This paper,largely written in 2009/2010,fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001.This point of view transparently brings in tropical di...This paper,largely written in 2009/2010,fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001.This point of view transparently brings in tropical disks of Maslov index 2 via the notion of broken lines,previously introduced in two dimensions by Mark Gross in his study of mirror symmetry for P2.A ma jor insight is the equivalence of properness of the Landau-Ginzburg potential with smoothness of the anticanonical divisor on the mirror side.We obtain proper superpotentials which agree on an open part with those classically known for toric varieties.Examples include mirror LG models for non-singular and singular del Pezzo surfaces,Hirzebruch surfaces and some Fano threefolds.展开更多
We investigate the electronic structure of NbGeSb with non-symmorphic symmetry.We employ angle-resolved photoemission spectroscopy(ARPES)to observe and identify the bulk and surface states over the Brillouin zone.By u...We investigate the electronic structure of NbGeSb with non-symmorphic symmetry.We employ angle-resolved photoemission spectroscopy(ARPES)to observe and identify the bulk and surface states over the Brillouin zone.By utilizing high-energy photons,we identify the bulk Fermi surface and bulk nodal line along the direction X–R,while the Fermi surface of the surface state is observed by using low-energy photons.We observe the splitting of surface bands away from the high-symmetry point X.The density functional theory calculations on bulk and 1 to 5-layer slab models,as well as spin textures of NbGeSb,verify that the band splitting could be attributed to the Rashba-like spin–orbit coupling caused by space-inversion-symmetry breaking at the surface.These splitted surface bands cross with each other,forming two-dimensional Weyl-like crossings that are protected by mirror symmetry.Our findings provide insights into the two-dimensional topological and symmetry-protected band inversion of surface states.展开更多
The Bloch band theory and Brillouin zone(BZ)that characterize wave-like behaviors in periodic mediums are two cornerstones of contemporary physics,ranging from condensed matter to topological physics.Recent theoretica...The Bloch band theory and Brillouin zone(BZ)that characterize wave-like behaviors in periodic mediums are two cornerstones of contemporary physics,ranging from condensed matter to topological physics.Recent theoretical breakthrough revealed that,under the projective symmetry algebra enforced by artificial gauge fields,the usual two-dimensional(2D)BZ(orientable Brillouin two-torus)can be fundamentally modified to a non-orientable Brillouin Klein bottle with radically distinct manifold topology.However,the physical consequence of artificial gauge fields on the more general three-dimensional(3D)BZ(orientable Brillouin three-torus)was so far missing.Here,we theoretically discovered and experimentally observed that the fundamental domain and topology of the usual 3D BZ can be reduced to a non-orientable Brillouin Klein space or an orientable Brillouin half-turn space in a 3D acoustic crystal with artificial gauge fields.We experimentally identify peculiar 3D momentum-space non-symmorphic screw rotation and glide reflection symmetries in the measured band structures.Moreover,we experimentally demonstrate a novel stacked weak Klein bottle insulator featuring a nonzero Z2 topological invariant and self-collimated topological surface states at two opposite surfaces related by a nonlocal twist,radically distinct from all previous 3D topological insulators.Our discovery not only fundamentally modifies the fundamental domain and topology of 3D BZ,but also opens the door towards a wealth of previously overlooked momentum-space multidimensional manifold topologies and novel gaugesymmetry-enriched topological physics and robust acoustic wave manipulations beyond the existing paradigms.展开更多
