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理解的一场革命。与传统绝缘体相比，拓扑绝缘体和金属的不同之处在于它们的拓扑不变量而不是有序参数，拓扑绝缘体和金属不仅重振了材料科学，而且激发了诸如冷原子系统和光子器件等领域的研究，并且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型多间隙拓扑相，在这一成功故事中建立新的篇章。最近，这种物理的首次表现形式出现在从扭曲层状石墨烯系统到磁性材料和淬火动力学的各种环境中，这概括了一种超越单间隙拓扑的范式转变。我们方法的一个核心要素依赖于利用几何方法，该方法不仅可以参数化和表征未知的多间隙依赖拓扑相类型，而且还是更深层框架的一部分，该框架承诺了新型可观测量与量子态距离的新概念之间的关系。利用这一独特的出发点，MultiTop提出使用这些当代手柄来探索非平衡系统、晶体材料和超导结构背景下的新拓扑相。这反过来又使我们能够在这些环境中发现新的物理可观测值，重点关注边界效应、缺陷特征和电磁感应响应。最后，我们将通过设计可行的实验途径，利用从头算评估和超材料建模来巩固该项目开创性理论性质的影响。考虑到提出的主题的多样性，但围绕着一个新的视角，我们预计我们的课程有很强的潜力来发现根本性的新理解。

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.