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Second-Order Topological Phases in Non-Hermitian Systems.

Tao Liu¹, Yu-Ran Zhang^1,2, Qing Ai^1,3

¹Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan.

Physical Review Letters

|March 9, 2019

Summary

Second-order topological insulators (SOTIs) exhibit unique boundary modes. This study reveals that non-Hermitian SOTIs can localize zero-energy modes at corners, breaking conventional bulk-boundary correspondence.

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Area of Science:

Condensed Matter Physics
Topological Matter
Quantum Mechanics

Background:

Second-order topological insulators (SOTIs) are characterized by topologically protected boundary modes.
Hermitian SOTIs typically exhibit (d-2)-dimensional boundary modes in d dimensions.

Purpose of the Study:

To investigate the behavior of boundary modes in non-Hermitian second-order topological insulators.
To explore the breakdown of the bulk-boundary correspondence in these systems.
To introduce a method for characterizing non-Hermitian topological phases.

Main Methods:

Theoretical analysis of non-Hermitian second-order topological insulators in 2D and 3D.
Utilizing winding numbers based on complex wave vectors for phase characterization.
Considering experimental realization with ultracold atoms.

Main Results:

Non-Hermitian 2D SOTIs can host zero-energy corner modes, localized to a single corner.
Non-Hermitian 3D SOTIs exhibit anomalous corner-localized second-order boundary modes, not hinge-localized.
The conventional bulk-corner (hinge) correspondence is shown to break down in these non-Hermitian systems.

Conclusions:

Non-Hermitian higher-order topology presents novel phenomena distinct from Hermitian counterparts.
The winding number approach provides a robust tool for classifying non-Hermitian topological phases.
This research establishes a foundation for future studies on non-Hermitian topological matter.