LiMn_(6) hexatomic-rings act as functional units in Li-rich layered oxides(LLOs),which determine the capacity,voltage,and structural stability of LLOs.However,the symmetry of the LiMn_(6) hexatomic-ring is always brok...LiMn_(6) hexatomic-rings act as functional units in Li-rich layered oxides(LLOs),which determine the capacity,voltage,and structural stability of LLOs.However,the symmetry of the LiMn_(6) hexatomic-ring is always broken,especially in the grain surface of LLOs,which will greatly affect its electrochemical performance.Herein,the symmetry-breaking of LiMn_(6) hexatomic-ring in the grain surface of Li_(2)MnO_(3) was studied,and their effect on charge compensation mechanism and structure evolution behavior was thoroughly investigated.The results show that the electrochemical activity of the symmetry-broken LiMn_(6) hexatomic-ring is higher than that of the unbroken LiMn_(6),and the former is more favorable for spinelization on the grain surface.Furthermore,the exposure proportion of crystallographic planes with different symmetry-broken LiMn_(6) hexatomic-ring has also been discussed,which can be adjusted by changing the partial pressure of oxygen.The in-depth understanding of the symmetry-breaking of LiMn_(6) hexatomic-ring will provide more targeted strategies for designing high-performance LLOs cathodes for lithium-ion batteries.展开更多
One of the challenges of remote sensing and computer vision lies in the three-dimensional(3-D)reconstruction of individual trees by using automated methods through very high-resolution(VHR)data sets.However,a successf...One of the challenges of remote sensing and computer vision lies in the three-dimensional(3-D)reconstruction of individual trees by using automated methods through very high-resolution(VHR)data sets.However,a successful and complete 3-D reconstruction relies on precise delineation of the trees in two dimensions.In this paper,we present an original approach to detect and delineate citrus trees using unmanned aerial vehicles based on photogrammetric digital surface models(DSMs).The symmetry of the citrus trees in a DSM is handled by an orientationbased radial symmetry transform which is computed in a unique way.Next,we propose an efficient strategy to accurately build influence regions of each tree,and then we delineate individual citrus trees through active contours by taking into account the influence region of each canopy.We also present two efficient strategies to filter out erroneously detected canopy regions without having any height thresholds.Experiments are carried out on eight test DSMs composed of different types of citrus orchards with varying densities and canopy sizes.Extensive comparisons to the state-of-the-art approaches reveal that our proposed approach provides superior detection and delineation performances through supporting a nice balance between precision and recall measures.展开更多
The formation of long-range ordered aperiodic molecular films on quasicrystalline substrates is a new challenge that provides an opportunity for further surface functionalization. This aim can be realized through the ...The formation of long-range ordered aperiodic molecular films on quasicrystalline substrates is a new challenge that provides an opportunity for further surface functionalization. This aim can be realized through the smart selection of molecular building blocks, based on symmetry-matching between the underlying quasicrystal and individual molecules. It was previously found that the geometric registry between the C60 molecules and the 5- and 10-fold surfaces was key to the growth of quasiperiodic organic layers. However, an attempt to form a quasiperiodic C60 network on i-Ag-In-Yb substrates was unsuccessful, resulting in disordered molecular films. Here we report the growth of 5-fold symmetric corannulene C20H10 molecules on the 5-fold surfaces of i-Ag-In-Yb quasicrystals. Low-energy electron diffraction （LEED） and scanning tunneling microscopy （STM） revealed long-range quasiperiodic order and 5-fold rotational symmetry in self-assembled corannulene films. Recurrent decagonal molecular rings were seen, resulting from the decoration of specific adsorption sites with local pentagonal symmetry by corannulenes, adsorbed with their bowl-openings pointing away from the surface. They were identified as （Ag, In）-containing rhombic triacontahedral （RTH） duster centers and pentagonal Yb motifs, which cannot be occupied simultaneously due to steric hindrance. It is proposed that symmetry-matching between the molecule and specific substrate sites drives this organization. Alteration of the molecular rim by the introduction of CH substituents appeared to increase molecule mobility on the potential energy surface and facilitate trapping at these specific sites. This finding suggests that rational selection of molecular moiety enables the templated self-assembly of molecules leading to an ordered aperiodic corannulene layer.展开更多
We determine the maximum order Eg of finite groups G acting on the closed surface E9 of genus g which extends over （S3, ∑g） for all possible embeddings ∑g → S3, where g 〉 1.
Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all perio...Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all periodical maps on Σ2. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair(S3, Σg). To do this the authors first list all periodic maps on Σ2, and indeed the authors exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself should be interesting. A by-product is that for each even g,the maximum order periodic map on Σg is extendable, which contrasts sharply with the situation in the orientation preserving category.展开更多
Glide symmetry,which is one kind of higher symmetry,is introduced in a special type of plasmonic metamaterial,the transmission lines(TLs)of spoof surface plasmon polaritons(SSPPs),in order to control the dispersion ch...Glide symmetry,which is one kind of higher symmetry,is introduced in a special type of plasmonic metamaterial,the transmission lines(TLs)of spoof surface plasmon polaritons(SSPPs),in order to control the dispersion characteristics and modal fields of the SSPPs.We show that the glide-symmetric TL presents merged pass bands and mode degeneracy,which lead to broad working bandwidth and extremely low coupling between neighboring TLs.Dual-conductor SSPP TLs with and without glide symmetry are arranged in parallel as two channels with very deep subwavelength separation(e.g.,λ0∕100 at 5 GHz)for the application of integrated circuits and systems.Mutual coupling between the hybrid channels is analyzed using coupled mode theory and characterized in terms of scattering parameters and near-field distributions.We demonstrate theoretically and experimentally that the hybrid TL array obtains significantly more suppressed crosstalk than the uniform array of two nonglide symmetric TLs.Hence,it is concluded that the glide symmetry can be adopted to flexibly design the propagation of SSPPs and benefit the development of highly compact plasmonic circuits.展开更多
Cobalt‐based materials have been considered as promising candidates to electrocatalyze water oxidation.However,the structure‐performance correlation remains largely elusive,due to the com‐plex material structures a...Cobalt‐based materials have been considered as promising candidates to electrocatalyze water oxidation.However,the structure‐performance correlation remains largely elusive,due to the com‐plex material structures and diverse performance‐influencing factors in those Co‐based catalysts.In this work,we designed two cobalt phosphates with distinct Co symmetry to explore the effect of coordination symmetry on electrocatalytic water oxidation.The two analogues have similar mor‐phology,Co valence and 6‐coordinated Co octahedron,but with different coordination symmetry.In contrast to symmetric Co_(3)(PO_(4))2·8H_(2)O,asymmetric NH_(4)CoPO_(4)·H_(2)O exhibited enhanced electrocata‐lytic water oxidation activity in a neutral aqueous solution.It is proven that,by experimental and theoretical studies,the asymmetric Co coordination sites can facilitate the surface reconstruction under anodic polarization to boost the electrocatalysis.Based on this contrastive platform with distinct symmetry differences,the preferred configuration in cobalt‐oxygen octahedrons for water oxidation has been straightforwardly assigned.展开更多
基金supported by the Studienstiftung des deutschen Volkessupported by NSF grant DMS-1903437。
文摘This paper,largely written in 2009/2010,fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001.This point of view transparently brings in tropical disks of Maslov index 2 via the notion of broken lines,previously introduced in two dimensions by Mark Gross in his study of mirror symmetry for P2.A ma jor insight is the equivalence of properness of the Landau-Ginzburg potential with smoothness of the anticanonical divisor on the mirror side.We obtain proper superpotentials which agree on an open part with those classically known for toric varieties.Examples include mirror LG models for non-singular and singular del Pezzo surfaces,Hirzebruch surfaces and some Fano threefolds.
基金Project supported by the National Key Research and Development Program of China(Grant No.2022YFA1403803)H.M.is supported by the Fundamental Research Funds for the Central Universities,and the Research Funds of Renmin University of China(Grant No.22XNH099)+7 种基金The results of DFT calculations described in this paper are supported by HPC Cluster of ITP-CAS.M.L.is supported by the National Natural Science Foundation of China(Grant No.12204536)the Fundamental Research Funds for the Central Universities,and the Research Funds of People’s Public Security University of China(PPSUC)(Grant No.2023JKF02ZK09)T.L.X.is supported by the National Key R&D Program of China(Grant No.2019YFA0308602)the National Natural Science Foundation of China(Grant Nos.12074425 and 11874422)Y.Y.W.is supported by the National Natural Science Foundation of China(Grant No.12104011)H.Y.L.is supported by the National Natural Science Foundation of China(Grant No.12074213)the Major Basic Program of Natural Science Foundation of Shandong Province(Grant No.ZR2021ZD01)the Project of Introduction and Cultivation for Young Innovative Talents in Colleges and Universities of Shandong Province.
文摘We investigate the electronic structure of NbGeSb with non-symmorphic symmetry.We employ angle-resolved photoemission spectroscopy(ARPES)to observe and identify the bulk and surface states over the Brillouin zone.By utilizing high-energy photons,we identify the bulk Fermi surface and bulk nodal line along the direction X–R,while the Fermi surface of the surface state is observed by using low-energy photons.We observe the splitting of surface bands away from the high-symmetry point X.The density functional theory calculations on bulk and 1 to 5-layer slab models,as well as spin textures of NbGeSb,verify that the band splitting could be attributed to the Rashba-like spin–orbit coupling caused by space-inversion-symmetry breaking at the surface.These splitted surface bands cross with each other,forming two-dimensional Weyl-like crossings that are protected by mirror symmetry.Our findings provide insights into the two-dimensional topological and symmetry-protected band inversion of surface states.
