Search for novel collective phenomena due to many-body correlations in low dimensional systems

低维系统是一类具有新颖量子现象的有趣系统。一些引起广泛关注的例子是非常规超导体和石墨烯基材料。它们为未来提供了巨大的希望，有助于发现新的量子相（涉及磁性，密度波，超导性甚至它们之间的共存）;并用自旋电子学取代电子学：一种更有效的信息传输手段。低维系统中另一个不可避免的因素是破坏宇称的自旋轨道耦合。当与超导性结合时，它可以导致像马约拉纳费米子这样的奇异激发，这对量子计算至关重要。然而，大部分的兴奋一直在单粒子物理学的水平。这使我们无法充分利用量子世界的好处。要做到这一点，人们需要理解多体相关性在这类系统中的作用。该研究计划旨在通过研究各种低维系统中的集体激发，以非常系统的方式精确地实现这一目标。一般来说，集体激发有可能告诉我们很多关于一个系统的信息，只要我们有一个能够适当处理相关性的理论。 作为该计划的一部分，我们将研究电子相关性对在过渡金属二硫属化物上生长的自旋轨道耦合单层/双层石墨烯的作用。它为我们提供了机会，从非自旋自由度，如子晶格，谷，层调查集体激发。我们将进一步研究在非常规超导相周围预期的各种量子相中的集体激发，如超导，超导与超导共存，磁性及其与超导共存。我们还将提供所有这些阶段的拉曼光谱的理论。使用我们的理论模型在实验上跟踪跨相边界的模式将提供对系统中存在的相关性的性质的更好的洞察。 该计划旨在开发理论工具来处理自旋轨道耦合系统中的多体相关性：这是研究物质更复杂相并将多体效应纳入自旋电子学和量子计算等领域的重要一步。几个团体将从该计划的输出中受益：它直接影响在石墨烯基设备上工作的团体;高Tc社区可以受益于这样一个事实，即预测类似基态的不同配对机制现在可以区分为集体激发在每种情况下都是不同的;我们在该计划中得出的许多结论也可以使用冷原子装置进行测试，从而鼓励在该领域进行实验;集体激发的知识也是测量非平衡系统性质的垫脚石。

Low dimensional systems are interesting class of systems exhibiting novel quantum phenomena. Some examples that has created a lot of buzz are unconventional superconductors and Graphene-based materials. They offer great promise for the future by aiding in discovery on novel quantum phases (involving magnetism, density waves, superconductivity and even coexistence amongst them); and replacing electronics with Spintronics: a more efficient means to transfer information. Another unavoidable ingredient in low dimensional systems is the spin-orbit coupling that breaks parity. When combined with superconductivity it can lead to exotic excitations like Majorana fermions which are essential for quantum computing. However, much of the excitement has been at the level of single-particle physics. This does not allow us to exploit the benefits of the quantum world to the fullest potential. To do that one needs to understand the role of many-body correlations in such systems. This research program is designed to achieve precisely that in a very systematic manner by studying collective excitations in various low-dimensional systems. Collective excitations in general have the potential to tell us a great deal about a system provided we are equipped with a theory that can appropriately handle correlations. As part of this program, we will investigate the role of electronic correlations on spin-orbit coupled single/bilayer Graphene grown on transition metal dichalcogenides. It provides us with the opportunity to investigate collective excitations from non-spin degrees of freedom like sublattice, valley, and layer. We will further investigate collective excitations in the various quantum phases expected around the unconventional superconductivity phase like nematic, coexistence of nematic with superconductivity, magnetic and its coexistence with superconductivity. We will also provide the theory of Raman spectrum in all of these phases. Experimentally tracking the modes across the phase-boundaries using our theoretical model will provide improved insight into the nature of correlations present in the system. This program is designed to develop theoretical tools to handle many-body correlations in spin-orbit coupled systems: an important step forward in studying more complex phases of matter and incorporating many-body effects into fields like Spintronics and quantum computation. Several groups stand to benefit from the output of this program: it directly impacts groups working on Graphene-based devices; the high Tc community can benefit from the fact that different pairing mechanisms that predict similar ground-states, can now be distinguished as the collective excitations are different in each case; many of the conclusions we form in this program can also be tested using cold-atom set-ups thereby encouraging experiments in that field; the knowledge of collective excitations is also a stepping stone towards gauging the properties of non-equilibrium systems.