标题： 半导体-超导体混合结构中的马约拉纳零模：通过马约拉纳分裂在短而无序的纳米线中定义拓扑性 显示英文标题

标题： Majorana zero modes in semiconductor-superconductor hybrid structures: Defining topology in short and disordered nanowires through Majorana splitting

摘要： 马约拉纳零模（MZMs）是1D拓扑超导体末端的束缚中间隙激发，必须成对出现。如果这对中的两个MZMs通过距离远大于它们各自的局域化长度而充分分离，则MZMs表现出非阿贝尔任意子，可以通过编织来进行容错的拓扑量子计算。在这种“拓扑”区域中，即分离的MZMs，它们的重叠呈指数级小，导致马约拉纳分裂呈指数级小，从而使得MZMs能够通过超导能隙进行拓扑保护。然而在实际实验样品中，无序的存在以及1D线的有限长度大大复杂化了情况，导致定义“拓扑性”时存在歧义，因为在短长度的无序线中，两个端模式之间的马约拉纳分裂可能并不一定很小。我们通过计算实验相关的短无序线中的分裂，并明确研究“指数保护”约束在无序、线长度和其他系统参数方面的适用性来理论研究这种情况。我们发现指数区域受到高度限制，并且在无序程度略低于拓扑超导能隙时被抑制。我们提供了详细的结果，并讨论了我们的理论对当前在超导-半导体混合平台中寻找MZMs的实验研究的意义。 显示英文摘要

摘要： Majorana zero modes (MZMs) are bound midgap excitations at the ends of a 1D topological superconductor, which must come in pairs. If the two MZMs in the pair are sufficiently well-separated by a distance much larger than their individual localization length, then the MZMs behave as non-Abelian anyons which can be braided to carry out fault-tolerant topological quantum computation. In this `topological' regime of well-separated MZMs, their overlap is exponentially small, leading to exponentially small Majorana splitting, thus enabling the MZMs to be topologically protected by the superconducting gap. In real experimental samples, however, the existence of disorder and the finite length of the 1D wire considerably complicates the situation leading to ambiguities in defining `topology' since the Majorana splitting between the two end modes may not necessarily be small in disordered wires of short length. We theoretically study this situation by calculating the splitting in experimentally relevant short disordered wires, and explicitly investigating the applicability of the `exponential protection' constraint as a function of disorder, wire length, and other system parameters. We find that the exponential regime is highly constrained, and is suppressed for disorder somewhat less than the topological superconducting gap. We provide detailed results and discuss the implications of our theory for the currently active experimental search for MZMs in superconductor-semiconductor hybrid platforms.