When A ∈ B（H） and B ∈ B（K） are given, we denote by Mc an operator acting on the Hilbert space HΘ K of the form Me = （ A0 CB）. In this paper, first we give the necessary and sufficient condition for Mc to be a...When A ∈ B（H） and B ∈ B（K） are given, we denote by Mc an operator acting on the Hilbert space HΘ K of the form Me = （ A0 CB）. In this paper, first we give the necessary and sufficient condition for Mc to be an upper semi-Fredholm （lower semi-Fredholm, or Fredholm） operator for some C ∈B（K,H）. In addition, let σSF＋（A） = {λ ∈ C ： A-λI is not an upper semi-Fredholm operator} bc the upper semi-Fredholm spectrum of A ∈ B（H） and let σrsF- （A） = {λ∈ C ： A-λI is not a lower semi-Fredholm operator} be the lower semi Fredholm spectrum of A. We show that the passage from σSF±（A） U σSF±（B） to σSF±（Mc） is accomplished by removing certain open subsets of σSF-（A） ∩σSF＋ （B） from the former, that is, there is an equality σSF±（A） ∪σSF± （B） = σSF± （Mc） ∪＆ where L is the union of certain of the holes in σSF±（Mc） which ilappen to be subsets of σSF- （A） A σSF＋ （B）. Weyl＇s theorem and Browder＇s theorem are liable to fail for 2 × 2 operator matrices. In this paper, we also explore how Weyl＇s theorem, Browder＇s theorem, a-Weyl＇s theorem and a-Browder＇s theorem survive for 2 × 2 upper triangular operator matrices on the Hilbert space.展开更多
A class of the associative and Lie algebras A[D] = A × F[D] of Weyl type are studied, where Ais a commutative associative algebra with an identity element over a field F of characteristic zero, and F[D] isthe pol...A class of the associative and Lie algebras A[D] = A × F[D] of Weyl type are studied, where Ais a commutative associative algebra with an identity element over a field F of characteristic zero, and F[D] isthe polynomial algebra of a finite dimensional commutative subalgebra of locally finite derivations of A suchthat A is D-simple. The derivations of these associative and Lie algebras are precisely determined.展开更多
A∈B（H） is called Drazin invertible if A has finite ascent and descent. Let σD （A）={λ∈ C ： A -λI is not Drazin invertible } be the Drazin .spectrum. This paper shows that if Mc =（A C 0 B）is a 2 × 2 upp...A∈B（H） is called Drazin invertible if A has finite ascent and descent. Let σD （A）={λ∈ C ： A -λI is not Drazin invertible } be the Drazin .spectrum. This paper shows that if Mc =（A C 0 B）is a 2 × 2 upper triangular operator matrix acting on the Hilbert space H ＋ K, then the passage from OσD（A） U σD（B） to σD（Mc） is accomplished by removing certain open subsets of σD（A）∩σD（B） from the former, that is, there is equality σD（A）∪σD（B）=σD（MC）∪Gwhere G is the union of certain holes in σD （Me） which happen to be subsets of σD （A）∩σD （B）. Weyl＇s theorem and Browder＇s theorem are liable to fail for 2×2 operator matrices. By using Drazin spectrum, it also explores how Weyl＇s theorem, Browder＇s theorem, a-Weyl＇s theorem and a-Browder＇s theorem survive for 2×2 upper triangular operator matrices on the Hilbert space.展开更多
Weyl fermion is a massless Dirac fermion with definite chirality,which has been long pursued since 1929.Though it has not been observed as a fundamental particle in nature,Weyl fermion can be realized as low-energy ex...Weyl fermion is a massless Dirac fermion with definite chirality,which has been long pursued since 1929.Though it has not been observed as a fundamental particle in nature,Weyl fermion can be realized as low-energy excitation around Weyl point in Weyl semimetal,which possesses Weyl fermion cones in the bulk and nontrivial Fermi arc states on the surface. As a firstly discovered Weyl semimetal,Ta As crystal possesses 12 pairs of Weyl points in the momentum space,which are topologically protected against small perturbations. Here,we report for the first time the tip induced superconductivity on Ta As crystal by point contact spectroscopy. The zero bias conductance peak as well as a conductance plateau with double conductance peaks and sharp double dips are observed in the point contact spectra simultaneously,indicating unconventional superconductivity. Our further theoretical study suggests that the induced superconductivity may have nontrivial topology. The present work opens a new route in investigating the novel superconducting states based on Weyl materials.展开更多
Let H be a complex separable infinite dimensional Hilbert space. In this paper, a variant of the Weyl spectrum is discussed. Using the new spectrum, we characterize the necessary and sufficient conditions for both T a...Let H be a complex separable infinite dimensional Hilbert space. In this paper, a variant of the Weyl spectrum is discussed. Using the new spectrum, we characterize the necessary and sufficient conditions for both T and f(T) satisfying Weyl’s theorem, where f ∈ Hol(σ(T)) and Hol(σ(T)) is defined by the set of all functions f which are analytic on a neighbourhood of σ(T) and are not constant on any component of σ(T). Also we consider the perturbations of Weyl’s theorem for f(T).展开更多
In this paper, we present some modules over the rank-three quantized Weyl algebra, which are closely related to modules over some vertex algebras. The isomorphism classes among these modules are also determined.
