Topological Invariants of Edge States for Periodic Two-Dimensional Models

Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define topological invariants by considering the associated Bott–Maslov indices which can be easily calculated numerically. For time-reversal symmetric systems in the symplectic universality class this leads to a ${\mathbb Z}_2$ -invariant for the edge states. It is shown that the edge state invariants are related to Chern numbers of the bulk systems and also to (spin) edge currents, in the spirit of the theory of topological insulators.     

Emerging Edge States in the Monolayer FeSe Superconductor with the Spin-Orbit Coupling

JETP Letters - Previously, the monolayer FeSe superconductor can be described qualitatively based on a two-orbital model. We here proposed theoretically that the edge states and vortex induced zero...     

Topological and Nontopological Edge States Induced by Qubit-Assisted Coupling Potentials

In the usual Su–Schrieffer–Heeger (SSH) chain, the topology of the energy spectrum is divided into two categories in different parameter regions. Here, the topological and nontopological edge states induced by qubit-assisted coupling potentials in circuit quantum electrodynamics (QED) lattice modeled as a SSH chain are studied. It is found that, when the coupling potential added on only one end of the system raises to a certain extent, the strong coupling potential will induce a new topologically nontrivial phase accompanied by the appearance of a nontopological edge state, and the novel phase transition leads to the inversion of odd–even effect directly. Furthermore, the topological phase transitions when two unbalanced coupling potentials are injected into both ends of the circuit QED lattice are studied, and it is found that the system exhibits three distinguishing phases with multiple flips of energy bands. These phases are significantly different from the previous phase induced via unilateral coupling potential due to the existence of a pair of nontopological edge states. The scheme provides a feasible and visible method to induce different topological and nontopological edge states through controlling the qubit-assisted coupling potentials in circuit QED lattice both in experiment and theory.     

Topological Vortices in a Spin-Triplet Superconductor

Based on the complex three-component order parameter model of a spin-triplet superconductor, by using the C-mapping theory, we derive a new equation describing the distribution of the magnetic field for vortices, which can be reduced to the modified London equation in the case of ｜ψ^2｜^2 ~- ｜ψ^3｜^2 = 0 and Wl^1= 1. A magnetic flux quantization condition for vortices in a spin-triplet superconductor is also derived, which is topological-invariant. Fhrthermore, the branch processes during the evolution of the vortices in a spin-triplet superconductor are discussed. We also point out that the sum of the magnetic flux quantization that those vortices carried is 2nФo （Фo is the unit magnetic flux）, that is to say, the sum of winding number is even, which needs to be proved by experiment.     

AuCu3 型超导体SrPb3 中德哈斯-范阿尔芬振荡及非平庸拓扑能带

AuCu3 型超导体兼具非平庸的拓扑能带, 是近期受到关注的拓扑超导体候选材料之一. 理论预言 SrPb3具有非平庸的拓扑能带, 然而, 实验上尚未得到证实. 本工作观察到德哈斯-范阿尔芬振荡, 验证了 SrPb3 中电子能带的非平庸拓扑性质. 通过分析提取出两个振荡频率Fα =3.54 T 和Fβ =7.43 T. 进一步利用 Lifshitz-Kosevich 公式以及朗道量子化理论, 得到两个对应费米面的载流子有效质量分别为 mα* =0.006m0 和 mβ* =0.008m0 , 同时它们的贝里相位分别为?αB = (1 .32±0.25)π 和?βB = (1 .10±0.25)π. 这些结果表明 SrPb3 中存在有效质量接近于零的相对论费米子和非平庸拓扑能带. SrPb3 中超导电性与非平庸拓扑能带的共存, 为研究超导与拓扑的关联以及探索拓扑超导体提供新的研究体系.     

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.     

Experimental Observations Indicating the Topological Nature of the Edge States on HfTe_5

The topological edge states of two-dimensional topological insulators with large energy gaps furnish ideal conduction channels for dissipationless current transport. Transition metal tellurides X_(Te5)X=Zr, Hf) are theoretically predicted to be large-gap two-dimensional topological insulators, and the experimental observations of their bulk insulating gap and in-gap edge states have been reported, but the topological nature of these edge states still remains to be further elucidated. Here, we report our low-temperature scanning tunneling microscopy/spectroscopy study on single crystals of HfTe5. We demonstrate a full energy gap of ～80 meV near the Fermi level on the surface monolayer of HfTe5 and that such an insulating energy gap gets filled with finite energy states when measured at the monolayer step edges. Remarkably, such states are absent at the edges of a narrow monolayer strip of one-unit-cell in width but persist at both step edges of a unit-cell wide monolayer groove. These experimental observations strongly indicate that the edge states of HfTe5 monolayers are not trivially caused by translational symmetry breaking, instead they are topological in nature protected by the 2 D nontrivial bulk properties.     

Reentrant Orbital Effect against Superconductivity in the Quasi-Two-Dimensional Superconductor NbS2

JETP Letters - We derive an integral equation for the superconducting gap, which takes into account the quantum nature of electron motion in a parallel magnetic field in a quasi-two-dimensional...     

