# Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems

**Authors:** Xiang Ji, Xiaosen Yang  
**arXiv:** [2403.18470](https://arxiv.org/abs/2403.18470)  
**Date:** 2024-03-27  
**Summary page:** https://www.summarizepaper.com/en/paper/2403.18470v1/

## Key points

- The article discusses the interplay between non-Hermitian skin effect and topology in periodically driven systems.
- It examines the establishment of generalized bulk-boundary correspondence in static non-Hermitian systems.
- The authors explore non-Bloch band theory in harmonically driven and periodically quenched non-Hermitian systems.
- Novel phenomena in higher-dimensional periodically driven non-Hermitian systems are highlighted, including Floquet non-Hermitian higher-order topological phases and Floquet hybrid skin-topological modes.
- Experimental realizations and recent advances in this field are surveyed, with a focus on electric circuits as a platform for investigating periodically driven non-Hermitian systems.

## Summary

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The review article titled "Generalized Bulk-Boundary Correspondence in Periodically Driven Non-Hermitian Systems" by Xiang Ji and Xiaosen Yang provides a comprehensive overview of the interplay between the non-Hermitian skin effect and topology in periodically driven systems. The authors examine the non-Bloch band theory of static non-Hermitian systems, discussing the establishment of generalized bulk-boundary correspondence. They also delve into the non-Bloch band theory of two typical periodically driven non-Hermitian systems: harmonically driven and periodically quenched systems. The article highlights the definition of non-Bloch topological invariants on the generalized Brillouin zone and real space wave functions to characterize Floquet non-Hermtian topological phases. It also explores novel phenomena in higher-dimensional periodically driven non-Hermitian systems, including Floquet non-Hermitian higher-order topological phases and Floquet hybrid skin-topological modes. Experimental realizations and recent advances in this field are surveyed as well. Furthermore, the authors discuss how electric circuits serve as a platform for investigating periodically driven non-Hermitian systems, showcasing phenomena such as evolution of non-Bloch waves, higher-order non-Hermitian skin effects, and many-body non-Hermitian skin effects observed in these circuits. Techniques like adding switches enable realization of periodically quenched systems in electric circuits, allowing for efficient energy conversion within a single cycle. Overall, this pedagogical review aims to inspire further research on Floquet non-Hermtian topological physics by providing insights into the intricate dynamics of periodically driven non-Hermitian systems and their implications on topology and quantum phenomena.