基金funding from the National Natural Science Foundation of China(62375118,6231101016,and 12104211)Shenzhen Science and Technology Innovation Commission(20220815111105001)+8 种基金SUSTech(Y01236148 and Y01236248)Zhengyou Liu acknowledges funding from the National Key R&D Program of China(2022YFA1404900 and 2018YFA0305800)the National Natural Science Foundation of China(11890701)the National Natural Science Foundation of China(12304484)Basic and Applied Basic Research Foundation of Guangdong Province(2414050002552)Shenzhen Science and Technology Innovation Commission(202308073000209)Perry Ping Shum acknowledges the National Natural Science Foundation of China(62220106006)Shenzhen Science and Technology Program(SGDX20211123114001001)Kexin Xiang acknowledges the Special Funds for the Cultivation of Guangdong College Students’Scientific and Technological Innovation(pdjh2023c21002).
文摘The Bloch band theory and Brillouin zone(BZ)that characterize wave-like behaviors in periodic mediums are two cornerstones of contemporary physics,ranging from condensed matter to topological physics.Recent theoretical breakthrough revealed that,under the projective symmetry algebra enforced by artificial gauge fields,the usual two-dimensional(2D)BZ(orientable Brillouin two-torus)can be fundamentally modified to a non-orientable Brillouin Klein bottle with radically distinct manifold topology.However,the physical consequence of artificial gauge fields on the more general three-dimensional(3D)BZ(orientable Brillouin three-torus)was so far missing.Here,we theoretically discovered and experimentally observed that the fundamental domain and topology of the usual 3D BZ can be reduced to a non-orientable Brillouin Klein space or an orientable Brillouin half-turn space in a 3D acoustic crystal with artificial gauge fields.We experimentally identify peculiar 3D momentum-space non-symmorphic screw rotation and glide reflection symmetries in the measured band structures.Moreover,we experimentally demonstrate a novel stacked weak Klein bottle insulator featuring a nonzero Z2 topological invariant and self-collimated topological surface states at two opposite surfaces related by a nonlocal twist,radically distinct from all previous 3D topological insulators.Our discovery not only fundamentally modifies the fundamental domain and topology of 3D BZ,but also opens the door towards a wealth of previously overlooked momentum-space multidimensional manifold topologies and novel gaugesymmetry-enriched topological physics and robust acoustic wave manipulations beyond the existing paradigms.
基金financially supported by the National Key R&D Program of China (2022YFB2404400)the National Natural Science Foundation of China (92263206,and 22002004)“The Youth Beijing Scholars program” (PXM2021_014204_000023)。
文摘LiMn_(6) hexatomic-rings act as functional units in Li-rich layered oxides(LLOs),which determine the capacity,voltage,and structural stability of LLOs.However,the symmetry of the LiMn_(6) hexatomic-ring is always broken,especially in the grain surface of LLOs,which will greatly affect its electrochemical performance.Herein,the symmetry-breaking of LiMn_(6) hexatomic-ring in the grain surface of Li_(2)MnO_(3) was studied,and their effect on charge compensation mechanism and structure evolution behavior was thoroughly investigated.The results show that the electrochemical activity of the symmetry-broken LiMn_(6) hexatomic-ring is higher than that of the unbroken LiMn_(6),and the former is more favorable for spinelization on the grain surface.Furthermore,the exposure proportion of crystallographic planes with different symmetry-broken LiMn_(6) hexatomic-ring has also been discussed,which can be adjusted by changing the partial pressure of oxygen.The in-depth understanding of the symmetry-breaking of LiMn_(6) hexatomic-ring will provide more targeted strategies for designing high-performance LLOs cathodes for lithium-ion batteries.
基金This work was supported by the Scientific and Technical Research Council of Turkey(TUBITAK)[grant number 114Y671].
文摘One of the challenges of remote sensing and computer vision lies in the three-dimensional(3-D)reconstruction of individual trees by using automated methods through very high-resolution(VHR)data sets.However,a successful and complete 3-D reconstruction relies on precise delineation of the trees in two dimensions.In this paper,we present an original approach to detect and delineate citrus trees using unmanned aerial vehicles based on photogrammetric digital surface models(DSMs).The symmetry of the citrus trees in a DSM is handled by an orientationbased radial symmetry transform which is computed in a unique way.Next,we propose an efficient strategy to accurately build influence regions of each tree,and then we delineate individual citrus trees through active contours by taking into account the influence region of each canopy.We also present two efficient strategies to filter out erroneously detected canopy regions without having any height thresholds.Experiments are carried out on eight test DSMs composed of different types of citrus orchards with varying densities and canopy sizes.Extensive comparisons to the state-of-the-art approaches reveal that our proposed approach provides superior detection and delineation performances through supporting a nice balance between precision and recall measures.
