Chern insulator boundary states are proven to follow corners and rough edges because the topological exponential map maps the bulk Chern class to a nonvanishing edge-translation invariant.
Topological phases on the hyperbolic plane: fractional bulk-boundary correspondence
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abstract
We study topological phases in the hyperbolic plane using noncommutative geometry and T-duality, and show that fractional versions of the quantised indices for integer, spin and anomalous quantum Hall effects can result. Generalising models used in the Euclidean setting, a model for the bulk-boundary correspondence of fractional indices is proposed, guided by the geometry of hyperbolic boundaries.
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Edge-following topological states
Chern insulator boundary states are proven to follow corners and rough edges because the topological exponential map maps the bulk Chern class to a nonvanishing edge-translation invariant.