In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem an...In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.展开更多
In this survey on extremum problems of Laplacian-Dirichlet eigenvalues of Euclidian domains, the author briefly presents some relevant classical results and recent progress. The main goal is to describe the well-known...In this survey on extremum problems of Laplacian-Dirichlet eigenvalues of Euclidian domains, the author briefly presents some relevant classical results and recent progress. The main goal is to describe the well-known conjecture due to Polya, its connections to Weyl's asymptotic formula for eigenvalues and shape optimizations. Many related open problems and some preliminary results are also discussed.展开更多
The paper presents an exact analysis leading to an accurate theoretical prediction of the amount of the mysteriously missing hypothetical dark energy density in the cosmos. The value found, namely 95.4915028% is in fu...The paper presents an exact analysis leading to an accurate theoretical prediction of the amount of the mysteriously missing hypothetical dark energy density in the cosmos. The value found, namely 95.4915028% is in full agreement with earlier analysis, the WMAP and the supernova cosmic measurements. The work follows first the strategy of finding a critical point which separates a semi-classical regime from a fully relativistic domain given by topological unit interval velocity parameter then proceeds to wider aspects of a topological quantum field of fractal unit interval. This idea of a critical velocity parameter was first advanced by Sigalotti and Mejias in 2006 who proposed a critical value equal . A second interesting proposal made in 2012 by Hendi and Sharifzadeh set the critical point at 0.8256645. The present analysis is based upon a light cone velocity quantized coordinate. This leads to the same quantum relativity energy mass relation found in earlier publications by rescaling that of Einstein’s special relativity. Two effective quantum gravity formulae are obtained. The first is for the ordinary measurable energy of the quantum particle while the second is for dark energy density of the quantum wave which we cannot measure directly and we can only infer its existence from the measured accelerated expansion of the universe E(D) = where . The critical velocity parameter in this case arises naturally to be . The results so obtained are validated using a heuristic Lorentzian transformation. Finally the entire methodology is put into the wider perspective of a fundamental scaling theory for the Planck scale proposed by G. Gross.展开更多
Inducing or enhancing superconductivity in topological materials is an important route toward topological superconductivity.Reducing the thickness of transition metal dichalcogenides(e.g.WTe2 and MoTe2)has provided an...Inducing or enhancing superconductivity in topological materials is an important route toward topological superconductivity.Reducing the thickness of transition metal dichalcogenides(e.g.WTe2 and MoTe2)has provided an important pathway to engineer superconductivity in topological matters.However,such monolayer sample is difficult to obtain,unstable in air,and with extremely low Tc.Here we report an experimentally convenient approach to control the interlayer coupling to achieve tailored topological properties,enhanced superconductivity and good sample stability through organic-cation intercalation of the Weyl semimetals MoTe2 and WTe2.The as-formed organic-inorganic hybrid crystals are weak topological insulators with enhanced Tc of 7.0 K for intercalated MoTe2(0.25 K for pristine crystal)and2.3 K for intercalated WTe2(2.8 times compared to monolayer WTe2).Such organic-cation intercalation method can be readily applied to many other layered crystals,providing a new pathway for manipulating their electronic,topological and superconducting properties.展开更多
Topological magnetic Weyl semimetals have been proposed to host controllable chiral domain walls which bear a great prospect in device applications. To exploit them in applications, it is important to have a proper wa...Topological magnetic Weyl semimetals have been proposed to host controllable chiral domain walls which bear a great prospect in device applications. To exploit them in applications, it is important to have a proper way to tune and manipulate these domain walls. One possible means is through magnetoelastic coupling. The involvement of rare earth in the lately proposed RAl X(R =rare earth, X = Si and Ge) family magnetic Weyl semimetals may provide such a platform. Here we present the transport and thermodynamic properties of Ce Al Ge under hydrostatic pressure. We find that pressure enhances the antiferromagnetic exchange in Ce Al Ge but essentially retains its magnetic structure. A large topological Hall effect with a pronounced loop shape is observed within the magnetically ordered state, and it splits into two regions under pressure. Such an unusual electromagnetic response is inferred to be a consequence of chiral magnetic domain walls. The unprecedented concomitance of its evolution under pressure and the reentrance of antiferromagnetic order strongly suggest the capability of switching on/off this electromagnetic response in noncentrosymmetric magnetic Weyl semimetals via magnetoelastic coupling.展开更多
