Probing valley phenomena with gate-defined valley splitters

1- timely (valley devices are of great interest of the community)

1- hard to follow

Torres Luna et al introduce theoretically valley-splitters defined using patterned gates on bilayer graphene, using KWANT to perform numerical simulations.
The manuscript presents successively a geometry to achieve valley splitting, the effect of a magnetic field and of misaligned gates on that geometry, before presenting two applications: resonant tunnelling through quantum dot levels and the influence of inter-valley coherent order in a cavity. I found the paper hard to follow, with the figures not introduced clearly in the text and a lack of connection between items.
This kind of architectures are highly appealing in the graphene device community, and this paper could provide novel strategies to induce and probe valley effects in practical devices, but much clarity would be needed.

1- The geometry in figure 1 is not described clearly, with the order of panels not matching the discussion in the text. I would suggest to add a schematic of the proposed device as an introduction
2- Panel 2b is not described
3- Figure 4 and 5 would benefit from a device schematics, or at least boundaries of the different elements in panel 4a and 5c.
4- description of the figures and their relation to the overarching story line is missing
5- Bilayer graphene was shown experimentally to present several phases, with different orders (discussed in ref 6 of the present manuscript and references therein), which are used in the cavity simulation. It would be beneficial to discuss how the phase diagram of bilayer graphene influences the simulation.

Ask for major revision

1. Clearly written, clear graphics and presentation
2. Gate-defined device architectures are of interest to the community at the moment

1. Several works already discuss similar device architectures in the literature, not all of them are cited in the manuscript (see below)
2. I have some questions about details of the numerical simulations (see below)

The manuscript "Probing valley phenomena with gate-defined valley splitters" theoretically investigates the transport properties of a gate-defined valley splitter in bilayer graphene using numerical tight-binding simulations implemented in KWANT.

The manuscript consists of the following parts:

*An Introduction
*The section "device" describes the gate-defined electrostatic landscape considered by the authors and introduces the bilayer graphene tight-binding Hamiltonian they implemented in KWANT. The section also contains Magnetotransport simulations studying the achieved valley polarisation and a study of misalignment effects when the gates are mutually not perfectly aligned. 
*A section on applications discussing resonant tunnelling through quantum dot levels and probing the valley-dependent order parameter in transmission through a cavity.
* A conclusion

Gate-defined architectures have attracted some attention in the community over recent years. In this context of recent research activities, the present work may be of some interest to colleagues in the field. However, I have some concerns about the work presented in the manuscript, mainly concerning some technical details and what novelty the results bring compared to earlier works (see detailed below). I can therefore not recommend publication as is.

1. On page 3, the authors report to use a scaling factor of s=16 to reduce computational cost. I assume they refer to scaling in tight binding models as introduced in ref Phys. Rev. Lett. 114, 036601 (2015). A scaling of s=16 seems very large. In Phys. Rev. Lett. 114, 036601 (2015) for monolayer and arXiv:2403.03155 for bilayer graphene (both references are not cited in the manuscript), a scaling of s=4 has been used. Did the authors check systematically as a function of the scaling factor that the tight-binding results, most notably the transport data, do not change for scalings that large?

2. I wonder about the role of edge states in the simulations, both along the edges of the gates and at the physical borders of their lattice in the simulations. Can the authors show plots of the local density of states to show where the wave functions are localised? If there is electronic density at the borders of the sample, how do the authors exclude their contribution to transport in the simulations?

3. The work discusses the effects of misalignment when the gates are not perfectly aligned. I am also wondering about the role of alignment of the gates wrt the BLG graphene lattice. Does it matter how the gates are aligned wrt to the lattice, i.e., e.g. along the armchair or the zigzag direction? If yes, I see significant challenges for any experimental realisation, as the orientation of the lattice is notoriously hard to determine in any experiment. How would the authors suggest to mitigate such experimental issues? If not, what is the reason for the device's design choice, as shown in Fig 6? Why are the gates at precisely this angle? Could one choose any shape of gates (curved, straight, bent,…), and the states would follow that shape at the D>0/D<0 interface?

4. On page 5, the authors discuss "a cavity with valley order". It is not clear to me what type of valley order the authors have in mind and what would be its origin. 

5. There exist a multitude of similar works on gate-defined valley polarisers in bilayer graphene, e.g. https://doi.org/10.1038/s41467-020-15117-y, DOI: 10.1126/science.aao5989, https://doi.org/10.1103/PhysRevApplied.11.044033 (references not cited in the manuscript). Therefore, I fail to see what novelty or advantage the current work brings compared to these earlier works.

Ask for major revision