Interplay between multiple topologically non-trivial phases of matter

Research into topologically non-trivial phases of matter has expanded rapidly in the last decade and is now a key research direction across multiple branches of condensed matter physics, atomic and molecular physics, and optics. This expansion is driven in large part by the increasing understanding of how the standard classification scheme for symmetry-protected topological phases of matter, the ten-fold way, can be extended to non-electronic systems and beyond the usually considered symmetries. The resulting zoo of topological phases means it is increasingly likely that multiple topologically non-trivial phases of matter will coexist, motivating the need to better understand phase transitions between distinct topologically non-trivial phases.

Cartoon picture of the interface between a topological skyrmion phase with non-trivial skyrmion number Q and a topological phase characterized by a non-trivial Chern number, such as the integer quantum Hall effect, represented in the semiclassical regime to pictorially illustrate some distinctive physics of the two-dimensional bulk. This project aims to study physics at the interface between a topological phase characterized by non-trivial Chern number C and a topological skyrmion phase, characterized by non-trivial skyrmion number Q.

This project focuses on the interplay between two particularly significant topological phases which can co-exist, the Chern insulator phase, and the recently discovered chiral topological skyrmion phase, which serves as the first counterexample to the flat band limit assumption at the heart of many key constructions in topological condensed matter physics. The project will focus on gaining further understanding of the topological skyrmion phases and their implications for topological condensed matter more broadly. The project will involve microscopic calculations, both analytical and numerical, using both simpler toy models and more physically-relevant models exhibiting these topological phases. A part of the work will also include the exploration of a novel criterion for the existence of topological states through the characteristics of surface Green's functions.

This theory project is expected to yield important experimental signatures for study of this physics, and experimentalists in Dresden and at the University of St. Andrew's will be part of on-going discussions of the work.

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