Gap solitons in parity-time symmetric moiré optical lattices

The authors investigated the gap solitons in parity-time symmetric moir’e optical lattices. The excitations and stability of 2D GSs supported by PT symmetric moir´e optical lattices have been addressed. Three categories of gap solitons, fundamental GSs, higher-order ones, gap vortices with topological charge, have been found. Most importantly, their stability are evaluated in linear-stability analysis and direct perturbed simulations.

This is a good manuscript. I find the manuscript to be scientifically sound and important to the field. As far as I know, such investigation of the combination of moir’e patterns and PT symmetryis not yet available in the current literature, and is quite timely, actual and interesting. The title clearly identifies subject matter and the abstract is succinct, comprehensible to a non-specialist. The manuscript seems me clearly written and logically organized. Length is appropriate to topic. Quality of writing is adequate.

Some suggestions are as follows,
(1) Some typoes in equation should be corrected, such as sin^2x and sin2x in Eq.(2).
(2) The band-gap structures are functions of twisting angle θ. Two angles are chosen in the work t θ=arctan(3/4) and θ=arctan(5/12). I wonder why this two angles are chosen in this work?

In summary, this is a fine and solid enough manuscript well deserving of publication. I really recommend accepting it for publication.

In this work, the authors investigated gap solitons in moire lattices with PT symmetry. For the first time, they found the formation, properties, and dynamics of fundamental and higher-order gap solitons as well as vortical ones with topological charge. The stability of these gap solitons are also inspected seriously. Even though this is a theoretical work, the authors provided the potential platforms for observing such gap solitons in experiments. I think the results not only connect periodic lattice and aperiodic lattices, but also link the Hermitian optics and the non-Herimitian optics. In addition, the paper is well organized and well written that will attract readers in optics, atomic physics, nonlinear physics, and condensed matter physics. Therefore, I am happy to recommend accepting it for publication in SciPost Physics. Here, I would like to raise some optional comments for author’s reference:
1. Second line below eq. 1: “chose” should be “chosen”;
2. Eq. 2: the term $\sin^2y$ should be $\sin2y$;
3. Third line below eq. 1: I suggest modify “matches PT symmetry” to “matches the requirement of PT symmetry”, because the relation after is only a requirement not sufficient condition;
4. Some small questions: In this paper the specific angles $\theta=\arctan(3/4)$ and $\theta=\arctan(5/12)$ are chosen for the moire lattices. At such angles, the moire lattices are periodic instead of aperiodic. In comparison with previous investigations on gap solitons, the lattices here are more complex, is this the only difference? Can the results reported in this paper be obtained in square lattices or honeycomb lattices? Since there are many flat bands that can be utilized to localize beams which are always stable (because the localization due to the flat band is a linear problem?), what is the advantage of gap solitons?

Please see the report for details.