SIMS accurate determination of matrix composition of topological crystalline insulator material Pb1 − xSnxSe

Substitutional alloy Pb_1 − xSn_xSe is a new class of electronic materials called topological crystalline insulators, which at the temperature range from 0 K to 300 K exhibit topological state at compositions in the range 0.18 < x < 0.40 (in the rock-salt structure). In this report, we present a secondary ion mass spectrometry (SIMS) analysis technique to provide accurate Pb and Sn composition based on the measurement of PbCs⁺ and SnCs⁺ cluster ions intensities. Studies of Pb_1 − xSn_xSe bulk samples with various values of x show that x/(1 − x) is linear in relation to the intensity ratio of PbCs⁺/SnCs⁺ over the range from x = 0.15 to x = 0.41. This technique allows us to obtain an accurate Sn content for multilayered heterostructures, quantum wells containing Pb_1 − xSn_xSe with different x values for each layer.     

群作用的几乎周期性与等度连续性

In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.     

拓扑材料中的超导

近来,人们在凝聚态体系中发现了由拓扑不变量定义的物相,其中最重要的有拓扑绝缘体、拓扑半金属和拓扑超导体等.这些物相的拓扑性质由非平凡的拓扑数描述,相应的材料被称为拓扑材料,具有诸多新奇的物理特性.其中拓扑超导体由于边界上有满足非阿贝尔统计的Majorana零能模,成为实现拓扑量子计算的主要候选材料.除了探索本征的拓扑超导体外,由于拓扑性质上的相似性,在不超导的拓扑材料中调制出超导自然成为了实现拓扑超导的重要手段.目前,人们发展了栅极调制、掺杂、高压、近邻效应调制和硬针尖点接触等多种技术,已经成功地在许多拓扑绝缘体和半金属中诱导出了超导,并对超导的拓扑性和Majorana零能模进行了研究.本文回顾了本征拓扑超导候选材料,以及拓扑绝缘体和半金属中诱导出超导的代表性工作,评述了不同实验手段的优势和缺陷、分析了其超导拓扑性的证据,并提出展望.     

Soliton and other solutions to the (1+2)-dimensional chiral nonlinear Schrödinger equation

The (1+2)-dimensional chiral nonlinear Schrödinger equation (2D-CNLSE) as a nonlinear evolution equation is considered and studied in a detailed manner. To this end, a complex transform is firstly adopted to arrive at the real and imaginary parts of the model, and then, the modified Jacobi elliptic expansion method is formally utilized to derive soliton and other solutions of the 2D-CNLSE. The exact solutions presented in this paper can be classified as topological and nontopological solitons as well as Jacobi elliptic function solutions.     

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.     

Topological insulating phase for anti-Hermitian Hamiltonians

We study classification of anti-Hermitian topological insulators based on the discrete symmetries: time-reversal, particle-hole and chiral symmetries. Contrary to the most general form of non-Hermitian systems, bulk boundary correspondence can hold in anti-Hermitian topological systems. We map a topologically nontrivial Hermitian Hamiltonians into an anti-Hermitian system and we show that the standard table of topological insulators can be used for anti-Hermitian Hamiltonians.