Multi-gap topological physics: from a new geometric perspective to materials

拓扑材料的发现引发了我们对物质认识的一场革命。拓扑绝缘体和金属的区别在于它们的拓扑不变量而不是序参数，它们不仅给材料科学注入了新的活力，而且激发了人们对冷原子系统和光子器件等领域的追求，并仍然影响着广泛的前沿理论和实验研究。在这个项目中，我们的目标是通过研究传统方法无法解决的新颖的多间隙拓扑阶段，在这个成功故事中建立新的篇章。封装了一个超越单间隙拓扑的范式转变，这种物理的第一个表现最近已经在从扭曲的层状石墨烯系统到磁性材料和猝灭动力学的各种背景下浮出水面。我们方法的一个中心元素依赖于利用几何方法，该方法不仅可以参数上升和描述未知种类的多间隙依赖的拓扑相，而且也是更深层次框架的一部分，该框架承诺了新类型的可观察量和新的量子态距离概念之间的关系。受益于这一独特的起点，MultiTop建议使用这些当代句柄在非平衡系统、晶体材料和超导结构的背景下探索新的拓扑相。这反过来将允许我们在聚焦于边界效应、缺陷特征和电磁感应响应时，在这些环境中发现新的物理观测。最后，我们将通过设计可行的实验路径，使用从头计算评估和超材料建模来强调该项目的开创性理论性质的影响。鉴于提议的主题多种多样，但以单一的新视角为中心，我们预计我们的计划有很大潜力从根本上揭示新奇的理解。

The discovery of topological materials has sparked a revolution in our understanding of matter. Distinguished from their conventional counterparts by topological invariants rather than order parameters, topological insulators and metals have not only reinvigorated materials science but also inspired pursuits in for example cold-atom systems and photonic devices, and still affect a broad range of cutting edge theoretical and experimental research. Within this programme, we aim to establish a new chapter in this success story by investigating novel multi-gap topological phases that cannot be addressed by conventional approaches. Encapsulating a paradigm shift beyond single-gap topology, the first manifestations of this physics have recently been surfacing in a variety of contexts ranging from twisted layered graphene systems to magnetic materials and quench dynamics.A central element of our approach relies on utilising a geometrical methodology that cannot only parametrise and characterise uncharted kinds of multi-gap dependent topological phases but is also part of a deeper framework that promises relations between new kinds of observable quantities and novel notions of quantum state distance. Profiting from this unique starting point, MultiTop proposes to use these contemporary handles to explore new topological phases in the contexts of out-of-equilibrium systems, crystalline materials and superconducting structures. This will in turn allow us to uncover new physical observables in these settings upon focussing on boundary effects, defect signatures and electromagnetically induced responses. Finally, we will underpin the impact of the pioneering theoretical nature of the project by designing viable pathways to experiment using ab-initio evaluations and metamaterial modelling. Given the variety of proposed subjects, yet centred around a single new perspective, we anticipate that our programme has a strong potential to uncover fundamentally novel understanding.