Non-Hermitian Band Topology and Edge States in Atomic Lattices

TL;DR

This paper explores the topological properties and edge states of atomic lattices with non-Hermitian Hamiltonians, revealing how long-range radiative coupling influences topological phases and edge phenomena.

Contribution

It introduces an effective non-Hermitian Hamiltonian framework for atomic lattices and demonstrates the non-Hermitian bulk-edge correspondence with analytical edge state solutions.

Findings

Topological phases depend on long-range dissipative coupling.

Edge states are analytically derived at domain boundaries.

Non-Hermitian bulk-edge correspondence is verified.

Abstract

We investigate the band structure and topological phases of one- and two-dimensional bipartite atomic lattices mediated by long-range dissipative radiative coupling. By deriving an effective non-Hermitian Hamiltonian for the single-excitation sector, we demonstrate that the low-energy dynamics of the system are governed by a Dirac equation with a complex Fermi velocity. We analyze the associated topological invariants for both the SSH and honeycomb models, utilizing synthetic gauge fields to break time-reversal symmetry in the latter. Finally, we explicitly verify the non-Hermitian bulk-edge correspondence by deriving analytical solutions for edge states localized at domain boundaries.