论文标题
Majorana Josephson连接的几何形状的贪婪优化
Greedy optimization of the geometry of Majorana Josephson junctions
论文作者
论文摘要
与自旋轨道耦合的二维电子气体中的约瑟夫森连接是实现拓扑超导性的有前途的候选人。尽管众所周知，连接的几何形状强烈影响拓扑间隙的大小，但如何构造最佳几何形状的问题仍未得到探索。我们引入了一种贪婪的数值算法，以优化Majorana连接的形状。该算法的核心依赖于扰动理论，并且令人尴尬地平行，这使其能够有效地探索设计空间。通过在Hamiltonian中引入随机变化，我们避免过度适合特定系统参数。此外，我们通过应用图像过滤和制造分辨率约束来限制优化器以产生光滑的几何形状。我们在各种设置中运行算法，发现它可靠地产生了几何形状，而拓扑间隙增加了大参数范围。结果对于优化起点和疾病的存在的变化是可靠的，这表明优化器能够找到全局最大值。
Josephson junctions in a two-dimensional electron gas with spin-orbit coupling are a promising candidate to realize topological superconductivity. While it is known that the geometry of the junction strongly influences the size of the topological gap, the question of how to construct optimal geometries remains unexplored. We introduce a greedy numerical algorithm to optimize the shape of Majorana junctions. The core of the algorithm relies on perturbation theory and is embarrassingly parallel, which allows it to explore the design space efficiently. By introducing stochastic variations in the junction Hamiltonian, we avoid overfitting geometries to specific system parameters. Furthermore, we constrain the optimizer to produce smooth geometries by applying image filtering and fabrication resolution constraints. We run the algorithm in various setups and find that it reliably produces geometries with increased topological gaps over large parameter ranges. The results are robust to variations in the optimization starting point and the presence of disorder, which suggests the optimizer is capable of finding global maxima.
