Uploaded May 2025 | Updated September 2026, 2 weeks ago
Speaker: Wojciech Jankowski (University of Cambridge)
Abstract: Multigap topological insulators, which fall beyond the conventional classifications of K-theory [1], are of vivid theoretical and experimental interest in condensed matter physics [2,3]. In this seminar, I will first introduce the homotopy classification of multigap topological phases with bulk topological invariants defined under PT (spacetime inversion) symmetry [3]. I will then cohomologically characterise non-Abelian bands of such phases, focusing on recently identified non-Abelian Hopf insulators with invariants underpinned by quaternion algebras [4]. Furthermore, I will discuss the momentum-space Riemannian geometry of quantum states realised by the multigap Bloch bundles, which I will connect to their physical manifestations in optical responses [5]. Finally, as quantised responses constitute a hallmark of topological phases of matter, I will show that three-dimensional multigap topological insulators can host quantised integrated non-linear shift photoconductivities [6]. I will demonstrate how the quantisation emerges from the momentum-space torsion tensors, connecting these to real Chern-Simons forms, and to virtual multiband optical transition amplitudes.
Speaker: Wojciech Jankowski (University of Cambridge)
Abstract: Multigap topological insulators, which fall beyond the conventional classifications of K-theory [1], are of vivid theoretical and experimental interest in condensed matter physics [2,3]. In this seminar, I will first introduce the homotopy classification of multigap topological phases with bulk topological invariants defined under PT (spacetime inversion) symmetry [3]. I will then cohomologically characterise non-Abelian bands of such phases, focusing on recently identified non-Abelian Hopf insulators with invariants underpinned by quaternion algebras [4]. Furthermore, I will discuss the momentum-space Riemannian geometry of quantum states realised by the multigap Bloch bundles, which I will connect to their physical manifestations in optical responses [5]. Finally, as quantised responses constitute a hallmark of topological phases of matter, I will show that three-dimensional multigap topological insulators can host quantised integrated non-linear shift photoconductivities [6]. I will demonstrate how the quantisation emerges from the momentum-space torsion tensors, connecting these to real Chern-Simons forms, and to virtual multiband optical transition amplitudes.
