We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider th...We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider the propagation of electrons in graphene as relativistic fermion quasi-particles,and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation.Next,to solve and analyze the Dirac equation,we obtain the eigenvalues and eigenvectors using the Legendre differential equation.After that,we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k.Then,the values of the energy spectrum for the ground state and the first excited state are calculated,and the wave functions and the corresponding probabilities are plotted in terms of coordinates r.In what follows,we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K_(x) and K_(y).Finally,the energy bands are plotted in terms of the wave vectors K_(x) and K_(y) with and without the magnetic term.展开更多
We report a new kagome quantum spin liquid candidate CuaZn（OH）6FBr, which does not experience any phase transition down to 50inK, more than three orders lower than the antiferromagnetic Curie-Weiss temperature （-20...We report a new kagome quantum spin liquid candidate CuaZn（OH）6FBr, which does not experience any phase transition down to 50inK, more than three orders lower than the antiferromagnetic Curie-Weiss temperature （-200 K）. A clear gap opening at low temperature is observed in the uniform spin susceptibility obtained from 19F nuclear magnetic resonance measurements. We observe the characteristic magnetic field dependence of the gap as expected for fractionalized spin-1/2 spinon excitations. Our experimental results provide firm evidence for spin fractionalization in a topologically ordered spin system, resembling charge fraetionalization in the fractional quantum Hall state.展开更多
We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian i...We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by （bi-） modules over Frobenius algebras.展开更多
In graphene,conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature.For this reason,the bounding of electrons in graphene in th...In graphene,conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature.For this reason,the bounding of electrons in graphene in the form of geometries of quantum dots is impossible.In gapless graphene,due to its unique electronic band structure,there is a minimal conductivity at Dirac points,that is,in the limit of zero doping.This creates a problem for using such a highly motivated new material in electronic devices.One of the ways to overcome this problem is the creation of a band gap in the graphene band structure,which is made by inversion symmetry breaking（symmetry of sublattices）.We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for ＂local chemical potential＂ and ＂local gap＂.The calculated energy spectrum exhibits quite different features with and without the perturbations.A characteristic equation for bound states（BSs） has been obtained.It is surprisingly found that the relation between the radial functions of sublattices wave functions,i.e.,f_m~＋（r）,g_m~＋（r）,and f_m^-（r）,g_m^-（r）,can be established by SO（2） group.展开更多
We study the effect of electron-phonon （e-ph） interaction on the elastic and inelastic electronic transport of a nanowire connected to two simple rigid leads within the tight-binding and harmonic approximations. The...We study the effect of electron-phonon （e-ph） interaction on the elastic and inelastic electronic transport of a nanowire connected to two simple rigid leads within the tight-binding and harmonic approximations. The model is constructed using Green＇s function and multi-channel techniques, taking into account the local and nonlocal e-ph interactions. Then, we examine the model for the gapless （simple chain） and gapped （PA-like nanowire） systems. The results show that the tunneling conductance is improved by the e-ph interaction in both local and nonlocal regimes, while for the resonance conductance, the coherent part mainly decreases and the incoherent part increases. At the corresponding energies which depend on the phonon frequency, two dips in the elastic and two peaks in the inelastic conductance spectra appear. The reason is the absorption of the phonon by the electron in transition into inelastic channels.展开更多
A novel hollow star-shaped chiral metamaterial(SCM)is proposed by incorporating chiral structural properties into the standard hollow star-shaped metamaterial,exhibiting a wide band gap over 1500 Hz.To broaden the ban...A novel hollow star-shaped chiral metamaterial(SCM)is proposed by incorporating chiral structural properties into the standard hollow star-shaped metamaterial,exhibiting a wide band gap over 1500 Hz.To broaden the band gap,solid single-phase and two-phase SCMs are designed and simulated,which produce two ultra-wide band gaps(approximately 5116 Hz and 6027 Hz,respectively).The main reason for the formation of the ultra-wide band gap is that the rotational vibration of the concave star of two novel SCMs drains the energy of an elastic wave.The impacts of the concave angle of a single-phase SCM and the resonator radius of a two-phase SCM on the band gaps are studied.Decreasing the concave angle leads to an increase in the width of the widest band gap,and the width of the widest band gap increases as the resonator radius of the two-phase SCM increases.Additionally,the study on elastic wave propagation characteristics involves analyzing frequency dispersion surfaces,wave propagation directions,group velocities,and phase velocities.Ultimately,the analysis focuses on the transmission properties of finite periodic structures.The solid single-phase SCM achieves a maximum vibration attenuation over 800,while the width of the band gap is smaller than that of the two-phase SCM.Both metamaterials exhibit high vibration attenuation capabilities,which can be used in wideband vibration reduction to satisfy the requirement of ultra-wide frequencies.展开更多