The article puts forward a hypothesis about the possibility of the existence of our Universe inside a supermassive black hole, analyzes the basic assumptions and verifiable physical consequences. The transformation of...The article puts forward a hypothesis about the possibility of the existence of our Universe inside a supermassive black hole, analyzes the basic assumptions and verifiable physical consequences. The transformation of the Primary Particles obtained from the decay of Borromeo rings into binary and ternary structures is considered separately, taking into account how the percentages between Dark Matter, Dark Energy and Baryonic matter are formed. A system of kinetic equations has been compiled, which makes it possible to develop a theoretical approach to obtain these values depending on the geometric and physical characteristics of interacting particles. The possibility and necessity of the existence of a Primary Relic of Primary Particles are substantiated. The nature of the voids and the analytical solution of the Einstein equations obtained from the generalized Papapetrou solution, which leads to the existence of strings with an arbitrary distribution of matter along the string and with lengths comparable to the size of the Universe, are considered. In the case of a string of finite size and constant density, this solution leads to the well-known Weyl solution. An assumption is put forward about the existence of an Einstein-Rosen type transition, when the dimensions of the white and black holes at the ends of this transition have different dimensions.展开更多
Two variants of the essential approximate point spectrum are discussed. We find for example that if one of them coincides with the left Drazin spectrum then the generalized a-Weyl＇s theorem holds, and conversely for ...Two variants of the essential approximate point spectrum are discussed. We find for example that if one of them coincides with the left Drazin spectrum then the generalized a-Weyl＇s theorem holds, and conversely for a-isoloid operators. We also study the generalized a-Weyl＇s theorem for Class A operators.展开更多
EuCd_(2)As_(2)was theoretically predicted to be a minimal model of Weyl semimetals with a single pair of Weyl points in the ferromagnet state.However,the heavily p-doped Eu Cd_(2)As_(2)crystals in previous experiments...EuCd_(2)As_(2)was theoretically predicted to be a minimal model of Weyl semimetals with a single pair of Weyl points in the ferromagnet state.However,the heavily p-doped Eu Cd_(2)As_(2)crystals in previous experiments prevent direct identification of the semimetal hypothesis.Here,we present a comprehensive magneto-transport study of high-quality Eu Cd_(2)As_(2)crystals with ultralow bulk carrier density(10^(13)cm^(-3)).In contrast to the general expectation of a Weyl semimetal phase,Eu Cd_(2)As_(2)shows insulating behavior in both antiferromagnetic and ferromagnetic states as well as surface-dominated conduction from band bending.Moreover,the application of a dc bias current can dramatically modulate the resistance by over one order of magnitude,and induce a periodic resistance oscillation due to the geometric resonance.Such nonlinear transport results from the high nonequilibrium state induced by an electrical field near the band edge.Our results suggest an insulating phase in Eu Cd_(2)As_(2)and put a strong constraint on the underlying mechanism of anomalous transport properties in this system.展开更多
We construct a three-dimensional topological superconductor Bogoliubov–de Gennes(BdG)Hamiltonian with the normal state being a three-dimensional topological insulator.By introducing inter-orbital spin-triplet pairing...We construct a three-dimensional topological superconductor Bogoliubov–de Gennes(BdG)Hamiltonian with the normal state being a three-dimensional topological insulator.By introducing inter-orbital spin-triplet pairings term△3,there are topological Majorana nodes in the bulk and they are connected by Majorana Fermi arcs on the surface,similar to the case of Weyl semimetal.Furthermore,by adding an inversion-breaking term to the normal state,momentum-independent pairing terms with different parities can coexist in the Bd G Hamiltonian,which creates more Majorana modes similar to Andreev bound states and a richer phase diagram.展开更多
