AI 中文总结
本文提出一种新的量子点链平台，通过手性马约拉纳表示的格林函数研究四量子点短链的相图，成功复现马约拉纳零能模的特征及费米子宇称变化边界。
AI 中文摘要
近期，在人工构建的一维p波超导体两端出现的马约拉纳零能模（MZM）已在理论和实验上得到广泛研究。在可能的平台中，邻近超导半导体线以及中间夹有超导体的短量子点（QD）链已被研究。本文中，我们提出了一种不同的平台，即由夹在s波超导体和强自旋轨道半导体之间的量子点（QD）链组成，并受到塞曼磁场作用。忽略QD之间的自旋守恒隧穿过程以及超导邻近效应诱导的局域QD上超导关联，哈密顿量可简化为两个具有独立希尔伯特空间的等效哈密顿量之和。由于相邻QD之间的自旋翻转过程$t_{so}$和交叉安德烈夫反射$\triangle_{CAR}$，所得模型具有交错结构。我们的核心结果是由四个QD组成并耦合到两个外部库的短链的相图，该相图通过手性马约拉纳表示下的格林函数获得。零能下计算的、探测整个链的推迟格林函数的模被证明包含马约拉纳零能模的拓扑和空间特征的信息。格林函数中观测到的特征与转移矩阵方法得到的特征吻合良好，特别是马约拉纳零能模显示振荡波函数的参数空间区域被很好地复现，同样，格林函数得到的费米子宇称变化的边界也与其他方法得到的结果一致。
英文摘要
Majorana zero modes (MZM) appearing at the ends of artificially created one-dimensional p-wave superconductors have been intensively studied recently both theoretically and experimentally. Among possible platforms, proximitised semiconducting wires, and short chains of quantum dots with a superconductor in between were investigated. Here, we propose a different platform consisting of a chain of quantum dots (QDs) sandwiched between an s-wave superconductor and a strong spin-orbit semiconductor, subject to a Zeeman magnetic field. Neglecting spin-conserving hopping processes between QDs and local on-dot superconducting correlations induced by the superconducting proximity effect, reduces the Hamiltonian to the sum of two equivalent Hamiltonians with two independent Hilbert spaces. The resulting model has a staggered structure due to spin-flipping processes $t_{so}$ and cross-Andreev reflections $Δ_{CAR}$ between neighbouring dots. Our central result is the phase diagram of a short chain consisting of four QDs and coupled to two external reservoirs, obtained by means of the Green function in chiral Majorana representation. The modulus of the retarded Green function, probing the whole chain and calculated for zero energy, is shown to contain information on topology and spatial character of Majorana zero modes. The features observed in the Green function nicely agree with those obtained from the transfer matrix approach. In particular the region in parameter space in which Majorana zero modes display oscillatory wave functions are well reproduced. Likewise the borders of the fermion parity changes obtained by the Green function agree with those obtained by other means.
Comments11 pages, 5 figures, presented at The European Conference Physics of Magnetism 2026, Poznań, POLAND
