New architectures for topological superconductors

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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.