434 research outputs found
Edge and corner states in 2D non-Abelian topological insulators from an eigenvector frame rotation perspective
We propose the concept of 2D non-Abelian topological insulator which can
explain the energy distributions of the edge states and corner states in
systems with parity-time symmetry. From the viewpoint of non-Abelian band
topology, we establish the constraints on the 2D Zak phase and polarization. We
demonstrate that the corner states in some 2D systems can be explained as the
boundary mode of the 1D edge states arising from the multi-band non-Abelian
topology of the system. We also propose the use of off-diagonal Berry phase as
complementary information to assist the prediction of edge states in
non-Abelian topological insulators. Our work provides an alternative approach
to study edge and corner modes and this idea can be extended to 3D systems
Four-band non-Abelian topological insulator and its experimental realization
Very recently, increasing attention has been focused on non-Abelian
topological charges, e.g. the quaternion group Q8. Different from Abelian
topological band insulators, these systems involve multiple tangled bulk
bandgaps and support non-trivial edge states that manifest the non-Abelian
topological features. Furthermore, a system with even or odd number of bands
will exhibit significant difference in non-Abelian topological classifications.
Up to now, there is scant research investigating the even-band non-Abelian
topological insulators. Here, we both theoretically explored and experimentally
realized a four-band PT (inversion and time-reversal) symmetric system, where
two new classes of topological charges as well as edge states are
comprehensively studied. We illustrate their difference from four-dimensional
rotation senses on the stereographically projected Clifford tori. We show the
evolution of bulk topology by extending the 1D Hamiltonian onto a 2D plane and
provide the accompanying edge state distributions following an analytical
method. Our work presents an exhaustive study of four-band non-Abelian
topological insulators and paves the way to other even band systems.Comment: Main text and supplementary informatio
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