Abstract
Topological invariants play a key role in the characterization of topological states. Due to the existence of exceptional points, it is a great challenge to detect topological invariants in non-Hermitian systems. We put forward a dynamic winding number, the winding of realistic observables in long-time average, for exploring band topology in both Hermitian and non-Hermitian two-band models via a unified approach. We build a concrete relation between dynamic winding numbers and conventional topological invariants. In one-dimension, the dynamical winding number directly gives the conventional winding number. In two-dimension, the Chern number relates to the weighted sum of dynamic winding numbers of all phase singularity points. This work opens a new avenue to measure topological invariants not requesting any prior knowledge of system topology via time-averaged spin textures.
Highlights
Topological invariant, a global quantity defined with static Bloch functions, has been widely used for classifying and characterizing topological states in various systems, including insulators, superconductors, semimetals, and waveguides [1,2,3,4,5,6]
When the system is changed from Hermiticity to non-Hermiticity, each singularity point will be split into two exceptional points (EPs); yet, the Chern number can still be extracted via the dynamic winding number (DWN) of all EPs
We put forward a new concept of dynamic winding number (DWN) and uncover its connections to conventional topological invariants in both Hermitian and non-Hermitian models
Summary
Topological invariant, a global quantity defined with static Bloch functions, has been widely used for classifying and characterizing topological states in various systems, including insulators, superconductors, semimetals, and waveguides [1,2,3,4,5,6]. When the system is changed from Hermiticity to non-Hermiticity, each singularity point will be split into two EPs (which are SPs); yet, the Chern number can still be extracted via the DWNs of all EPs. Without requesting any prior knowledge of their topology, our approach provides general guidance for measuring topological invariants in both Hermitian and non-Hermitian systems.
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