In a recent online seminar for RIKEN iTHEMS' QMSG series, Dr. Ashley Cook of the Max Planck Institute for Complex Systems delved into her interesting research on topological skyrmion phases in electronic systems. The talk was centered on non-interacting electronic topological phases that feature a skyrmion in their momentum-space spin polarization.

After a succinct introduction that framed the talk within the broader context of topological classification in condensed matter physics, Dr. Cook pivoted to explore quantum skyrmion structures in momentum space. She specifically discussed these structures in the context of expected spin polarization in the ground state of centrosymmetric superconductors. Intriguingly, she demonstrated that the topological protection of the skyrmion number extends to the electronic structure through a generalized bulk-boundary correspondence, after accounting for non-spin degrees of freedom. This results in the formation of unique edge states that bridge one types of the energy bands (conduction bands and valence bands).

Moreover, Dr. Cook emphasized that the adiabatic pumping of these edge states signifies the flow of quantum skyrmions. She suggested that this insight necessitates a reevaluation of the theoretical framework for the quantum Hall effects, which was initially conceived around point charges nearly half a century ago. Her work, therefore, not only suggests a pathway to discover new forms of topological boundary states but also calls for a more nuanced classification of topological states in electronic matter, beyond the limitations of the "tenfold way."

The talk sparked a lively discussion, underscoring its significance and the excitement it generated among the participants. We extend our gratitude to Dr. Ashley Cook for her illuminating and thought-provoking contribution.

Reported by Ching-Kai Chiu (iTHEMS) and Thore Posske (University of Hamburg, Germany)