Majorana zero modes induced by skyrmion lattice

One-dimensional s-wave superconductor with spin-orbit coupling is a platform for the realization of Majorana zero modes. The spin-exchange with the magnetic skyrmion lattice can induce spin-orbit coupling in a s-wave superconductor system and the effects are different from the constant spin-orbit coupling. The strength of the effective spin-orbit coupling as well as the rich topoloigcal phase diagram are directly connected to the radius of the skyrmion lattice R. We obtain the rich topological phase diagram of this system with different skyrmion lattice radii by numerically evaluating the spectrum of the system under the periodic boundary condition, and we also find the Majorana zero modes under the open boundary condition to verify the bulk-edge correspondence.     

关于光栅衍射和单缝衍射的讨论

本文试想说明在大学物理教材及其相关参考书中,对于光栅和单缝在单行光线斜入射时衍射条纹的叙述不明确而展开的讨论． ［例１］用每１ｍｍ有５００条栅纹的光栅,观察钠光谱线（λ＝ ５９０ｎｍ）．向（ｌ）光线垂直入射时;（２）光线以入射角３０°入射时,最多能看到第几级条纹？ 首先分析平行光线垂直入射时,可由光栅公式：（ａ＋ ｂ）ｓｉｎ＝±Ｋλ; 而最大衍射角＝９０°,ｓｉｎ＝１所以, Ｋ＝±ａ＋ｂ／λ＝±３．３８ 显然取Ｋ＝±３． 即在中央明条纹（ｘ＝０）两侧分别有３条明条纹,这样最多能看到第三级明条纹． 其次当…     

Topological Lifshitz transition and novel edge states induced by non-Abelian SU(2) gauge field on bilayer honeycomb lattice

We investigate the SU(2) gauge effects on bilayer honeycomb lattice thoroughly. We discover a topological Lifshitz transition induced by the non-Abelian gauge potential. Topological Lifshitz transitions are determined by topologies of Fermi surfaces in the momentum space. Fermi surface consists of N = 8 Dirac points at π-flux point instead of N = 4 in the trivial Abelian regimes. A local winding number is defined to classify the universality class of the gapless excitations. We also obtain the phase diagram of gauge fluxes by solving the secular equation. Furthermore, the novel edge states of biased bilayer nanoribbon with gauge fluxes are also investigated.