Exceptional non-Hermitian topological edge mode and its application to active matter

Area of Science:

• Condensed matter physics
• Topological materials
• Non-Hermitian systems

Background:

• Topological materials possess scattering-free edge modes protected by bulk topology in Hermitian systems.
• The behavior of edge modes in non-Hermitian systems, which include dissipation and injection, is not fully understood.
• Existing frameworks for non-Hermitian topological phases do not fully explain edge mode phenomena.

Purpose of the Study:

• To reveal a new mechanism for robust edge modes in non-Hermitian systems.
• To demonstrate the breakdown of the bulk-edge correspondence in non-Hermitian topological phenomena.
• To explore applications of these edge modes in novel devices.

Main Methods:

• Investigation of edge mode emergence in non-Hermitian systems.
• Analysis of topological structures associated with exceptional points and branchpoint singularities.
• Numerical confirmation in prototypical lattice models.
• Application to a chiral active matter model based on hydrodynamic description.

Main Results:

• Robust gapless edge modes appear in non-Hermitian systems via a mechanism distinct from bulk topology.
• The bulk-edge correspondence breaks down due to a novel topological structure around exceptional points.
• Complex eigenenergy spectra of these modes enable lasing wave packets propagating along sample edges.
• Edge modes are observed in lattice models and active matter systems.

Conclusions:

• A new mechanism for robust edge modes in non-Hermitian systems is identified, distinct from bulk topology.
• Exceptional points and associated topological structures are key to understanding these edge modes.
• The findings provide an alternative design principle for scattering-free edge currents in non-Hermitian devices.
• Active matter can exhibit inherent non-Hermitian topological features.