Abstract A topological superconductor is characterized by having a pairing gap in the bulk and gapless self-hermitian Majorana modes at its boundary. In one dimension, these are zero-energy modes bound to the ends, while in two dimensions these are chiral gapless modes traveling along the edge. Majorana modes have attracted a lot of interest due to their exotic properties, which include non-abelian exchange statistics. Progress in realizing topological superconductivity has been made by combining spin–orbit coupling, conventional superconductivity, and magnetism. The existence of protected Majorana modes, however, does not inherently require the breaking of time-reversal symmetry by magnetic fields. Indeed, pairs of Majorana modes can reside at the boundary of a time-reversal-invariant topological superconductor (TRITOPS). It is the time-reversal symmetry which then protects this so-called Majorana Kramers’ pair from gapping out. This is analogous to the case of the two-dimensional topological insulator, with its pair of helical gapless boundary modes, protected by time-reversal symmetry. Realizing the TRITOPS phase will be a major step in the study of topological phases of matter. In this paper we describe the physical properties of the TRITOPS phase, and review recent proposals for engineering and detecting them in condensed matter systems, in one and two spatial dimensions. We mostly focus on extrinsic superconductors, where superconductivity is introduced through the proximity effect. We emphasize the role of interplay between attractive and repulsive electron–electron interaction as an underlying mechanism. When discussing the detection of the TRITOPS phase, we focus on the physical imprint of Majorana Kramers’ pairs, and review proposals of transport measurement which can reveal their existence.

中文翻译：

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一维和二维时间反转不变的拓扑超导性

摘要 拓扑超导体的特点是在其边界处具有块体和无间隙自厄米马约拉纳模式的配对间隙。在一维中，这些是绑定到末端的零能量模式，而在二维中，这些是沿着边缘行进的手性无间隙模式。Majorana 模式因其奇异的特性而引起了很多兴趣，其中包括非阿贝尔交换统计数据。通过结合自旋轨道耦合、常规超导和磁性，在实现拓扑超导方面取得了进展。然而，受保护的马约拉纳模式的存在本身并不需要磁场破坏时间反转对称性。事实上，马约拉纳模式对可以驻留在时间反转不变拓扑超导体 (TRITOPS) 的边界上。正是时间反转对称性保护了这对所谓的 Majorana Kramers 对免于脱臼。这类似于二维拓扑绝缘体的情况，其具有一对螺旋无间隙边界模式，受时间反转对称性保护。实现 TRITOPS 相将是研究物质拓扑相的重要一步。在本文中，我们描述了 TRITOPS 相的物理特性，并回顾了最近的工程建议，并在凝聚态系统中，在一维和二维空间中检测它们。我们主要关注外在超导体，其中超导是通过邻近效应引入的。我们强调吸引力和排斥性电子 - 电子相互作用之间的相互作用作为潜在机制的作用。在讨论 TRITOPS 相位的检测时，