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 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
Thermal Hall effect, where a transverse temperature difference is generated by implementing a longitudinal temperature gradient and an external magnetic field in the perpendicular direction to systems, is a useful too...Thermal Hall effect, where a transverse temperature difference is generated by implementing a longitudinal temperature gradient and an external magnetic field in the perpendicular direction to systems, is a useful tool to reveal transport properties of quantum materials. A systematic study of the thermal Hall effect in a Chern insulator is still lacking. Here,using the Landauer–Büttiker formula, we investigated the thermal Hall transport of the Harper–Hofstadter model with flux φ= 1/2 and its generalizations. We demonstrated that the Wiedemann–Franz law, which states that the thermal Hall conductivity is linearly proportional to the quantum Hall conductivity in the low temperature limit, is still valid in this Chern insulator, and that the thermal Hall conductivity can be used to characterize the topological properties of quantum materials.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
The introduction of non-Hermiticity provides photonic systems with more design degrees of freedom, along with unique properties, which have aroused widespread interest. On the other hand, the concept of synthetic dime...The introduction of non-Hermiticity provides photonic systems with more design degrees of freedom, along with unique properties, which have aroused widespread interest. On the other hand, the concept of synthetic dimensions has also been introduced into non-Hermitian topological physics. In this work, we theoretically investigate the two-dimensional(2D) band structure of a 1D non-Hermitian photonic crystal(PC) by introducing globally a translation deformation as a synthetic dimension. The resulting two-dimensional photonic crystal is a Chern insulator, which is numerically verified by calculated Chern numbers and edge dispersions. We find that this property stems from the inherent topology of synthetic space(kx, Δx), which does not depend on the crystal's structural and material parameters. It guarantees robust edge states traversing the gap along the synthetic dimension. To provide deeper insight, we derive the reflection phase of a 1D crystal using the plane wave expansion method and give a clear physical picture of the topological edge states generated by translation deformation.These findings may pave the way for translation-based photonic devices, including topological filters and lasers.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
Chern number is usually characterized by Berry curvature.Here,by investigating the Dirac model of even-dimensional Chern insulator,we give the general relation between Berry curvature and quantum metric,which indicate...Chern number is usually characterized by Berry curvature.Here,by investigating the Dirac model of even-dimensional Chern insulator,we give the general relation between Berry curvature and quantum metric,which indicates that the Chern number can be encoded in quantum metric as well as the surface area of the Brillouin zone on the hypersphere embedded in Euclidean parameter space.We find that there is a corresponding relationship between the quantum metric and the metric on such a hypersphere.We give the geometrical property of quantum metric.Besides,we give a protocol to measure the quantum metric in the degenerate system.展开更多
The quantum anomalous Hall effect(QAHE) has special quantum properties that are ideal for possible future spintronic devices. However, the experimental realization is rather challenging due to its low Curie temperatur...The quantum anomalous Hall effect(QAHE) has special quantum properties that are ideal for possible future spintronic devices. However, the experimental realization is rather challenging due to its low Curie temperature and small non-trivial bandgap in two-dimensional(2D) materials. In this paper, we demonstrate through first-principles calculations that monolayer Co2Te material is a promising 2D candidate to realize QAHE in practice. Excitingly, through Monte Carlo simulations, it is found that the Curie temperature of single-layer Co2Te can reach 573 K. The band crossing at the Fermi level in monolayer Co2Te is opened when spin–orbit coupling is considered, which leads to QAHE with a sizable bandgap of Eg= 96 me V, characterized by the non-zero Chern number(C = 1) and a chiral edge state. Therefore, our findings not only enrich the study of quantum anomalous Hall effect, but also broaden the horizons of the spintronics and topological nanoelectronics applications.展开更多
The Haldane model is the simplest yet most powerful topological lattice model exhibiting various phases,including the Dirac semimetal phase and the anomalous quantum Hall phase(also known as the Chern insulator).Altho...The Haldane model is the simplest yet most powerful topological lattice model exhibiting various phases,including the Dirac semimetal phase and the anomalous quantum Hall phase(also known as the Chern insulator).Although considered unlikely to be physically directly realizable in condensed matter systems,it has been experimentally demonstrated in other physical settings such as cold atoms,where Hermiticity is usually preserved.Extending this model to the non-Hermitian regime with energy non-conservation can significantly enrich topological phases that lack Hermitian counterparts;however,such exploration remains experimentally challenging due to the lack of suitable physical platforms.Here,based on electric circuits,we report the experimental realization of a genuine non-Hermitian Haldane model with asymmetric next-nearest-neighbor hopping.We observe two previously uncovered phases:a non-Hermitian Chern insulator and a non-Hermitian semimetal phase,both exhibiting boundary-dependent amplifying or dissipative chiral edge states.Our work paves the way for exploring non-Hermiticity-induced unconventional topological phases in the Haldane model.展开更多
