Topological Structure of Phase Vortex in Resonating Valence Bond Superconductivity

In this paper, based on the Schrodinger equation and the ψ-mapping theory, the accurate expression for the gradient of resonating valence bond superconducting phase Θs is found. The expression of (△→)Θs is just the velocity flow (V) without considering the coefficient. The curl of (△→)Θs is where the vortex lies, and has important relation to δ2(ψ) and an important relation to the zero points of resonating valence bond superconducting order parameter ψ. The topological structure of the vortex is characterized by the ψ-mapping topological numbers Hopf-index and Brouwer degrees. The Ginzberg-Landau equation in resonating valence bond state also is discussed in this theory. The magnetic property is discussed also.     

Topological Structure of Chern-Simons Vortex

Based on the gauge potential decomposition theory and the φ-mapping method, the topological inner structure of the Chern-Sirnons-Higgs vortex has been studied strictly. It is shown that there exits a multi-charged vortex at every zero point of the Higgs scalar field φ. The multivortex solutions in the Chern-Simons-Higgs model are obtained strictly.     

Topological Structure of Vortex Solution in Jackiw-Pi Model

By using o-mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortex solution and topological number, which is determined by Hopf index and Brouwer degree. We also give the quantization of flux in this case. Then, we study the angular momentum of the vortex, which can be expressed in terms of the flux.     

Topological Structure of Vortex Solution in Jackiw-Pi Model

By using φ-mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortex solution and topological number, which is determined by Hopf index and Brouwer degree. We also give the quantization of flux in this case. Then, we study the angular momentum of the vortex, which can be expressed in terms of the flux.     

Topological Structure of Knotted Vortex Lines in Liquid Crystals

In this paper, a novel decomposition expression for the U（1） gauge field in liquid crystals （LCs） is derived. Using this decomposition expression and the b-mapping topological current theory, we investigate the topological structure of the vortex lines in LCs in detail. A topological invariant, i.e., the Chern-Simons （CS） action for the knotted vortex lines is presented, and the CS action is shown to be the total sum of all the self-linking and linking numbers of the knot family. Moreover, it is pointed out that the CS action is preserved in the branch processes of the knotted vortex lines.     

Topological Scenario for High-Temperature Superconductivity in Cuprates

The structure of the joint phase diagram of high-temperature superconducting cuprates has been studied within the theory of fermion condensation. Prerequisites of the topological rearrangement of the Landau state with the formation of a flat band adjacent to the nominal Fermi surface have been established. The related non-Fermi-liquid behavior of cuprates in the normal phase has been studied with focus on the non-Fermi-liquid behavior of the resistivity ρ(T), including the observed crossover from the linear temperature behavior ρ(T, x) = A₁(x)T at doping levels x below the critical value x _c ^h corresponding to the boundary of the superconducting region to the quadratic temperature behavior at x > x _c ^h , which is incompatible with predictions of the conventional quantum-critical-point scenario. It has been demonstrated that the slope of the coefficient A₁(x) is universal and is the same on both boundaries of the joint phase diagram of cuprates in agreement with available experimental data. It has also been shown that the fermion condensate is responsible for pairing in the D-wave state in cuprates. The effective Coulomb repulsion in the Cooper channel, which prevents the existence of superconductivity in normal metals in the S channel, leads to high-temperature superconductivity in the D channel.     

利用柱透镜调控涡旋光束的拓扑结构

提出了一种利用柱透镜调控涡旋光束拓扑结构的方法.利用计算全息法制作的叉形光栅掩模板,实验获得了具有不同拓扑荷的涡旋光束,分析了涡旋光束通过柱透镜变换后的强度和相位分布.结果表明,涡旋光束经柱透镜变换后,其拓扑荷符号将发生改变,并且高阶涡旋光束退化为多个分离的一阶涡旋光束.利用高阶激光模式的线性叠加特性以及古依相移对实验结果进行了理论解释,并通过数值模拟对实验结果进行了验证.     

Complete Gluonic Phase in Two-Flavour Colour Superconductivity

We study a typical complete gluonic phase （LGP） in two-flavour colour superconductivity （2SC） by calculating the essential cubic and quartic interfering term between the gluonic condensates （Az^（8）） and/Az^（6）） with a gauged NJL model. It is proven that the coefficients of the cubic interfering term and the vacuum contributions of the cubic and quartic interfering term are all equal to zeroes. The coefficients of the quartic interfering term and the /Az^（6）） ＇s quartic self-interaction term at stationary points of Larkin-Ovchinnikov-Fulde-Ferrell （LOFF） phase are calculated. Comparisons among the effective potentials of LOP, g2SC and LOFF phase indicate that LOP could be the genuine ground state of 2SC for some reasonable paxameters.     

