Formation of Majorana fermions in finite-size graphene strips

Accessible and well readable. Timely and interesting topic. Detailed numerical study. Good illustration with figures.

1.) Marginal originality. The setup at hand has been investigated in various previous publications. In particular Ref. [47] investigates almost the same systems just with partly different methods. The new physical insights of this specific manuscript are very limited.

2.) Large parts consist of blackbox numerical analysis without clear physical pictures. For example, the physics behind observations such as the importance of the ribbon width for the stability of the Majoranas is hardly discussed.

3.) No immediate experimental relevance. As a main motivation for the the present study, the authors state the need for finding experimentally more accessible/realistic material systems hosting Majorana bound states. However, as reflected in the conclusion "As a future extension of the present work we propose to perform fully-realistic studies...", the manuscript falls short of really answering relevant experimental questions such as localization and coherence properties of the Majoranas, realistic numbers for the involved energy gaps, etc.

The authors study the occurrence of Majorana bound states in graphene ribbons in proximity to a conventional superconductor. They consider two situations, one which relies on strong spin orbit coupling (possibly realized for graphene on a metallic substrate) and one where a spatially rotating magnetic field generates similar effects (proposed in Ref. [47]). While I generally find the topic very interesting and the present analysis seems sound in content, its low originality and limited experimental relevance in my opinion makes it a candidate (upon minor revision) only for publication in the Tier III section of this journal. For my specific comments and amendments, see the other fields of this review form.

I ask the authors to clearly state how the phase diagram in Fig. 2b) is computed. Furthermore, a clear physical discussion of how the finite size of the ribbons affects their topological properties would be in order, given that this point is strongly emphasized in the introduction.