Fate of moiré flat bands for a weakly repulsive Bose-Einstein condensate in one-dimensional 𝒫𝒯-symmetric bichromatic optical lattices
Abstract
One-dimensional (1D) superlattices provide one simplified platform for exploring moiré physics from a low-dimensional perspective, with the ratio of lattice constants playing a role analogous to the twist angle in two-dimensional bilayers. Here, we propose a 1D 𝒫𝒯-symmetric bichromatic optical lattice for a weakly repulsive Bose-Einstein condensate and investigate how the interplay of dissipation and interaction impacts the lowest moiré flat band. Without interaction, we find that the lowest-band flatness induced by commensurate ratios exhibits a parity-dependent response to the 𝒫𝒯-symmetric imaginary potential due to the distinct 𝒫𝒯 pairing mechanism for the energy spectrum. For ratios with even denominators (i.e., even parities), the level attraction and thus the 𝒫𝒯-symmetry breaking occur within the lowest two bands, leading to a monotonic broadening of the lowest flat band, whereas odd denominators (i.e., odd parities) yield a nonmonotonic response due to the 𝒫𝒯-symmetry breaking within the second and the third lowest bands instead while the lowest band remains purely real. This parity-dependent phenomenon can be understood by the perturbation theory. Furthermore, by solving the Gross-Pitaevskii equation, we also find that although the weak repulsive interaction can broaden the moiré bands alone, the combined effects of interaction and imaginary potential also lead to parity-dependent behaviors. For even parities, band flattening is consistently diminished, whereas for odd parities, the imaginary potential can either enhance or reduce the degree of flattening. These results pave the way for experimental studies of dissipation and interaction effects on band flatness in moiré systems.
Versions
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BibTeX
@misc{cheng2026fate,
title = {{Fate of moiré flat bands for a weakly repulsive Bose-Einstein condensate in one-dimensional $\mathcalPT$-symmetric bichromatic optical lattices}},
author = {Enhong Cheng and Yu Tan and Yanzhen Xu and Li-Jun Lang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.01680},
eprint = {2608.01680},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.01680},
}
RIS
TY - UNPB
TI - Fate of moiré flat bands for a weakly repulsive Bose-Einstein condensate in one-dimensional 𝒫𝒯-symmetric bichromatic optical lattices
AU - Enhong Cheng
AU - Yu Tan
AU - Yanzhen Xu
AU - Li-Jun Lang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2608.01680
UR - https://arxiv.org/abs/2608.01680
AB - One-dimensional (1D) superlattices provide one simplified platform for exploring moiré physics from a low-dimensional perspective, with the ratio of lattice constants playing a role analogous to the twist angle in two-dimensional bilayers. Here, we propose a 1D 𝒫𝒯-symmetric bichromatic optical lattice for a weakly repulsive Bose-Einstein condensate and investigate how the interplay of dissipation and interaction impacts the lowest moiré flat band. Without interaction, we find that the lowest-band flatness induced by commensurate ratios exhibits a parity-dependent response to the 𝒫𝒯-symmetric imaginary potential due to the distinct 𝒫𝒯 pairing mechanism for the energy spectrum. For ratios with even denominators (i.e., even parities), the level attraction and thus the 𝒫𝒯-symmetry breaking occur within the lowest two bands, leading to a monotonic broadening of the lowest flat band, whereas odd denominators (i.e., odd parities) yield a nonmonotonic response due to the 𝒫𝒯-symmetry breaking within the second and the third lowest bands instead while the lowest band remains purely real. This parity-dependent phenomenon can be understood by the perturbation theory. Furthermore, by solving the Gross-Pitaevskii equation, we also find that although the weak repulsive interaction can broaden the moiré bands alone, the combined effects of interaction and imaginary potential also lead to parity-dependent behaviors. For even parities, band flattening is consistently diminished, whereas for odd parities, the imaginary potential can either enhance or reduce the degree of flattening. These results pave the way for experimental studies of dissipation and interaction effects on band flatness in moiré systems.
ER -