CMT Forum: Nur Ünal

While a significant fraction of topological materials has been characterized using symmetry requirements, the last couple of years have been witnessing the rise of new multi-gap topologies that go beyond all previously-known classification. Here, I will present these exotic topologies involving non-Abelian braiding of band nodes in multi-level non-interacting settings. In systems with C₂T or PT symmetry, band singularities can be characterised by a non-Abelian frame charges. The ability of these band nodes to annihilate pairwise is path dependent, and the sign of their charges can be changed by braiding nodes in adjacent gaps.  I will show that the combination of periodic driving and these recent multi-gap topological insights galvanize a new direction, arriving at new anomalous topological phases in out-of-equilibrium settings that have no static counterparts. I will identify observable signatures within reach of state-of-the-art quantum simulators and present specific interferometry schemes.

Furthermore, reaching beyond the non-Abelian band topology, many of these topological evaluations are related to the underlying quantum geometry. New structures emerge beyond minimal two-level models and the simple Bloch sphere picture, where the larger Hilbert spaces become hard to visualise. I will conclude by introducing a geometric description for generic N-level systems in terms of nested two-spheres and potential applications.

Slager, Bouhon, Ünal, Nature Communications 15, 1144 (2024)
Breach, Slager, Ünal, arXiv:2401.01928
Kemp, Cooper, Ünal, Phys. Rev. Research 4, 023120 (2022)