108,and 61427901)the Starting Research Fund from Guangzhou University(Grant Nos.RQ2020082 and 62104360).
文摘In a quantum Hall effect,flat Landau levels may be broadened by disorder.However,it has been found that in the thermodynamic limit,all extended(or current carrying)states shrink to one single energy value within each Landau level.On the other hand,a quantum anomalous Hall effect consists of dispersive bands with finite widths.We numerically investigate the picture of current carrying states in this case.With size scaling,the spectrum width of these states in each bulk band still shrinks to a single energy value in the thermodynamic limit,in a power law way.The magnitude of the scaling exponent at the intermediate disorder is close to that in the quantum Hall effects.The number of current carrying states obeys similar scaling rules,so that the density of states of current carrying states is finite.Other states in the bulk band are localized and may contribute to the formation of a topological Anderson insulator.
基金Project supported by the National Natural Science Foundation of China (Grant No. 1217040857)。
文摘We proposed a model with non reciprocal coupling coefficients, in which the imaginary parts γ indicate the phase delay or exceed term. The distributions of band structure and the group velocity are both characterized as a function of the coupling. we studied the system’s topological states and group velocity control. The results show that the movement and breaking of Dirac points exist in the energy band of the system. By changing the coupling coefficients, the conversion between any topological states corresponds to different Chern number. Topological edge states exist in topological nontrivial systems that correspond to the two different Chern numbers. Besides, it is also found that both the coupling coefficient and the wave vector can cause the oscillation of the pulse group velocity. At the same time, the topological state can suppress the amplitude of the group velocity profiles. Our findings enrich the theory of light wave manipulation in high-dimensional photonic lattices and provide a novel view for realizing linear localization and group velocity regulation of light waves,which has potential application in high-speed optical communication and quantum information fields.
基金supported by the National Key Research and Development Program of China(2020YFA0308800)the National Natural Science Foundation of China(12004035,12234003 and 12321004)+1 种基金the China Postdoctoral Science Foundation(2021TQ0043 and 2021M700437)Beijing Institute of Technology Research Fund Program for Young Scholars。
文摘Despite the rapid progress in the study of planar Hall effect(PHE)in recent years,all the previous works only showed that the PHE is connected to local geometric quantities,such as Berry curvature.Here,for the first time,we point out that the PHE in magnetic Weyl semimetals is directly related to a global quantity,namely,the Chern number of the Weyl point.This leads to a remarkable consequence that the PHE observation predicted here is robust against many system details,including the Fermi energy.The main difference between non-magnetic and magnetic Weyl points is that the latter breaks time-reversal symmetry T,thus generally possessing an energy tilt.Via semiclassical Boltzmann theory,we investigate the PHE in generic magnetic Weyl models with energy tilt and arbitrary Chern number.We find that by aligning the magnetic and electric fields in the same direction,the trace of the PHE conductivity contributed by Berry curvature and orbital moment is proportional to the Chern number and the energy tilt of the Weyl points,resulting in a previously undiscovered quantized PHE plateau by varying the Fermi energy.We further confirm the existence of PHE plateaus in a more realistic lattice model without T symmetry.By proposing a new quantized physical quantity,our work not only provides a new tool for extracting the topological character of the Weyl points but also suggests that the interplay between topology and magnetism can give rise to intriguing physics.
文摘In this paper,we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S.Cheung,Bun Wong and Stephen S.T.Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.
基金the National Natural Science Foundation of China for the support(Grant No.11874271).
文摘We theoretically study the band structures and the valley Chern numbers of the AB-AB and AB-BA stacked twisted double bilayer graphene under heterostrain effect.In the absence of heterostrain,due to the constrains by the spatial symmetries,the central two flat bands of the AB-AB are topological trivial bands,while in the AB-BA they have a finite Chern number.The heterostrain breaks all the point group symmetries and the constrains are lifted,hence the topological properties of the two arrangements can be tuned by different strain magnitudesεand directionsφ.The heterostrain has dissimilar impacts on the Chern numbers of the AB-AB and AB-BA,owing to their different band gaps,and these gaps can be modified by a vertical electric field.Our results show that the topological transitions for both arrangements occur in theεrange of 0.1%-0.4%,which can be realized in the graphene-based sample.