Magnetic materials could realize the intriguing quantum anomalous Hall effect and metal-to-insulator transition when combined with band topology or electronic correlation,which have broad prospects in quantum informat...Magnetic materials could realize the intriguing quantum anomalous Hall effect and metal-to-insulator transition when combined with band topology or electronic correlation,which have broad prospects in quantum information,spintronics,and valleytronics.Here,we propose the approach of designing novel two-dimensional(2D)magnetic states via d-orbital-based superatomic lattices.Specifically,we chose triangular zirconium dichloride disks as superatoms to construct the honeycomb superatomic lattices.Using first-principles calculations,we identified a series of 2D magnetic states with varying sizes of superatoms.We found the non-uniform stoichiometries and geometric effect of superatomic lattice give rise to spin-polarized charges arranged in different magnetic configurations,containing ferromagnetic coloring triangles,antiferromagnetic honeycomb,and ferromagnetic kagome lattices.Attractively,these magnetic states are endowed with nontrivial band topology or strong correlation,forming an ideal Chern insulator or antiferromagnetic Dirac Mott insulator.Our work not only reveals the potential of d-orbital-based superatoms for generating unusual magnetic configurations,but also supplies a new avenue for material engineering at the nanoscale.展开更多
Energy dissipation is of fundamental interest and crucial importance in quantum systems. However,whether energy dissipation can emerge without backscattering inside topological systems remains a question. As a hallmar...Energy dissipation is of fundamental interest and crucial importance in quantum systems. However,whether energy dissipation can emerge without backscattering inside topological systems remains a question. As a hallmark, we propose a microscopic picture that illustrates energy dissipation in the quantum Hall(QH) plateau regime of graphene. Despite the quantization of Hall, longitudinal, and two-probe resistances(dubbed as the quantum limit), we find that the energy dissipation emerges in the form of Joule heat. It is demonstrated that the non-equilibrium energy distribution of carriers plays much more essential roles than the resistance on energy dissipation. Eventually, we suggest probing the phenomenon by measuring local temperature increases in experiments and reconsidering the dissipation typically ignored in realistic topological circuits.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.
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. U2032164 and 12174394)the Start-up Fund from Anhui University in China。
文摘Thermal Hall effect, where a transverse temperature difference is generated by implementing a longitudinal temperature gradient and an external magnetic field in the perpendicular direction to systems, is a useful tool to reveal transport properties of quantum materials. A systematic study of the thermal Hall effect in a Chern insulator is still lacking. Here,using the Landauer–Büttiker formula, we investigated the thermal Hall transport of the Harper–Hofstadter model with flux φ= 1/2 and its generalizations. We demonstrated that the Wiedemann–Franz law, which states that the thermal Hall conductivity is linearly proportional to the quantum Hall conductivity in the low temperature limit, is still valid in this Chern insulator, and that the thermal Hall conductivity can be used to characterize the topological properties of quantum materials.
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National Natural Science Foundation of China(62035016)Basic and Applied Basic Research Foundation of Guangdong Province (2023B1515040023)+1 种基金Natural Science Foundation of Jiangxi Province (20242BAB20023)Training Program for Academic and Technical Leaders of Major Disciplines in Jiangxi Province (20243BCE51163)。
文摘The introduction of non-Hermiticity provides photonic systems with more design degrees of freedom, along with unique properties, which have aroused widespread interest. On the other hand, the concept of synthetic dimensions has also been introduced into non-Hermitian topological physics. In this work, we theoretically investigate the two-dimensional(2D) band structure of a 1D non-Hermitian photonic crystal(PC) by introducing globally a translation deformation as a synthetic dimension. The resulting two-dimensional photonic crystal is a Chern insulator, which is numerically verified by calculated Chern numbers and edge dispersions. We find that this property stems from the inherent topology of synthetic space(kx, Δx), which does not depend on the crystal's structural and material parameters. It guarantees robust edge states traversing the gap along the synthetic dimension. To provide deeper insight, we derive the reflection phase of a 1D crystal using the plane wave expansion method and give a clear physical picture of the topological edge states generated by translation deformation.These findings may pave the way for translation-based photonic devices, including topological filters and lasers.
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.
文摘Chern number is usually characterized by Berry curvature.Here,by investigating the Dirac model of even-dimensional Chern insulator,we give the general relation between Berry curvature and quantum metric,which indicates that the Chern number can be encoded in quantum metric as well as the surface area of the Brillouin zone on the hypersphere embedded in Euclidean parameter space.We find that there is a corresponding relationship between the quantum metric and the metric on such a hypersphere.We give the geometrical property of quantum metric.Besides,we give a protocol to measure the quantum metric in the degenerate system.
