Topological semimetals are newly discovered states of quantum matter, which have extended the con- cept of topological states from insulators to metals and attracted great research interest in recent years. In general...Topological semimetals are newly discovered states of quantum matter, which have extended the con- cept of topological states from insulators to metals and attracted great research interest in recent years. In general, there are three kinds of topological semimetals, namely Dirac semimetals, Weyl semimet- als, and nodal line semimetals. Nodal line semimetals can be considered as precursor states for other topological states. For example, starting from such nodal line states, the nodal line structure might evolve into Weyl points, convert into Dirac points, or become a topological insulator by introducing the spin-orbit coupling （SOC） or mass term. In this review paper, we introduce theoretical materials that show the nodal line semimetal state, including the all-carbon Mackay-Terrones crystal （MTC）, anti-perovskite Cu3PdN, pressed black phosphorus, and the CaP3 family of materials, and we present the design principles for obtaining such novel states of matter.展开更多
The past decade has witnessed a surge of interest in exploring emergent particles in condensed matter systems.Novel particles,emerged as excitations around exotic band degeneracy points,continue to be reported in real...The past decade has witnessed a surge of interest in exploring emergent particles in condensed matter systems.Novel particles,emerged as excitations around exotic band degeneracy points,continue to be reported in real materials and artificially engineered systems,but so far,we do not have a complete picture on all possible types of particles that can be achieved.Here,via systematic symmetry analysis and modeling,we accomplish a complete list of all possible particles in time-reversal-invariant systems.This includes both spinful particles such as electron quasiparticles in solids,and spinless particles such as phonons or even excitations in electric-circuit and mechanical networks.We establish detailed correspondence between the particle,the symmetry condition,the effective model,and the topological character.This obtained encyclopedia concludes the search for novel emergent particles and provides concrete guidance to achieve them in physical systems.展开更多
Topological materials have novel properties both in their bulk and boundaries,thereby attracting a wide interest in the theoretical and experimental communities.The recent development of the topological quantum chemis...Topological materials have novel properties both in their bulk and boundaries,thereby attracting a wide interest in the theoretical and experimental communities.The recent development of the topological quantum chemistry and symmetrybased indicator theory in this field has significantly simplified the procedure for determining the topological properties of nonmagnetic crystalline materials.Accordingly,a large number of new topological materials have been found by scanning large crystal databases.This study provides details on the algorithm used in the Catalogue of Topological Electronic Materials.Moreover,based on the algorithm,we develop an automatic package named SymTopo,which calculates the symmetry representations of any given nonmagnetic crystalline material and predicts its topological properties.This package may facilitate the discovery of more topological materials in the future.展开更多
Recently, the non-centrosymmetric WC-type materials(i.e., MoP, ZrTe, TaN, etc) have attracted extensive interest due to the discovery of their topological properties.By means of the first-principles calculations, here...Recently, the non-centrosymmetric WC-type materials(i.e., MoP, ZrTe, TaN, etc) have attracted extensive interest due to the discovery of their topological properties.By means of the first-principles calculations, here we have investigated the structural, thermodynamic, elastic, and electronic properties of the WC-type MX compounds(TiS, TiSe, TiTe, ZrS, ZrSe,ZrTe, HfS, HfSe, and HfTe).Among these nine compounds, five of them(TiS, ZrS, ZrSe0.9, ZrTe, and Hf0.92 Se) have been experimentally synthesized to crystallize in the WC-type structure and other four members have never been reported.Our calculations demonstrated that they are all structurally, thermodynamically, and dynamically stable, indicating that all of them should be possibly synthesized.We have also derived their elastic constants of single crystalline and their bulk and shear moduli in terms of the R.Hill approximations.Furthermore, in similarity to ZrTe, all these compounds have been theoretically derived to be topological semimetals.Whereas TiS is unique because of the coexistence of the Dirac nodal lines(DNLs) and sixfold degenerate nodal points(sixfold DNPs), the other eight members are revealed to exhibit coexisted Weyl nodes(WPs) and triply degenerate nodal points(TDNPs).Their electronic and topological properties have been further discussed.展开更多
Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopol...Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topo- logical semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity nmy not be a com- pelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.展开更多
PtTe2 and PtSe2 with trigonal structure have attracted extensive research interests since the discovery of type-II Dirac fermions in the bulk crystals. The evolution of the electronic structure from bulk 3D topologica...PtTe2 and PtSe2 with trigonal structure have attracted extensive research interests since the discovery of type-II Dirac fermions in the bulk crystals. The evolution of the electronic structure from bulk 3D topological semimetal to 2D atomic thin films is an important scientific question. While a transition from 3D type-II Dirac semimetal in the bulk to 2D semiconductor in monolayer(ML) film has been reported for PtSe2, so far the evolution of electronic structure of atomically thin PtTe2 films still remains unexplored.Here we report a systematic angle-resolved photoemission spectroscopy(ARPES) study of the electronic structure of high quality PtTe2 films grown by molecular beam epitaxy with thickness from 2 ML to 6 ML.ARPES measurements show that PtTe2 films still remain metallic even down to 2 ML thickness, which is in sharp contrast to the semiconducting property of few layer PtSe2 films. Moreover, a transition from 2D metal to 3D type-II Dirac semimetal occurs at film thickness of 4–6 ML. In addition, Spin-ARPES measurements reveal helical spin textures induced by local Rashba effect in the bulk PtTe2 crystal, suggesting that similar hidden spin is also expected in few monolayer PtTe2 films. Our work reveals the transition from2D metal to 3D topological semimetal and provides new opportunities for investigating metallic 2D films with local Rashba effect.展开更多
We review the recent progress in the study of topological phases in systems with space–time inversion symmetry IST.ISTis an anti-unitary symmetry which is local in momentum space and satisfies I2 ST= 1 such as PT in ...We review the recent progress in the study of topological phases in systems with space–time inversion symmetry IST.ISTis an anti-unitary symmetry which is local in momentum space and satisfies I2 ST= 1 such as PT in two dimensions(2 D)and three dimensions(3 D) without spin–orbit coupling and C2 T in 2 D with or without spin–orbit coupling, where P, T, C2 indicate the inversion, time-reversal, and two-fold rotation symmetries, respectively. Under IST, the Hamiltonian and the periodic part of the Bloch wave function can be constrained to be real-valued, which makes the Berry curvature and the Chern number vanish. In this class of systems, gapped band structures of real wave functions can be topologically distinguished by the Stiefel–Whitney numbers instead. The first and second Stiefel–Whitney numbers w1 and w2, respectively,are the corresponding invariants in 1 D and 2 D, which are equivalent to the quantized Berry phase and the Z2 monopole charge, respectively. We first describe the topological phases characterized by the first Stiefel–Whitney number, including1 D topological insulators with quantized charge polarization, 2 D Dirac semimetals, and 3 D nodal line semimetals. Next we review how the second Stiefel–Whitney class characterizes the 3 D nodal line semimetals carrying a Z2 monopole charge.In particular, we explain how the second Stiefel–Whitney number w2, the Z2 monopole charge, and the linking number between nodal lines are related. Finally, we review the properties of 2 D and 3 D topological insulators characterized by the nontrivial second Stiefel Whitney class.展开更多
文摘Topological semimetals are newly discovered states of quantum matter, which have extended the con- cept of topological states from insulators to metals and attracted great research interest in recent years. In general, there are three kinds of topological semimetals, namely Dirac semimetals, Weyl semimet- als, and nodal line semimetals. Nodal line semimetals can be considered as precursor states for other topological states. For example, starting from such nodal line states, the nodal line structure might evolve into Weyl points, convert into Dirac points, or become a topological insulator by introducing the spin-orbit coupling （SOC） or mass term. In this review paper, we introduce theoretical materials that show the nodal line semimetal state, including the all-carbon Mackay-Terrones crystal （MTC）, anti-perovskite Cu3PdN, pressed black phosphorus, and the CaP3 family of materials, and we present the design principles for obtaining such novel states of matter.