Background In Central Europe,forests are increasingly affected by various disturbances,resulting in an increasing gap formation in the canopy.In order to support goal-oriented management,more knowledge is required abo...Background In Central Europe,forests are increasingly affected by various disturbances,resulting in an increasing gap formation in the canopy.In order to support goal-oriented management,more knowledge is required about the acclimation of the crown and its effects on the basal area growth of trees at the edge of a gap.Methods This work compared trees'growth and crown structure at the edge of a transient gap,with a gap size of more than 80m^(2),with trees in the stand that were at least 30m away from the gap.A total of 249 European beeches(Fagus sylvatica L.),Norway spruces(Picea abies L.Karst),Scots pines(Pinus sylvestris L.),oaks(Quercus spp.;Quercus petraea(Matt.)Liebl.,Quercus robur L.),and silver firs(Abies alba Mill.)were examined on long-term experimental plots in southern Germany.Various crown measures were developed and calculated using high-resolution terrestrial laser scanning(TLiDAR)to capture the three-dimensional crown structures.Growth responses to edge conditions were measured based on tree rings.Using linear mixed models,we predict the basal area increment of edge trees relative to trees in the stand under wet and dry soil moisture conditions after the gap formation.Results We identified i)species-specific acclimation of the crown of edge trees after the gap formation,ii)under wet soil moisture conditions a growth increase of 25%–45%for beech,pine,and oak edge trees and growth losses of 5%–60%for spruce and fir and iii)coniferous tree species benefited from the edge position regarding their basal area increment under dry soil moisture conditions and deciduous tree species grew regardless of the soil moisture conditions at the edge of a gap.Conclusion Gaps have a species-specific effect on the habitus and growth of edge trees and can have both positive and negative impacts on silviculture.展开更多
文摘We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider the propagation of electrons in graphene as relativistic fermion quasi-particles,and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation.Next,to solve and analyze the Dirac equation,we obtain the eigenvalues and eigenvectors using the Legendre differential equation.After that,we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k.Then,the values of the energy spectrum for the ground state and the first excited state are calculated,and the wave functions and the corresponding probabilities are plotted in terms of coordinates r.In what follows,we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K_(x) and K_(y).Finally,the energy bands are plotted in terms of the wave vectors K_(x) and K_(y) with and without the magnetic term.
基金Supported by the National Key Research and Development Program of China under Grant Nos 2016YFA0300502,2016YFA0300503,2016YFA0300604,2016YF0300300 and 2016YFA0300802the National Natural Science Foundation of China under Grant Nos 11421092,11474330,11574359,11674406,11374346 and 11674375+3 种基金the National Basic Research Program of China(973 Program)under Grant No 2015CB921304the National Thousand-Young-Talents Program of Chinathe Strategic Priority Research Program(B) of the Chinese Academy of Sciences under Grant Nos XDB07020000,XDB07020200 and XDB07020300supported by DOE-BES under Grant No DE-FG02-04ER46148
文摘We report a new kagome quantum spin liquid candidate CuaZn（OH）6FBr, which does not experience any phase transition down to 50inK, more than three orders lower than the antiferromagnetic Curie-Weiss temperature （-200 K）. A clear gap opening at low temperature is observed in the uniform spin susceptibility obtained from 19F nuclear magnetic resonance measurements. We observe the characteristic magnetic field dependence of the gap as expected for fractionalized spin-1/2 spinon excitations. Our experimental results provide firm evidence for spin fractionalization in a topologically ordered spin system, resembling charge fraetionalization in the fractional quantum Hall state.
文摘We report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen string-net model. The full Hamiltonian in our approach yields a topologically protected, gapped energy spectrum, with the corresponding wave functions robust under topology-preserving transformations of the lattice of the system. We explicitly present the wavefunctions of the ground states and boundary elementary excitations. The creation and hopping operators of boundary quasi-particles are constructed. It is found that given a bulk topological order, the gapped boundary conditions are classified by Frobenius algebras in its input data. Emergent topological properties of the ground states and boundary excitations are characterized by （bi-） modules over Frobenius algebras.
文摘In graphene,conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature.For this reason,the bounding of electrons in graphene in the form of geometries of quantum dots is impossible.In gapless graphene,due to its unique electronic band structure,there is a minimal conductivity at Dirac points,that is,in the limit of zero doping.This creates a problem for using such a highly motivated new material in electronic devices.One of the ways to overcome this problem is the creation of a band gap in the graphene band structure,which is made by inversion symmetry breaking（symmetry of sublattices）.We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for ＂local chemical potential＂ and ＂local gap＂.The calculated energy spectrum exhibits quite different features with and without the perturbations.A characteristic equation for bound states（BSs） has been obtained.It is surprisingly found that the relation between the radial functions of sublattices wave functions,i.e.,f_m~＋（r）,g_m~＋（r）,and f_m^-（r）,g_m^-（r）,can be established by SO（2） group.