Magnetic topological semimetal can host various topological non-trivial states leading to exotic novel transport properties.Here we report the systematic magneto-transport studies on the Heusler alloy Nb_(x)Zr_(1-x)Co...Magnetic topological semimetal can host various topological non-trivial states leading to exotic novel transport properties.Here we report the systematic magneto-transport studies on the Heusler alloy Nb_(x)Zr_(1-x)Co_(2)Sn considered as a ferromagnetic(FM)Weyl semimetal.The cusp anomaly of temperature-dependent resistivity and large isotropic negative magneto-resistivity(MR)emerge around the FM transition consistent with the theoretical half-metallic predictions.The prominent anomalous Hall effect(AHE)has the same behavior with the applied field along various crystal directions.The Nb doping introduces more disorder resulting in the enhancement of the upturn for the temperature-dependent resistivity in low temperatures.With Nb doping,the AHE exhibits systemic evolution with the Fermi level lifted.At the doping level of x=0.25,the AHE mainly originates from the intrinsic contribution related to non-trivial topological Weyl states.展开更多
Using angle-resolved photoemission spectroscopy and density functional theory calculations methods,we investigate the electronic structures and topological properties of ternary tellurides NbIrTe_(4),a candidate for t...Using angle-resolved photoemission spectroscopy and density functional theory calculations methods,we investigate the electronic structures and topological properties of ternary tellurides NbIrTe_(4),a candidate for type-II Weyl semimetal.We demonstrate the presence of several Fermi arcs connecting their corresponding Weyl points on both termination surfaces of the topological material.Our analysis reveals the existence of Dirac points,in addition to Weyl points,giving both theoretical and experimental evidences of the coexistence of Dirac and Weyl points in a single material.These findings not only confirm NbIrTe_(4) as a unique topological semimetal but also open avenues for exploring novel electronic devices based on its coexisting Dirac and Weyl fermions.展开更多
Let G be a special linear group over the real,the complex or the quaternion,or a special unitary group.In this note,we determine all special unipotent representations of G in the sense of Arthur and Barbasch-Vogan,and...Let G be a special linear group over the real,the complex or the quaternion,or a special unitary group.In this note,we determine all special unipotent representations of G in the sense of Arthur and Barbasch-Vogan,and show in particular that all of them are unitarizable.展开更多
A Weyl node is characterized by its chirality and tilt.We develop a theory of how nth-order nonlinear optical conductivity behaves under transformations of anisotropic tensor and tilt, which clarifies how chirality-de...A Weyl node is characterized by its chirality and tilt.We develop a theory of how nth-order nonlinear optical conductivity behaves under transformations of anisotropic tensor and tilt, which clarifies how chirality-dependent and-independent parts of optical conductivity transform under the reversal of tilt and chirality.Built on this theory, we propose ferromagnetic Mn Bi2Te4as a magnetoelectrically regulated, terahertz optical device, by magnetoelectrically switching the chiralitydependent and-independent DC photocurrents.These results are useful for creating nonlinear optical devices based on the topological Weyl semimetals.展开更多
文摘When A ∈ B（H） and B ∈ B（K） are given, we denote by Mc an operator acting on the Hilbert space HΘ K of the form Me = （ A0 CB）. In this paper, first we give the necessary and sufficient condition for Mc to be an upper semi-Fredholm （lower semi-Fredholm, or Fredholm） operator for some C ∈B（K,H）. In addition, let σSF＋（A） = {λ ∈ C ： A-λI is not an upper semi-Fredholm operator} bc the upper semi-Fredholm spectrum of A ∈ B（H） and let σrsF- （A） = {λ∈ C ： A-λI is not a lower semi-Fredholm operator} be the lower semi Fredholm spectrum of A. We show that the passage from σSF±（A） U σSF±（B） to σSF±（Mc） is accomplished by removing certain open subsets of σSF-（A） ∩σSF＋ （B） from the former, that is, there is an equality σSF±（A） ∪σSF± （B） = σSF± （Mc） ∪＆ where L is the union of certain of the holes in σSF±（Mc） which ilappen to be subsets of σSF- （A） A σSF＋ （B）. Weyl＇s theorem and Browder＇s theorem are liable to fail for 2 × 2 operator matrices. In this paper, we also explore how Weyl＇s theorem, Browder＇s theorem, a-Weyl＇s theorem and a-Browder＇s theorem survive for 2 × 2 upper triangular operator matrices on the Hilbert space.