文摘Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics.We propose a generalized local–global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states.We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation.We demonstrate this approach by the non-Hermitian Chern insulator model.We give the consistent topological phases obtained from the Chern number and vorticity.We also find some novel topological invariants embedded in the topological phases of the Chern insulator model,which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity.We also propose a generalized vorticity and its flipping index to understand physics behind this novel local–global correspondence and discuss the relationships between the local–global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane.These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states,which is expected to be applicable in more generic non-Hermitian systems.
文摘The author shows that if a locally conformal K?hler metric is Hermitian YangMills with respect to itself with Einstein constant c≤0,then it is a Kahler-Einstein metric.In the case of c>0,some identities on torsions and an inequality on the second Chern number are derived.
基金supported by the National Natural Science Foundation of China(Grant Nos.11974076,11925408,11921004,and 12188101)Key Project of Natural Science Foundation of Fujian Province(Grant No.2021J02012)+4 种基金Ministry of Science and Technology of China(Grant No.2018YFA0305700)Chinese Academy of Sciences(Grant No.XDB33000000)K.C.Wong Education Foundation(Grant No.GJTD-2018-01)Informatization Plan of Chinese Academy of Sciences(Grant No.CAS-WX2021SF-0102)supported by the Swiss National Science Foundation(Grant No.200021-196966)。
文摘The magnetic Weyl semimetal(WSM)is important for fundamental physics and potential applications due to its spontaneous magnetism,robust band topology,and enhanced Berry curvature.It possesses many unique quantum effects,including a large intrinsic anomalous Hall effect,Fermi arcs,and chiral anomaly.In this work,using ab initio calculations,we propose that Nidoped pyrochlore Tl2Nb2O7is a magnetic WSM caused by the exchange field splitting on bands around its quadratic band crossing point.The exchange field tuned by Ni 3d on-site Coulomb interaction parameter U drives the evolution of Weyl nodes and the resulting topological phase transition.As Weyl nodes can exist at generic points in the Brillouin zone and are hard to identify exactly,their creation and annihilation,i.e.,the change in their number,chirality,and distribution,have been consistently confirmed with a combined theoretical approach,which employs parity criterion,symmetry indicator analysis,and the Wilson loop of the Wannier center.We find that Weyl nodes remain in a large range of U and are close to the Fermi level,which makes the experimental observation very possible.We think that this method and our proposal of magnetic WSM will be useful in finding more WSMs and add to the understanding of the topological phase transition.
基金supported by National Key Research and Development Program of China(Grants No.2023YFA1407700,2023YFA1406901)National Natural Science Foundation China(Grants No.12374343)+2 种基金the start-up funding of Fudan University(JIH1232133Y)the New Cornerstone Science Foundation,the Research Grants Council of Hong Kong(AoE/P-502/20,STG3/E-704/23-N,17309021)Guangdong Provincial Quantum Science Strategic Initiative(GDZX2204004,GDZX2304001).
文摘Higher-order topological insulators(HOTIs)can support boundary states at least two dimensions lower than the bulk,attracting intensive attention from both fundamental science and application sides.Lattice-based tight-binding models such as Benalcazar-Bernevig-Hughes model have driven significant advancements in realizing HOTIs across various physical systems.Here,beyond lattice model,we demonstrate that a cylinder with an arbitrary cross section,composed of a homogeneous electromagnetic medium featuring nontrivial second Chern numbers c_(2)=±1 in a synthetic five-dimensional space,can exhibit topologically protected HOTI-type hinge states in three-dimensional laboratory space.Interestingly,this hinge state is essentially a chiral zero mode arising from the interaction between Weyl arc surface states,guaranteed by a nontrivial c_(2),and an effective magnetic field induced by the curvature of the cylinder surface.Compared to conventional schemes to generate HOTIs,our approach is more robust,as it is an intrinsic topological phase and therefore does not rely on additional symmetry protections such as time-reversal,parity,or chiral symmetry.We experimentally realize such a cylinder using a photonic metamaterial and confirm the existence of hinge states via microwave near-field measurements.Our work introduces the concept of boundary gauge fields and establishes the link between synthetic-space c_(2) and real-space HOTI states,thereby generalizing HOTIs to cornerless systems.
