Physicists have discovered a new class of topological phases in materials that depend on multiple energy gaps rather than just one, and they are building a geometric framework to describe them. Topological materials conduct electricity along their edges without loss, protected by their internal quantum structure. Until now, theory has focused on materials with a single energy gap. But recent experiments on twisted graphene layers and magnetic crystals have revealed behaviour that cannot be explained by single-gap topology alone. This project fills that gap by developing a mathematical language—based on quantum state distances—to classify and predict these multi-gap phases. If successful, the research could uncover new physical observables: edge currents, defect signatures, and electromagnetic responses that do not exist in conventional topological materials. The team will also design practical pathways to experiment using computer simulations and metamaterial models. This is fundamental science with no immediate application. But single-gap topology already underpins proposals for fault-tolerant quantum computers and ultra-efficient electronics. Multi-gap topology could open an entirely new family of materials with similarly transformative properties, though that remains years away.
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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.
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