基金This work was supported by the Natronal Natural Science Foundation of China(Grant No.10171064)and an EYTP grant of MOE of China.
文摘A class of the associative and Lie algebras A[D] = A × F[D] of Weyl type are studied, where Ais a commutative associative algebra with an identity element over a field F of characteristic zero, and F[D] isthe polynomial algebra of a finite dimensional commutative subalgebra of locally finite derivations of A suchthat A is D-simple. The derivations of these associative and Lie algebras are precisely determined.
基金the National Natural Science Foundation of China (10571099)
文摘A∈B（H） is called Drazin invertible if A has finite ascent and descent. Let σD （A）={λ∈ C ： A -λI is not Drazin invertible } be the Drazin .spectrum. This paper shows that if Mc =（A C 0 B）is a 2 × 2 upper triangular operator matrix acting on the Hilbert space H ＋ K, then the passage from OσD（A） U σD（B） to σD（Mc） is accomplished by removing certain open subsets of σD（A）∩σD（B） from the former, that is, there is equality σD（A）∪σD（B）=σD（MC）∪Gwhere G is the union of certain holes in σD （Me） which happen to be subsets of σD （A）∩σD （B）. Weyl＇s theorem and Browder＇s theorem are liable to fail for 2×2 operator matrices. By using Drazin spectrum, it also explores how Weyl＇s theorem, Browder＇s theorem, a-Weyl＇s theorem and a-Browder＇s theorem survive for 2×2 upper triangular operator matrices on the Hilbert space.
基金financially supported by National Basic Research Program of China (2013CB934600,2012CB927400,2012CB921300,and 2016YFA0301604)the Research Fund for the Doctoral Program of Higher Education (RFDP) of China+2 种基金the Open Project Program of the Pulsed High Magnetic Field Facility (PHMFF2015002)Huazhong University of Science and Technology,Open Research Fund Program of the State Key Laboratory of Low Dimensional Quantum Physicsthe National Natural Science Foundation of China (11474008 and 11574008)
文摘Weyl fermion is a massless Dirac fermion with definite chirality,which has been long pursued since 1929.Though it has not been observed as a fundamental particle in nature,Weyl fermion can be realized as low-energy excitation around Weyl point in Weyl semimetal,which possesses Weyl fermion cones in the bulk and nontrivial Fermi arc states on the surface. As a firstly discovered Weyl semimetal,Ta As crystal possesses 12 pairs of Weyl points in the momentum space,which are topologically protected against small perturbations. Here,we report for the first time the tip induced superconductivity on Ta As crystal by point contact spectroscopy. The zero bias conductance peak as well as a conductance plateau with double conductance peaks and sharp double dips are observed in the point contact spectra simultaneously,indicating unconventional superconductivity. Our further theoretical study suggests that the induced superconductivity may have nontrivial topology. The present work opens a new route in investigating the novel superconducting states based on Weyl materials.
