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
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
This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the author...This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the authors point out a difference between Finsler submanifolds and Riemann submanifolds.展开更多
The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.
Chern-Simon theory and the holographic principle as well as scale relativity are used to find out the exact value of cosmic ordinary and dark energy density. The result agrees completely with previously obtained ones ...Chern-Simon theory and the holographic principle as well as scale relativity are used to find out the exact value of cosmic ordinary and dark energy density. The result agrees completely with previously obtained ones as well as with accurate cosmic measurements.展开更多
This paper reconstructs,based on American and Chinese primary sources,the visits of Chinese mathematicians Shiing-shen Chern陈省身(Chen Xingshen)and Hua Luogeng华罗庚(Loo-Keng Hua)4 to the Institute for Advanced Study...This paper reconstructs,based on American and Chinese primary sources,the visits of Chinese mathematicians Shiing-shen Chern陈省身(Chen Xingshen)and Hua Luogeng华罗庚(Loo-Keng Hua)4 to the Institute for Advanced Study in Princeton in the United States in the 1940s,especially their interactions with Oswald Veblen and Hermann Weyl,two leading mathematicians at the IAS.It argues that Chern’s and Hua’s motivations and choices in regard to their transnational movements between China and the US were more nuanced and multifaceted than what is presented in existing accounts,and that socio-political factors combined with professional-personal ones to shape their decisions.The paper further uses their experiences to demonstrate the importance of transnational scientific interactions for the development of science in China,the US,and elsewhere in the twentieth century.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.
文摘This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the authors point out a difference between Finsler submanifolds and Riemann submanifolds.
文摘The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.
文摘Chern-Simon theory and the holographic principle as well as scale relativity are used to find out the exact value of cosmic ordinary and dark energy density. The result agrees completely with previously obtained ones as well as with accurate cosmic measurements.
文摘This paper reconstructs,based on American and Chinese primary sources,the visits of Chinese mathematicians Shiing-shen Chern陈省身(Chen Xingshen)and Hua Luogeng华罗庚(Loo-Keng Hua)4 to the Institute for Advanced Study in Princeton in the United States in the 1940s,especially their interactions with Oswald Veblen and Hermann Weyl,two leading mathematicians at the IAS.It argues that Chern’s and Hua’s motivations and choices in regard to their transnational movements between China and the US were more nuanced and multifaceted than what is presented in existing accounts,and that socio-political factors combined with professional-personal ones to shape their decisions.The paper further uses their experiences to demonstrate the importance of transnational scientific interactions for the development of science in China,the US,and elsewhere in the twentieth century.