Mott Transition and Superconductivity in Quantum Spin Liquid Candidate NaYbSe_2

The Mott transition is one of the fundamental issues in condensed matter physics,especially in the system with antiferromagnetic long-range order.However,such a transition is rare in quantum spin liquid(QSL) systems without long-range order.Here we report the experimental pressure-induced insulator to metal transition followed by the emergence of superconductivity in the QSL candidate NaYbSe₂ with a triangular lattice of 4 f Yb³⁺ ions.Detail analysis of transport properties...     

Coexistence of Quasi-two-dimensional Superconductivity and Tunable Kondo Lattice in a van der Waals Superconductor

Realization of Kondo lattice in superconducting van der Waals materials not only provides a unique opportunity for tuning the Kondo lattice behavior by electrical gating or intercalation, but also is helpful for further understanding the heavy fermion superconductivity. Here we report a low-temperature and vector-magneticfield scanning tunneling microscopy and spectroscopy study on a superconducting compound（4Hb-TaS₂） with alternate stacking of 1T-TaS₂ and 1H-TaS₂     

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.     

Scattering of Electrons between Edge and Two-Dimensional States of a Two-Dimensional Topological Insulator and the Conductivity of the Topological Insulator Strip in a Metallic State

JETP Letters - The lifetime of electrons on edge states of a two-dimensional topological insulator against the background of an allowed two-dimensional band has been determined. It has been shown...     

Topological Structure of Phase Vortex in Resonating Valence Bond Superconductivity

In this paper, based on the Schrfdinger equation and the ψ mapping theory, the accurate expression for the gradient of resonating valence bond superconducting phase Θ^2s is found. The expression of Δ↓Θ^2s is just the velocity flow without considering the coefficient. The curl of Δ↓Θ^2s 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.     

Fantastic Behaviour of High-TC Superconductor Junctions: Tunable Superconductivity

Carrier injection performed in oxygen-deficient YBa2 Cu307_~ （YBCO） hetero-structure junctions exhibits tunable resistance that is entirely different from the behaviour of semiconductor devices. Tunable superconductivity in YBCO junctions, increasing over 20 K in transition temperature, has achieved by using electric processes. To our knowledge, this is the first observation that intrinsic property of high Tc superconductors＇ superconductivity can be adjusted as tunable functional parameters of devices. The fantastic phenomenon caused by carrier injection is discussed based on a proposed charge carrier seff-trapping model and BCS theorv.     

Topological Superconductivity in Cu(x)Bi(2)Se(3)

A topological superconductor (TSC) is characterized by the topologically protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topological insulator Cu(x)Bi(2)Se(3), which superconducts below ～3 K, has been predicted to possess a topological superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting Cu(x)Bi(2)Se(3) present a zero-bias conductance peak (ZBCP) which signifies unconventional superconductivity. Theoretical considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana fermions and gives evidence for a topological superconductivity in Cu(x)Bi(2)Se(3). In addition, we found an unusual pseudogap that develops below ～20 K and coexists with the topological superconducting state.     

Charge Density Wave States and Structural Transition in Layered Chalcogenide TaSe_(2-x)Te_x

The structural features and three-dimensional nature of the charge density wave(CDW) state of the layered chalcogenide 1 T-TaSe_(2-x)Te_x(0≤x≤2.0) are characterized by Cs-corrected transmission electron microscopy measurements. Notable changes of both average structure and the CDW state arising from Te substitution for Se are clearly demonstrated in samples with x 0.3. The commensurate CDW state characterized by the known star-of-David clustering in the 1 T-TaSe_2 crystal becomes visibly unstable with Te substitution and vanishes when x=0.3. The 1 T-TaSe_(2-x)Te_x(0.3≤x≤1.3) samples generalily adopt a remarkable incommensurate CDW state with monoclinic distortion, which could be fundamentally in correlation with the strong q-dependent electronphonon coupling-induced period-lattice-distortion as identified in TaTe2. Systematic analysis demonstrates that the occurrence of superconductivity is related to the suppression of the commensurate CDW phase and the presence of discommensuration is an evident structural feature observed in the superconducting samples.     

凝聚体中的拓扑量子态

探寻拓扑上非平庸的凝聚体物质状态,特别是其电子结构和输运性质,是当前凝聚体物理 学领域非常重要的前沿研究方向。本文讨论的大多数主题都与电子波函数的拓扑性质有关。全文 除简短的引言外,包括拓扑量子现象、各种拓扑相、拓扑性准粒子的异常输运性质、拓扑性集 体激发和耦合激发,以及继续发展的拓扑量子态研究五个章节。这些章节着重反映拓扑量子态研 究的各个侧面,汇总起来方可以凸显凝聚体中拓扑量子态的全貌。     

Flux States,Anyons and High Tc Superconductivity

In this paper, we studied the statistical behavior of anyons with isospin degrees of freedom, in which the fluctuation of isospjn degrees of freedom satisfies the O(3) nonlinear σ model. Under the mean field treatment, this model is in somewhat equivalent to the doped or frustrated Heisenberg an tiferromagnetic (AFM) model. We also studied the relation between the statistical field A_μ, and Skyrmion current B_μ. Finally, we set up the relation between flux states and spinon statistics, and the conditions of Bose condensation of holons. In particular, for π-flux state of A_μ, the spinons are bosons, the holons satisfy 2/3 fractional statistics.     

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...