基金Supported by the Fundamental Research Funds For the Central Universities(Grant No.2016CSY020)the National Natural Science Foundation of China(Grant No.11701351)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2018JQ1082)
文摘Let H be a complex separable infinite dimensional Hilbert space. In this paper, a variant of the Weyl spectrum is discussed. Using the new spectrum, we characterize the necessary and sufficient conditions for both T and f(T) satisfying Weyl’s theorem, where f ∈ Hol(σ(T)) and Hol(σ(T)) is defined by the set of all functions f which are analytic on a neighbourhood of σ(T) and are not constant on any component of σ(T). Also we consider the perturbations of Weyl’s theorem for f(T).
基金NSF Grant No.Z0511046 of Fujian and NSF Grant No.10471091 of China
文摘In this paper, we present some modules over the rank-three quantized Weyl algebra, which are closely related to modules over some vertex algebras. The isomorphism classes among these modules are also determined.
文摘In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.
文摘In this survey on extremum problems of Laplacian-Dirichlet eigenvalues of Euclidian domains, the author briefly presents some relevant classical results and recent progress. The main goal is to describe the well-known conjecture due to Polya, its connections to Weyl's asymptotic formula for eigenvalues and shape optimizations. Many related open problems and some preliminary results are also discussed.
文摘The paper presents an exact analysis leading to an accurate theoretical prediction of the amount of the mysteriously missing hypothetical dark energy density in the cosmos. The value found, namely 95.4915028% is in full agreement with earlier analysis, the WMAP and the supernova cosmic measurements. The work follows first the strategy of finding a critical point which separates a semi-classical regime from a fully relativistic domain given by topological unit interval velocity parameter then proceeds to wider aspects of a topological quantum field of fractal unit interval. This idea of a critical velocity parameter was first advanced by Sigalotti and Mejias in 2006 who proposed a critical value equal . A second interesting proposal made in 2012 by Hendi and Sharifzadeh set the critical point at 0.8256645. The present analysis is based upon a light cone velocity quantized coordinate. This leads to the same quantum relativity energy mass relation found in earlier publications by rescaling that of Einstein’s special relativity. Two effective quantum gravity formulae are obtained. The first is for the ordinary measurable energy of the quantum particle while the second is for dark energy density of the quantum wave which we cannot measure directly and we can only infer its existence from the measured accelerated expansion of the universe E(D) = where . The critical velocity parameter in this case arises naturally to be . The results so obtained are validated using a heuristic Lorentzian transformation. Finally the entire methodology is put into the wider perspective of a fundamental scaling theory for the Planck scale proposed by G. Gross.
基金supported by the National Natural Science Foundation of China(11725418,21975140)Ministry of Science and Technology of China(2016YFA0301004,2016YFA0301001 and2015CB921001)+1 种基金the Basic Science Center Program of NSFC(51788104)Beijing Advanced Innovation Center for Future Chip(ICFC).
文摘Inducing or enhancing superconductivity in topological materials is an important route toward topological superconductivity.Reducing the thickness of transition metal dichalcogenides(e.g.WTe2 and MoTe2)has provided an important pathway to engineer superconductivity in topological matters.However,such monolayer sample is difficult to obtain,unstable in air,and with extremely low Tc.Here we report an experimentally convenient approach to control the interlayer coupling to achieve tailored topological properties,enhanced superconductivity and good sample stability through organic-cation intercalation of the Weyl semimetals MoTe2 and WTe2.The as-formed organic-inorganic hybrid crystals are weak topological insulators with enhanced Tc of 7.0 K for intercalated MoTe2(0.25 K for pristine crystal)and2.3 K for intercalated WTe2(2.8 times compared to monolayer WTe2).Such organic-cation intercalation method can be readily applied to many other layered crystals,providing a new pathway for manipulating their electronic,topological and superconducting properties.
