Anti-$\mathcal{P}\mathcal{T}$ flatbands

Abstract

We consider tight-binding single particle lattice Hamiltonians which are invariant under an antiunitary antisymmetry: the anti-$\mathcal{P}\mathcal{T}$ symmetry. The Hermitian Hamiltonians are defined on $d$-dimensional non-Bravais lattices. For an odd number of sublattices, the anti-$\mathcal{P}\mathcal{T}$ symmetry protects a flatband at energy $E=0$. We derive the anti-$\mathcal{P}\mathcal{T}$ constraints on the Hamiltonian and use them to generate examples of generalized kagome networks in two and three lattice dimensions. Furthermore, we show that the anti-$\mathcal{P}\mathcal{T}$ symmetry persists in the presence of uniform DC fields and ensures the presence of flatbands in the corresponding irreducible Wannier-Stark band structure. We provide examples of the Wannier-Stark band structure of generalized kagome networks in the presence of DC fields, and their implementation using Floquet engineering.

15 pages, 3 figures. Supplemental Material included. Similar to the published version. Comments are welcome

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