基金Project supported by the Iranian Nanotechnology Initiativesupported by Shahrekord University through a research fund
文摘We study the effect of electron-phonon （e-ph） interaction on the elastic and inelastic electronic transport of a nanowire connected to two simple rigid leads within the tight-binding and harmonic approximations. The model is constructed using Green＇s function and multi-channel techniques, taking into account the local and nonlocal e-ph interactions. Then, we examine the model for the gapless （simple chain） and gapped （PA-like nanowire） systems. The results show that the tunneling conductance is improved by the e-ph interaction in both local and nonlocal regimes, while for the resonance conductance, the coherent part mainly decreases and the incoherent part increases. At the corresponding energies which depend on the phonon frequency, two dips in the elastic and two peaks in the inelastic conductance spectra appear. The reason is the absorption of the phonon by the electron in transition into inelastic channels.
基金supported by the National Natural Science Foundation of China(Nos.12372019,12072222,12132010,12021002,and 11991032)the Open Projects of State Key Laboratory for Strength and Structural Integrity of China(No.ASSIKFJJ202303002)+1 种基金the State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures of China(No.SKLTESKF1901)the Aeronautical Science Foundation of China(No.ASFC-201915048001)。
文摘A novel hollow star-shaped chiral metamaterial(SCM)is proposed by incorporating chiral structural properties into the standard hollow star-shaped metamaterial,exhibiting a wide band gap over 1500 Hz.To broaden the band gap,solid single-phase and two-phase SCMs are designed and simulated,which produce two ultra-wide band gaps(approximately 5116 Hz and 6027 Hz,respectively).The main reason for the formation of the ultra-wide band gap is that the rotational vibration of the concave star of two novel SCMs drains the energy of an elastic wave.The impacts of the concave angle of a single-phase SCM and the resonator radius of a two-phase SCM on the band gaps are studied.Decreasing the concave angle leads to an increase in the width of the widest band gap,and the width of the widest band gap increases as the resonator radius of the two-phase SCM increases.Additionally,the study on elastic wave propagation characteristics involves analyzing frequency dispersion surfaces,wave propagation directions,group velocities,and phase velocities.Ultimately,the analysis focuses on the transmission properties of finite periodic structures.The solid single-phase SCM achieves a maximum vibration attenuation over 800,while the width of the band gap is smaller than that of the two-phase SCM.Both metamaterials exhibit high vibration attenuation capabilities,which can be used in wideband vibration reduction to satisfy the requirement of ultra-wide frequencies.
基金funded by the Bavarian Ministry of Nutrition,Agriculture and Forestry through the projects“Acclimation of Forest Trees”(grant#kliffw006)“Maintenance and Monitoring of long term experiments”(W007,grant#Gz:7831-1/874).
文摘Background In Central Europe,forests are increasingly affected by various disturbances,resulting in an increasing gap formation in the canopy.In order to support goal-oriented management,more knowledge is required about the acclimation of the crown and its effects on the basal area growth of trees at the edge of a gap.Methods This work compared trees'growth and crown structure at the edge of a transient gap,with a gap size of more than 80m^(2),with trees in the stand that were at least 30m away from the gap.A total of 249 European beeches(Fagus sylvatica L.),Norway spruces(Picea abies L.Karst),Scots pines(Pinus sylvestris L.),oaks(Quercus spp.;Quercus petraea(Matt.)Liebl.,Quercus robur L.),and silver firs(Abies alba Mill.)were examined on long-term experimental plots in southern Germany.Various crown measures were developed and calculated using high-resolution terrestrial laser scanning(TLiDAR)to capture the three-dimensional crown structures.Growth responses to edge conditions were measured based on tree rings.Using linear mixed models,we predict the basal area increment of edge trees relative to trees in the stand under wet and dry soil moisture conditions after the gap formation.Results We identified i)species-specific acclimation of the crown of edge trees after the gap formation,ii)under wet soil moisture conditions a growth increase of 25%–45%for beech,pine,and oak edge trees and growth losses of 5%–60%for spruce and fir and iii)coniferous tree species benefited from the edge position regarding their basal area increment under dry soil moisture conditions and deciduous tree species grew regardless of the soil moisture conditions at the edge of a gap.Conclusion Gaps have a species-specific effect on the habitus and growth of edge trees and can have both positive and negative impacts on silviculture.