基金supported by the Taishan Scholar Program of Shandong Province, China (Grant No. ts20190939)the Independent Cultivation Program of Innovation Team of Jinan City (Grant No. 2021GXRC043)the National Natural Science Foundation of China (Grant No. 52173238)。
文摘The quantum anomalous Hall effect(QAHE) has special quantum properties that are ideal for possible future spintronic devices. However, the experimental realization is rather challenging due to its low Curie temperature and small non-trivial bandgap in two-dimensional(2D) materials. In this paper, we demonstrate through first-principles calculations that monolayer Co2Te material is a promising 2D candidate to realize QAHE in practice. Excitingly, through Monte Carlo simulations, it is found that the Curie temperature of single-layer Co2Te can reach 573 K. The band crossing at the Fermi level in monolayer Co2Te is opened when spin–orbit coupling is considered, which leads to QAHE with a sizable bandgap of Eg= 96 me V, characterized by the non-zero Chern number(C = 1) and a chiral edge state. Therefore, our findings not only enrich the study of quantum anomalous Hall effect, but also broaden the horizons of the spintronics and topological nanoelectronics applications.
基金sponsored by the National Key Research and Development Program of China(Grant No.2022YFA1404902)the National Natural Science Foundation of China(Grant No.12104353),the Fundamental Research Funds for the Central Universities(Grant No.QTZX25086)+4 种基金the Open Foundation of the State Key Laboratory of Modern Optical Instrumentation.B.L.was sponsored by the National Natural Science Foundation of China(Grant No.61901133)the Fundamental Research Funds for the Central Universities(No.3072024XX2504)the Forward Design Technology Special Fund Project of Harbin Engineering University(Nos.KYWZ220242504,KYW220240807,and KYWZ220240807)P.L.was sponsored by the National Natural Science Foundation of China(Grant No.11805141)and Basic Research Program of Shanxi Province(No.202203021222250)Y.L.was sponsored by the National Natural Science Foundation of China(Grant No.62271366)and the 111 Project.
文摘The Haldane model is the simplest yet most powerful topological lattice model exhibiting various phases,including the Dirac semimetal phase and the anomalous quantum Hall phase(also known as the Chern insulator).Although considered unlikely to be physically directly realizable in condensed matter systems,it has been experimentally demonstrated in other physical settings such as cold atoms,where Hermiticity is usually preserved.Extending this model to the non-Hermitian regime with energy non-conservation can significantly enrich topological phases that lack Hermitian counterparts;however,such exploration remains experimentally challenging due to the lack of suitable physical platforms.Here,based on electric circuits,we report the experimental realization of a genuine non-Hermitian Haldane model with asymmetric next-nearest-neighbor hopping.We observe two previously uncovered phases:a non-Hermitian Chern insulator and a non-Hermitian semimetal phase,both exhibiting boundary-dependent amplifying or dissipative chiral edge states.Our work paves the way for exploring non-Hermiticity-induced unconventional topological phases in the Haldane model.
基金supported in part by the Key R&D of the Ministry of Science and Technology(No.2022YFA1204103).
文摘Magnetic materials could realize the intriguing quantum anomalous Hall effect and metal-to-insulator transition when combined with band topology or electronic correlation,which have broad prospects in quantum information,spintronics,and valleytronics.Here,we propose the approach of designing novel two-dimensional(2D)magnetic states via d-orbital-based superatomic lattices.Specifically,we chose triangular zirconium dichloride disks as superatoms to construct the honeycomb superatomic lattices.Using first-principles calculations,we identified a series of 2D magnetic states with varying sizes of superatoms.We found the non-uniform stoichiometries and geometric effect of superatomic lattice give rise to spin-polarized charges arranged in different magnetic configurations,containing ferromagnetic coloring triangles,antiferromagnetic honeycomb,and ferromagnetic kagome lattices.Attractively,these magnetic states are endowed with nontrivial band topology or strong correlation,forming an ideal Chern insulator or antiferromagnetic Dirac Mott insulator.Our work not only reveals the potential of d-orbital-based superatoms for generating unusual magnetic configurations,but also supplies a new avenue for material engineering at the nanoscale.
基金supported by the National Key R&D Program of China (2019YFA0308403, and 2022YFA1403700)the Innovation Program for Quantum Science and Technology (2021ZD0302400)+2 种基金the National Natural Science Foundation of China (12350401, 12304052, 12374034, and 11921005)the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB28000000)funded by China Postdoctoral Science Foundation (BX20220005)。
文摘Energy dissipation is of fundamental interest and crucial importance in quantum systems. However,whether energy dissipation can emerge without backscattering inside topological systems remains a question. As a hallmark, we propose a microscopic picture that illustrates energy dissipation in the quantum Hall(QH) plateau regime of graphene. Despite the quantization of Hall, longitudinal, and two-probe resistances(dubbed as the quantum limit), we find that the energy dissipation emerges in the form of Joule heat. It is demonstrated that the non-equilibrium energy distribution of carriers plays much more essential roles than the resistance on energy dissipation. Eventually, we suggest probing the phenomenon by measuring local temperature increases in experiments and reconsidering the dissipation typically ignored in realistic topological circuits.