基金supported by the National Key R&D Program of China(2020YFA0308800,2016YFA0300600,and 2017YFB0701600)the National Natural Science Foundation of China(11734003,12061131002,12004028,and 12004035)+3 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(XDB30000000)the China Postdoctoral Science Foundation(2020M670106)the Singapore Ministry of Education AcRF Tier 2(MOE2019-T2-1-001)Beijing Institute of Technology Research Fund Program for Young Schola。
文摘The past decade has witnessed a surge of interest in exploring emergent particles in condensed matter systems.Novel particles,emerged as excitations around exotic band degeneracy points,continue to be reported in real materials and artificially engineered systems,but so far,we do not have a complete picture on all possible types of particles that can be achieved.Here,via systematic symmetry analysis and modeling,we accomplish a complete list of all possible particles in time-reversal-invariant systems.This includes both spinful particles such as electron quasiparticles in solids,and spinless particles such as phonons or even excitations in electric-circuit and mechanical networks.We establish detailed correspondence between the particle,the symmetry condition,the effective model,and the topological character.This obtained encyclopedia concludes the search for novel emergent particles and provides concrete guidance to achieve them in physical systems.
基金Project supported by the Information Program of the Chinese Academy of Sciences(Grant No.XXH13506-202)
文摘Topological materials have novel properties both in their bulk and boundaries,thereby attracting a wide interest in the theoretical and experimental communities.The recent development of the topological quantum chemistry and symmetrybased indicator theory in this field has significantly simplified the procedure for determining the topological properties of nonmagnetic crystalline materials.Accordingly,a large number of new topological materials have been found by scanning large crystal databases.This study provides details on the algorithm used in the Catalogue of Topological Electronic Materials.Moreover,based on the algorithm,we develop an automatic package named SymTopo,which calculates the symmetry representations of any given nonmagnetic crystalline material and predicts its topological properties.This package may facilitate the discovery of more topological materials in the future.
基金supported by the National Natural Science Foundation of China(12274112)the Overseas Scientists Sponsorship Program of Hebei Province(C20210330)+2 种基金the S&T Program of Hebei(215676146H and 225676163GH)the State Key Laboratory of Reliability and Intelligence of Electrical Equipment of Hebei University of Technology(EERI_PI2020009)the Australian Research Council(DP190100150 and DP210101436)。
基金the support by the strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA18000000)the Key Scientific Research Projects of Higher Institutions in Henan Province (19A140018)+1 种基金the starting grant of ShanghaiTech University and the Program for Professor of Special Appointment (Shanghai Eastern Scholar)the support from Analytical Instrumentation Center (# SPST-AIC10112914), SPST, ShanghaiTech University
基金Project supported by the National Natural Science Foundation of China(Grant No.51671193)
文摘Recently, the non-centrosymmetric WC-type materials(i.e., MoP, ZrTe, TaN, etc) have attracted extensive interest due to the discovery of their topological properties.By means of the first-principles calculations, here we have investigated the structural, thermodynamic, elastic, and electronic properties of the WC-type MX compounds(TiS, TiSe, TiTe, ZrS, ZrSe,ZrTe, HfS, HfSe, and HfTe).Among these nine compounds, five of them(TiS, ZrS, ZrSe0.9, ZrTe, and Hf0.92 Se) have been experimentally synthesized to crystallize in the WC-type structure and other four members have never been reported.Our calculations demonstrated that they are all structurally, thermodynamically, and dynamically stable, indicating that all of them should be possibly synthesized.We have also derived their elastic constants of single crystalline and their bulk and shear moduli in terms of the R.Hill approximations.Furthermore, in similarity to ZrTe, all these compounds have been theoretically derived to be topological semimetals.Whereas TiS is unique because of the coexistence of the Dirac nodal lines(DNLs) and sixfold degenerate nodal points(sixfold DNPs), the other eight members are revealed to exhibit coexisted Weyl nodes(WPs) and triply degenerate nodal points(TDNPs).Their electronic and topological properties have been further discussed.