基金supported by the Open Research Fund of Songshan Lake Materials Laboratory(Grant No.2022SLABFN27)National Natural Science Foundation of China(Grant Nos.12274364,and U1932155)+3 种基金Fundamental Research Funds for the Central Universities of China(Grant No.2019kfy XMBZ071)National Key R&D Program of China(Grant No.2022YFA1602602)Guangdong Basic and Applied Basic Research Foundation(Grant No.2022B1515120020)Pioneer and Leading Goose R&D Program of Zhejiang(Grant No.2022SDXHDX0005)。
文摘Topological magnetic Weyl semimetals have been proposed to host controllable chiral domain walls which bear a great prospect in device applications. To exploit them in applications, it is important to have a proper way to tune and manipulate these domain walls. One possible means is through magnetoelastic coupling. The involvement of rare earth in the lately proposed RAl X(R =rare earth, X = Si and Ge) family magnetic Weyl semimetals may provide such a platform. Here we present the transport and thermodynamic properties of Ce Al Ge under hydrostatic pressure. We find that pressure enhances the antiferromagnetic exchange in Ce Al Ge but essentially retains its magnetic structure. A large topological Hall effect with a pronounced loop shape is observed within the magnetically ordered state, and it splits into two regions under pressure. Such an unusual electromagnetic response is inferred to be a consequence of chiral magnetic domain walls. The unprecedented concomitance of its evolution under pressure and the reentrance of antiferromagnetic order strongly suggest the capability of switching on/off this electromagnetic response in noncentrosymmetric magnetic Weyl semimetals via magnetoelastic coupling.
文摘The article puts forward a hypothesis about the possibility of the existence of our Universe inside a supermassive black hole, analyzes the basic assumptions and verifiable physical consequences. The transformation of the Primary Particles obtained from the decay of Borromeo rings into binary and ternary structures is considered separately, taking into account how the percentages between Dark Matter, Dark Energy and Baryonic matter are formed. A system of kinetic equations has been compiled, which makes it possible to develop a theoretical approach to obtain these values depending on the geometric and physical characteristics of interacting particles. The possibility and necessity of the existence of a Primary Relic of Primary Particles are substantiated. The nature of the voids and the analytical solution of the Einstein equations obtained from the generalized Papapetrou solution, which leads to the existence of strings with an arbitrary distribution of matter along the string and with lengths comparable to the size of the Universe, are considered. In the case of a string of finite size and constant density, this solution leads to the well-known Weyl solution. An assumption is put forward about the existence of an Einstein-Rosen type transition, when the dimensions of the white and black holes at the ends of this transition have different dimensions.
文摘Two variants of the essential approximate point spectrum are discussed. We find for example that if one of them coincides with the left Drazin spectrum then the generalized a-Weyl＇s theorem holds, and conversely for a-isoloid operators. We also study the generalized a-Weyl＇s theorem for Class A operators.
基金sponsored by the National Key R&D Program of China(Grant No.2022YFA1405700)the National Natural Science Foundation of China(Grant Nos.12174069,and 92365104)+6 种基金the Shuguang Program supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commissionsupported by the Double First-Class Initiative Fund of Shanghai Tech Universitythe open project from Beijing National Laboratory for Condensed Matter Physicssupported by the National Key R&D Program of China(Grant No.2022YFA1602603)the National Natural Science Foundation of China(Grant No.12122411)supported by the National Natural Science Foundation of China(Grant No.12274090)the Natural Science Foundation of Shanghai(Grant No.22ZR1406300)。
文摘EuCd_(2)As_(2)was theoretically predicted to be a minimal model of Weyl semimetals with a single pair of Weyl points in the ferromagnet state.However,the heavily p-doped Eu Cd_(2)As_(2)crystals in previous experiments prevent direct identification of the semimetal hypothesis.Here,we present a comprehensive magneto-transport study of high-quality Eu Cd_(2)As_(2)crystals with ultralow bulk carrier density(10^(13)cm^(-3)).In contrast to the general expectation of a Weyl semimetal phase,Eu Cd_(2)As_(2)shows insulating behavior in both antiferromagnetic and ferromagnetic states as well as surface-dominated conduction from band bending.Moreover,the application of a dc bias current can dramatically modulate the resistance by over one order of magnitude,and induce a periodic resistance oscillation due to the geometric resonance.Such nonlinear transport results from the high nonequilibrium state induced by an electrical field near the band edge.Our results suggest an insulating phase in Eu Cd_(2)As_(2)and put a strong constraint on the underlying mechanism of anomalous transport properties in this system.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12174067 and 11804223)。
文摘We construct a three-dimensional topological superconductor Bogoliubov–de Gennes(BdG)Hamiltonian with the normal state being a three-dimensional topological insulator.By introducing inter-orbital spin-triplet pairings term△3,there are topological Majorana nodes in the bulk and they are connected by Majorana Fermi arcs on the surface,similar to the case of Weyl semimetal.Furthermore,by adding an inversion-breaking term to the normal state,momentum-independent pairing terms with different parities can coexist in the Bd G Hamiltonian,which creates more Majorana modes similar to Andreev bound states and a richer phase diagram.
