Anti-$\mathcal{PT}$ flatbands

TL;DR

This paper explores anti-$\mathcal{PT}$ symmetry in lattice Hamiltonians, demonstrating its role in protecting flatbands at zero energy in odd-sublattice systems, and extends the analysis to Wannier-Stark bands under DC fields.

Contribution

It introduces the concept of anti-$\mathcal{PT}$ symmetry in lattice Hamiltonians, derives symmetry constraints, and constructs examples in kagome networks, including effects of DC fields and Floquet engineering.

Findings

Anti-$\mathcal{PT}$ symmetry protects flatbands at zero energy.

Flatbands persist in Wannier-Stark bands under DC fields.

Examples of generalized kagome networks in 2D and 3D are provided.

Abstract

We consider tight-binding single particle lattice Hamiltonians which are invariant under an antiunitary antisymmetry: the anti-$\mathcal{PT}$ symmetry. The Hermitian Hamiltonians are defined on $d$-dimensional non-Bravais lattices. For an odd number of sublattices, the anti-$\mathcal{PT}$ symmetry protects a flatband at energy $E = 0$. We derive the anti-$\mathcal{PT}$ 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-$\mathcal{PT}$ 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.