文摘Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topo- logical semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity nmy not be a com- pelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.
基金supported by the National Natural Science Foundation of China(11725418 and 11334006)the National Basic Research Program of China(2016YFA0301004,2016YFA0301001,and 2015CB921001)+1 种基金Science Challenge Project(TZ2016004)Beijing Advanced Innovation Center for Future Chip(ICFC)
文摘PtTe2 and PtSe2 with trigonal structure have attracted extensive research interests since the discovery of type-II Dirac fermions in the bulk crystals. The evolution of the electronic structure from bulk 3D topological semimetal to 2D atomic thin films is an important scientific question. While a transition from 3D type-II Dirac semimetal in the bulk to 2D semiconductor in monolayer(ML) film has been reported for PtSe2, so far the evolution of electronic structure of atomically thin PtTe2 films still remains unexplored.Here we report a systematic angle-resolved photoemission spectroscopy(ARPES) study of the electronic structure of high quality PtTe2 films grown by molecular beam epitaxy with thickness from 2 ML to 6 ML.ARPES measurements show that PtTe2 films still remain metallic even down to 2 ML thickness, which is in sharp contrast to the semiconducting property of few layer PtSe2 films. Moreover, a transition from 2D metal to 3D type-II Dirac semimetal occurs at film thickness of 4–6 ML. In addition, Spin-ARPES measurements reveal helical spin textures induced by local Rashba effect in the bulk PtTe2 crystal, suggesting that similar hidden spin is also expected in few monolayer PtTe2 films. Our work reveals the transition from2D metal to 3D topological semimetal and provides new opportunities for investigating metallic 2D films with local Rashba effect.
基金supported by IBS-R009-D1supported by the Institute for Basic Science in Korea (Grant No. IBS-R009-D1)+6 种基金Basic Science Research Program through the National Research Foundation of Korea (NRF) (Grant No. 0426-20180011)the POSCO Science Fellowship of POSCO TJ Park Foundation (No. 042620180002)supported in part by the U.S. Army Research Office under Grant Number W911NF-18-1-0137supported by Institute for Basic Science (IBS-R011D1)NRF grant funded by the Korea government (MSIP) (NRF-2017R1G1B5018169)supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1701-07Basic Science Research Program through NRF funded by the Ministry of Education (NRF2018R1A6A3A11044335)
文摘We review the recent progress in the study of topological phases in systems with space–time inversion symmetry IST.ISTis an anti-unitary symmetry which is local in momentum space and satisfies I2 ST= 1 such as PT in two dimensions(2 D)and three dimensions(3 D) without spin–orbit coupling and C2 T in 2 D with or without spin–orbit coupling, where P, T, C2 indicate the inversion, time-reversal, and two-fold rotation symmetries, respectively. Under IST, the Hamiltonian and the periodic part of the Bloch wave function can be constrained to be real-valued, which makes the Berry curvature and the Chern number vanish. In this class of systems, gapped band structures of real wave functions can be topologically distinguished by the Stiefel–Whitney numbers instead. The first and second Stiefel–Whitney numbers w1 and w2, respectively,are the corresponding invariants in 1 D and 2 D, which are equivalent to the quantized Berry phase and the Z2 monopole charge, respectively. We first describe the topological phases characterized by the first Stiefel–Whitney number, including1 D topological insulators with quantized charge polarization, 2 D Dirac semimetals, and 3 D nodal line semimetals. Next we review how the second Stiefel–Whitney class characterizes the 3 D nodal line semimetals carrying a Z2 monopole charge.In particular, we explain how the second Stiefel–Whitney number w2, the Z2 monopole charge, and the linking number between nodal lines are related. Finally, we review the properties of 2 D and 3 D topological insulators characterized by the nontrivial second Stiefel Whitney class.