文摘The formation of long-range ordered aperiodic molecular films on quasicrystalline substrates is a new challenge that provides an opportunity for further surface functionalization. This aim can be realized through the smart selection of molecular building blocks, based on symmetry-matching between the underlying quasicrystal and individual molecules. It was previously found that the geometric registry between the C60 molecules and the 5- and 10-fold surfaces was key to the growth of quasiperiodic organic layers. However, an attempt to form a quasiperiodic C60 network on i-Ag-In-Yb substrates was unsuccessful, resulting in disordered molecular films. Here we report the growth of 5-fold symmetric corannulene C20H10 molecules on the 5-fold surfaces of i-Ag-In-Yb quasicrystals. Low-energy electron diffraction （LEED） and scanning tunneling microscopy （STM） revealed long-range quasiperiodic order and 5-fold rotational symmetry in self-assembled corannulene films. Recurrent decagonal molecular rings were seen, resulting from the decoration of specific adsorption sites with local pentagonal symmetry by corannulenes, adsorbed with their bowl-openings pointing away from the surface. They were identified as （Ag, In）-containing rhombic triacontahedral （RTH） duster centers and pentagonal Yb motifs, which cannot be occupied simultaneously due to steric hindrance. It is proposed that symmetry-matching between the molecule and specific substrate sites drives this organization. Alteration of the molecular rim by the introduction of CH substituents appeared to increase molecule mobility on the potential energy surface and facilitate trapping at these specific sites. This finding suggests that rational selection of molecular moiety enables the templated self-assembly of molecules leading to an ordered aperiodic corannulene layer.
基金partially supported by National Natural Science Foundation of China(Grant No.11371034)
文摘We determine the maximum order Eg of finite groups G acting on the closed surface E9 of genus g which extends over （S3, ∑g） for all possible embeddings ∑g → S3, where g 〉 1.
基金supported by the National Natural Science Foundation of China(No.10631060)
文摘Call a periodic map h on the closed orientable surface Σg extendable if h extends to a periodic map over the pair(S3, Σg) for possible embeddings e : Σg→ S3. The authors determine the extendabilities for all periodical maps on Σ2. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair(S3, Σg). To do this the authors first list all periodic maps on Σ2, and indeed the authors exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself should be interesting. A by-product is that for each even g,the maximum order periodic map on Σg is extendable, which contrasts sharply with the situation in the orientation preserving category.
基金This work was supported in part from the National Natural Science Foundation of China under Grant Nos.61631007 and 61971134,in part from the 111 Project under Grant No.111-2-05in part from the Fundamental Research Funds for the Central Universities under Grant No.2242020R40079.Xiao Tian Yan and Wenxuan Tang contributed equally to this work.
文摘Glide symmetry,which is one kind of higher symmetry,is introduced in a special type of plasmonic metamaterial,the transmission lines(TLs)of spoof surface plasmon polaritons(SSPPs),in order to control the dispersion characteristics and modal fields of the SSPPs.We show that the glide-symmetric TL presents merged pass bands and mode degeneracy,which lead to broad working bandwidth and extremely low coupling between neighboring TLs.Dual-conductor SSPP TLs with and without glide symmetry are arranged in parallel as two channels with very deep subwavelength separation(e.g.,λ0∕100 at 5 GHz)for the application of integrated circuits and systems.Mutual coupling between the hybrid channels is analyzed using coupled mode theory and characterized in terms of scattering parameters and near-field distributions.We demonstrate theoretically and experimentally that the hybrid TL array obtains significantly more suppressed crosstalk than the uniform array of two nonglide symmetric TLs.Hence,it is concluded that the glide symmetry can be adopted to flexibly design the propagation of SSPPs and benefit the development of highly compact plasmonic circuits.
文摘Cobalt‐based materials have been considered as promising candidates to electrocatalyze water oxidation.However,the structure‐performance correlation remains largely elusive,due to the com‐plex material structures and diverse performance‐influencing factors in those Co‐based catalysts.In this work,we designed two cobalt phosphates with distinct Co symmetry to explore the effect of coordination symmetry on electrocatalytic water oxidation.The two analogues have similar mor‐phology,Co valence and 6‐coordinated Co octahedron,but with different coordination symmetry.In contrast to symmetric Co_(3)(PO_(4))2·8H_(2)O,asymmetric NH_(4)CoPO_(4)·H_(2)O exhibited enhanced electrocata‐lytic water oxidation activity in a neutral aqueous solution.It is proven that,by experimental and theoretical studies,the asymmetric Co coordination sites can facilitate the surface reconstruction under anodic polarization to boost the electrocatalysis.Based on this contrastive platform with distinct symmetry differences,the preferred configuration in cobalt‐oxygen octahedrons for water oxidation has been straightforwardly assigned.
