Braiding electrons in out-of-equilibrium topological patterns

Researchers from the Cavendish Laboratory have uncovered a new realm of topological phases, advancing our understanding of quantum phenomena.

Topological phases, characterised by electrons forming intricate collective entangled structures or knots that cannot be undone, have long intrigued physicists for their distinct properties. These phases hold promise for applications ranging from advanced electronics to quantum computing, representing a holy grail in modern physics.

Recently, a whole new class of topological materials were discovered in which electrons perform a precise dance in which emergent particles arise that have non-commuting charges. “This means when they move around each other, or `braid’, their topological charges change, giving rise to new kinds of collective knots with novel types of mathematical abstractions to describe them,” said Dr Robert-Jan Slager, co-author of the study from Cambridge’s Cavendish Laboratory. “These phases were by and large pioneered in Cambridge and recently, more and more esoteric physical properties of these phases are being discovered.”

In this new study published in Nature Communications, the team of researchers from the Cavendish Laboratory predict that these new topological properties come to full glory in a dynamical context.

“When the system is shaken periodically, unexpected physics emerges,” said Dr Nur Ünal, co-author of the study also from the Cavendish. “We find new, anomalous, topological phases which cannot exist in a static context and have distinct properties.”

In particular, these phases exhibit remarkable resilience to external perturbations, thanks to effective braiding processes that are intrinsically out of equilibrium, offering promising avenues for robust information storage and processing.

Even more excitingly, these new topological phases and their properties can be induced and observed in the laboratory, by shaking an optical lattice or shining a laser light on it for instance. In such systems, moving packets of atoms around results in distinctive interference patterns that depend on the non-commuting, or so-called non-Abelian charges.

“The periodic driving gives rise to more kinds of possible moves, or braids, ensuring new patterns for the system to arrange in,” said Slager. “This means there is a whole new world of uncharted topological phases and properties to explore.”

“These results not only inspire new theoretical treasure hunts, but they are also within reach of state-of-the-art ultracold quantum gases in laboratories around the world and also here at the Cavendish,” said Ünal.

“These novel anomalous topological phases provide a glimpse of the richness of driven multiband systems, and we are looking forward to searching for their experimental signatures in driven optical lattices,” said Professor Ulrich Schneider, head of the Many Body Quantum Dynamics group at the Cavendish, which will explore these new topological phases in experimental settings. “It is amazing that after many years of fast progress, band-structure topology can still reveal ever more novel phenomena.”

Reference: 

Slager, RJ., Bouhon, A. & Ünal, F.N, ‘Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems.’ Nat Commun 15, 1144 (2024). DOI:10.1038/s41467-024-45302-2

Image: 

Illustration of changing topological charges via braiding upon periodic driving by light. Credit: Nur Ünal, Robert-Jan Slager