Topological invariant of non-Hermitian space-time modulated photonic crystals

TL;DR

This paper introduces a new method to analyze topological invariants in non-Hermitian, space-time modulated photonic crystals, revealing quantized Zak phases, symmetry differences at band edges, and topological phase transitions.

Contribution

It proposes a medium transformation approach for calculating topological invariants in non-Hermitian photonic systems, simplifying analysis without non-Bloch band theory.

Findings

Zak phase is quantized to 0 or 1 in STMPCs.

Eigenmode symmetry differs at Brillouin zone edges for non-trivial phases.

Topological phase transitions occur due to band inversion.

Abstract

We propose a medium transformation approach to formulate the adjoint system of space-time modulated photonic crystals (STMPCs), essential for the bi-orthogonal Berry connection when calculating the topological invariant. We show that the non-Abelian Zak phase of STMPCs comprising stacked photonic time crystals and dielectrics is quantized to 0 or 1 for both the entangled and isolated bands. We find that the eigenmodes at the center and edge of the Brillouin zone differ in symmetry for the band with non-trivial Zak phases, while they share the same symmetry for the trivial Zak phases. In addition, topological phase transitions owing to band inversion are observed. Moreover, a generalized Brillouin zone of the non-Hermitian STMPCs is established, which is identical to the Hermitian counterpart, implicating that the non-Bloch band theory is not required in this regard. The proposed medium transformation method may serve as an alternative approach to exploring more intricate topological phenomena in non-Hermitian systems when incorporating non-Bloch band theory.