Measurement of Superconductivity and Edge States in Topological Superconductor Candidate TaSe_3

Topological superconductors(TSCs) have been widely investigated in recent years due to their novel physics and ability to host Majorana fermions(MFs) which are key to topological quantum computation. Despite the great interest, only a few compounds have been proposed as candidates of intrinsic TSCs, such as ironbased superconductor FeSe_(0.55)Te_(0.45) and 2 M-WS_2. Among them, quasi-one-dimensional superconductor TaSe_3 possesses fascinating properties such as its simple stoichiometry, layered nature and chemical stability. Here,using scanning tunneling microscope/spectroscopy(STM/STS), we systematically investigate the topography and electronic structure of TaSe_3. Our STM/STS measurement reveals large atomically flat, defect-free surfaces suitable for the search of MF; electronic density of states consistent with our angle-resolved photoemission result and band-structure calculations, and a uniform superconducting gap with a typical size of ~0.25 meV. Remarkably,additional edge states are observed in the vicinity of the terrace edge, suggesting they may have a topological origin. Our result proves the coexistence of superconductivity and topological electronic structure in TaSe_3,making it an intriguing platform to investigate topological superconductivity.     

Theory of Nematic Superconductivity in Doped Topological Insulators (Brief Review)

JETP Letters - Theoretical studies of the theory of nematic superconductivity in doped insulators of the Bi2Se3 family have been reviewed. It is experimentally shown that their transition to the...     

Topological Phase in Non-centrosymmetric Material NaSnBi

We predict that a non-centrosymmetric material NaSnBi locates in a three-dimensional non-trivial topological phase under ambient pressure based on first-principle calculations.By deriving the effective model around the Γpoint,we find that the topological phase transition is driven by a Rashba spin-orbital coupling through an odd number of pairs of band touch due to a small anisotropic gap caused by quintic dispersion terms.In contrast to conventional topological insulators,the spin texture of the surface Dirac cone is right-handed and the surface states are strikingly different for different surface terminations.     

Pressure-Induced Topological and Structural Phase Transitions in an Antiferromagnetic Topological Insulator

Recently,natural van der Waals heterostructures of(MnBi₂ Te₄)_m(Bi₂ Te₃)_n have been theoretically predicted and experimentally shown to host tunable magnetic properties and topologically nontrivial surface states.We systematically investigate both the structural and electronic responses of MnBi₂ Te₄ and MnBi₄ Te₇ to external pressure.In addition to the suppression of antiferromagnetic ord...     

Topological Aspects of the Berry Phase

We shall explore here the relationship between chiral anomaly and Berry phase from the view-point of the topological investigations of anomaly. This will be extended in the coherent state representation of a quantized spinor. The relevance of Berry phase will also be studied in an unified formalism of integral and fractional quantum Hall effect. Finally we shall study the role of this topological phase in polarised light.     

Knotted Topological Phase Singularities of Electromagnetic Field

In this paper, knotted objects （RS vortices） in the theory of topological phase singularity in electromagnetic field have been investigated in details. By using the Duan＇s topological current theory, we rewrite the topological current form of RS vortices and use this topological current we reveal that the Hopf invariant of RS vortices is just the sum of the linking and self-linking numbers of the knotted RS vortices. Furthermore, the conservation of the Hopf invariant in the splitting, the mergence and the intersection processes of knotted RS vortices is also discussed.     

Topological Phase Transition of Non-Hermitian Crosslinked Chain

The contents of topological classification of matter are enriched by non-Hermiticity, such as exceptional points, bulk-edge correspondence, and skin effects. Physically, gain and loss can be introduced by imaginary on-site potentials of lattice Hamiltonians, and the topological phase transition for a cross-linked chain in the presence of such non-Hermiticity is investigated. The topological phase diagram in terms of a winding number is obtained analytically with phase boundaries coinciding with the surfaces of exceptional points. The topologically original edge states with distribution mainly at the joints between domains of different phases are protected even for long chains. The non-Hermitian topological feature can also be reflected by vortex structures in the vector fields of complex eigenenergies, expected values of Pauli matrices, and trajectories of these quantities. This model may be implemented in coupled photonic crystals, fermions trapped in optical lattice, or non-Hermitian electrical-circuit lattices, and the edge states are immune to various kinds of disorders until topological phase transition occurs. This work gives insight into the influence of non-Hermiticity on topological phase of matter.     

Knotted Topological Phase Singularities of Electromagnetic Field

In this paper, knotted objects (RS vortices) in the theory of topological phase singularity in electromagnetic field have been investigated in details. By using the Duan's topological current theory, we rewrite the topological current form of RS vortices and use this topological current we reveal that the Hopf invariant of RS vortices is just the sum of the linking and self-linking numbers of the knotted RS vortices. Furthermore, the conservation of the Hopf invariant in the splitting, the mergence and the intersection processes of knotted RS vortices is also discussed.     

Spin Structure of Baryons in Orbiting Valence Quark Model

The quark model with orbital motion of the valence quarks is constructed to reproduce the spin structure of baryons. The relations between the spin-averaged sum rules and baryon magnetic moments found in the previous works do not remain, unless the small orbital magnetic moments are neglected. In particular, when the orbital motion of the valence quarks leads to the small contribution of quark orbit-spin to baryon magnetic moments, the sum rules for polarized nucleon are in agreement with the recent experiment.