New architectures for topological superconductors

该提案旨在探索创建物质拓扑超导态的新平台。在过去的十年中，拓扑概念已经发展成为材料研究的一个核心方面，这些概念的基础与超导体薄片或强磁场中的导体的研究有关，正如2016年诺贝尔奖对拓扑相变和物质拓扑相的认可。拓扑学处理几何对象的分类属性，这些属性在对象平滑重塑时保持不变。例如，人们可以将咖啡杯顺利地塑造成甜甜圈，因此这些物体具有相同的拓扑结构，其特征是单个孔穿透这些物体。同样，在材料科学中，物质量子态的拓扑关系到即使在材料的某些方面发生变化时仍保持不变的性质类型。量子霍尔效应是一个很好的例子，当一个薄的二维导体被放置在强磁场中时，产生的霍尔电阻是普遍的，即所有材料（在相同的电荷密度下）都是相同的，而与它们的化学结构或纯度无关。换句话说，拓扑阶段在表现出实际的行为变化之前，实际上需要施加很大的外部影响。这种稳定性吸引了拓扑物质作为存储和处理量子信息的平台：构建健壮的量子计算机的挑战恰恰是控制量子信息并使其免受环境的影响。虽然目前的量子计算机开始产生在经典机器上难以获得的初步结果，但它们只能在大部分初始信息丢失之前的短时间内处理信息。这意味着这些计算机只能运行足够短的算法，因此限制了它们的实用性。用拓扑超导体中的马约拉纳自由度取代他们目前的超导通量量子比特硬件，可能是消除过度信息丢失和实现高性能量子计算机的可能途径。我们已经知道拓扑超导体是如何在传统超导体和自旋轨道耦合材料制成的夹层结构中产生的。这些系统构成了马约拉纳线技术的基础，一维拓扑超导体被认为在其末端携带马约拉纳费米子态，外来量子态受益于拓扑保护。在这些系统中，自旋轨道耦合是所使用材料固有的，通常与重元素有关，并且对其大小或特性的控制有限。在这里，我们提出从理论上研究一种由普通超导体层与工程层结合而成的新型异质结构，这种异质结构可以在局部水平上设计有效的自旋轨道耦合。基于如何从一系列不同的物理机制中创建合成规范场或有效引力指标的见解，我们将为一个有前途的平台创建一个理论模型，以实现可以方便地用电场操纵的合成自旋-轨道耦合。我们期望将这种材料与普通超导体耦合可以提供细粒度的控制，以针对特定的拓扑超导状态。此外，考虑到在这些系统中创建更复杂的有效自旋轨道耦合空间模式的能力，我们将探索是否可以利用这种局部控制来构建用于量子信息处理的新型量子器件。最后，我们的系统也可以被视为引力场的类似物，因此我们将从这个角度考虑它们，并探索与天体物理设置的联系。

This proposal aims to explore a new platform for creating topological superconducting states of matter.During the last decade, concepts of topology have evolved into a central aspect of the study of materials, with foundations of these ideas relating to the study of thin sheets of superconductors or conductors in strong magnetic fields, as recognised in the 2016 Nobel Prize for topological phase transitions and topological phases of matter. Topology deals with classifying properties of geometrical objects that remain unchanged when the object is smoothly reshaped. For example, one can smoothly mould a coffee cup into a doughnut, so these objects have the same topology, characterised by a single hole piercing these bodies.Similarly, in materials science, the topology of quantum states of matter relates to the type of properties that remain constant even when some aspects of the material are changed. The quantum Hall effect, measured when a thin two-dimensional conductor is placed into strong magnetic fields, is a good example in that the resulting Hall resistance is universal, i.e. it is the same for all materials (at the same density of charge), independently of their chemical structure or purity. In other words, topological phases actually require a large external influence to be applied before they display an actual change in behaviour. This stability leads to attraction of topological matter as a platform for storing and processing quantum information: the challenge for building robust quantum-computers is precisely to control quantum information and shield it from the influence of the environment. While current-day quantum computers start to produce first results that would be difficult to obtain on classical machines, they can only process information for a short amount of time before most of the initial information is lost. This means that these computers can only run algorithms that are sufficiently short, hence limiting their usefulness. Replacing their current hardware of superconducting flux qubits with Majorana degrees of freedom in topological superconductors could be a possible route to eliminate excessive loss of information and enable highly performing quantum computers.It is already known how topological superconductors can be created in sandwich structures made of conventional superconductors and materials with spin-orbit coupling. These systems form the basis for the technology of Majorana wires, one dimensional topological superconductors which are thought to carry Majorana fermion states at their ends, exotic quantum states that benefit from topological protection. In these systems, the spin-orbit coupling is inherent to the materials used, which is generally tied to heavy elements, and there is limited control of its magnitude or characteristics.Here, we propose to theoretically study a new type of heterostructures built from a layer of ordinary superconductors combined with an engineered layer in which an effective spin-orbit coupling can be engineered at a local level. Building on insights of how synthetic gauge fields or effective gravitational metrics can be created from a range of different physical mechanisms, we will create a theoretical model for a promising platform to realise synthetic spin-orbit couplings which can be conveniently manipulated with electric fields. We expect that coupling such materials to ordinary superconductors can provide fine-grained control to target specific topological superconducting states. Additionally, given the ability to create more complex spatial patterns of effective spin-orbit coupling in these systems, we will explore whether this local control could be exploited to build new types of quantum devices for quantum information processing.Finally, our systems can also be regarded as analogues of gravitational fields, so we will consider them from this angle and explore connections with astrophysical settings.