标题： 驱动 Rashba 纳米线中的耗散诱导马约拉纳$0$- 和$π$- 模式 显示英文标题

标题： Dissipation induced Majarona $0$- and $π$-modes in a driven Rashba nanowire

摘要： 周期驱动是在非拓扑设置中创建拓扑相的一种引人入胜的方法。 然而，尽管系统总是与环境接触并导致耗散，大多数系统通常被研究为一个封闭系统。 在这里，我们研究了一个在耗散背景中与$s$波超导体邻近的周期性驱动的Rashba纳米线。 该系统的动力学由一个周期性李普诺夫算子描述，我们从其中构建了李普诺夫时间演化算子，并使用第三量子化方法获得“弗洛凯阻尼矩阵”，该矩阵捕捉了系统的谱和拓扑特性。 我们展示了系统表现出边缘局域化的拓扑马约拉纳$0$模式（MZMs）和$\pi$模式（MPMs）。 此外，系统还支持一个平凡的$0$模式（TZMs）和$\pi$模式（TPMs），这些模式也局域在系统的边缘。 MZMs 和 MPMs 与体拓扑相关，并携带体拓扑不变量，而 TZMs 和 TPMs 的出现主要与异常点有关，并且是拓扑平凡的。 我们根据拓扑不变量研究了拓扑相图，并表明耗散可以显著改变拓扑相图，甚至在系统中诱导拓扑相。 我们的工作扩展了对驱动-耗散拓扑超导体的理解。 显示英文摘要

摘要： Periodic drive is an intriguing way of creating topological phases in a non-topological setup. However, most systems are often studied as a closed system, despite being always in contact with the environment, which induces dissipation. Here, we investigate a periodically driven Rashba nanowire in proximity to an $s$-wave superconductor in a dissipative background. The system's dynamics is governed by a periodic Liouvillian operator, from which we construct the Liouvillian time-evolution operator and use the third-quantization method to obtain the `Floquet damping matrix', which captures the spectral and topological properties of the system. We show that the system exhibits edge-localized topological Majorana $0$-modes (MZMs) and $\pi$-modes (MPMs). Additionally, the system also supports a trivial $0$-modes (TZMs) and $\pi$-modes (TPMs), which are also localized at the edges of the system. The MZMs and the MPMs are connected to the bulk topology and carry a bulk topological invariant, while the emergence of TZMs and TPMs is primarily tied to exceptional points and is topologically trivial. We study the topological phase diagrams in terms of the topological invariants and show that the dissipation can modify the topological phase diagram substantially and even induce topological phases in the system. Our work extends the understanding of a driven-dissipative topological superconductor.