基金Project supported by the National Key Research and Development Program of China (Grant Nos.2023YFF0718400 and 2023YFA1406500)the National Natural Science Foundation of China (Grant Nos.U2130101 and 92165204)+2 种基金the Natural Science Foundation of Guangdong Province,China (Grant No.2022A1515010035)the Open Project of Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices (Grant No.2022B1212010008)the Open Project of Key Laboratory of Optoelectronic Materials and Technologies (Grant No.OEMT-2023-ZTS-01)。
文摘Magnetic topological semimetal can host various topological non-trivial states leading to exotic novel transport properties.Here we report the systematic magneto-transport studies on the Heusler alloy Nb_(x)Zr_(1-x)Co_(2)Sn considered as a ferromagnetic(FM)Weyl semimetal.The cusp anomaly of temperature-dependent resistivity and large isotropic negative magneto-resistivity(MR)emerge around the FM transition consistent with the theoretical half-metallic predictions.The prominent anomalous Hall effect(AHE)has the same behavior with the applied field along various crystal directions.The Nb doping introduces more disorder resulting in the enhancement of the upturn for the temperature-dependent resistivity in low temperatures.With Nb doping,the AHE exhibits systemic evolution with the Fermi level lifted.At the doping level of x=0.25,the AHE mainly originates from the intrinsic contribution related to non-trivial topological Weyl states.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12274455,12274459,and 12204533)the National Key R&D Program of China (Grant No.2022YFA1403800)the Beijing Natural Science Foundation (Grant No.Z200005)。
文摘Using angle-resolved photoemission spectroscopy and density functional theory calculations methods,we investigate the electronic structures and topological properties of ternary tellurides NbIrTe_(4),a candidate for type-II Weyl semimetal.We demonstrate the presence of several Fermi arcs connecting their corresponding Weyl points on both termination surfaces of the topological material.Our analysis reveals the existence of Dirac points,in addition to Weyl points,giving both theoretical and experimental evidences of the coexistence of Dirac and Weyl points in a single material.These findings not only confirm NbIrTe_(4) as a unique topological semimetal but also open avenues for exploring novel electronic devices based on its coexisting Dirac and Weyl fermions.
基金supported by NSF grant (Award Number 2000254)supported by the National Natural Science Foundation of China (Grant Nos. 11701364 and 11971305)+4 种基金Xiamen University Malaysia Research Fund (Grant No. XMUMRF/2022-C9/IMAT/0019)supported by National Key R&D Program of China (Grant Nos. 2022YFA1005300 and 2020YFA0712600)New Cornerstone Investigator Programsupported by MOE AcRF Tier 1 grant A-0004280-00-00Provost’s Chair grant E-146-000-052-001 in NUS
文摘Let G be a special linear group over the real,the complex or the quaternion,or a special unitary group.In this note,we determine all special unipotent representations of G in the sense of Arthur and Barbasch-Vogan,and show in particular that all of them are unitarizable.
基金Project supported by the National Key R&D Program of China (Grant Nos.2018YFA, 0305601, and 2021YFA1400100)the National Natural Science Foundation of China (Grant Nos.12274003, 11725415, and 11934001)the Innovation Program for Quantum Science and Technology (Grant No.2021ZD0302600)。
文摘A Weyl node is characterized by its chirality and tilt.We develop a theory of how nth-order nonlinear optical conductivity behaves under transformations of anisotropic tensor and tilt, which clarifies how chirality-dependent and-independent parts of optical conductivity transform under the reversal of tilt and chirality.Built on this theory, we propose ferromagnetic Mn Bi2Te4as a magnetoelectrically regulated, terahertz optical device, by magnetoelectrically switching the chiralitydependent and-independent DC photocurrents.These results are useful for creating nonlinear optical devices based on the topological Weyl semimetals.
