Questions regarding order parameters in the twisted MoS2 bilayer

[李嘉恒]

Hi!

My doubt is about how to calculate order parameters of twisted MoS2 bilayer in the real space. I wonder how to compare the shifted structures with the highest-energy stacking order? What describes the local similarity of two structures? 

Best,

Jiaheng Li

IOP, CAS, China

[Mit Naik]

Hi Jiaheng,

You can compute the order parameter at each Mo or S atom of the bottom layer. For each Mo atom in the bottom layer (px, py) you can find the nearest Mo atom in the top layer (coordinate: qx, qy). The in-plane displacement between the two sqrt( (qx-px)**2 + (qy-py)**2 ) is the local order parameter. 

For AA stacking region this should be small since the neared Mo in the other layer will be very close by. For other stackings it will be large. 

Best,

Mit

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[Jiaheng Li]

Thanks for your kind response. I have adopted this method in my code, but I realized that this method cannot distinguish AB and BA stacking with each other, which is the different case for 1H MoS2.

Best, 

Jiaheng

[Indrajit Maity]

Hi Jiaheng,

The inspiration to compute order parameters primarily comes from the interlayer (sliding) binding energy landscapes. If I remember correctly, the energies of both AB/BA stackings are the same right? The only difference in the order parameter space of AB and BA stackings is the domain walls (i.e. if you want to move from AB -> BA you have to cross the domain walls, or, the topological AA defect).

Does this help?

Best regards,

Indrajit 

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[Jiaheng Li]

Hi Indrajit,

Thanks for your answer. Interlayer binding energy landscapes of MoS2 with 0 deg and 180 deg are given below (PRB 98, 224102), but AB and BA is nonequivalent in the 180 deg case. So it may be more useful to distinguish them, what I try to tackle up with.

Best,

Jiaheng

[Indrajit Maity]

Dear Jiaheng,

Ahh. You want the order parameters for AA', AB', A'B (or, 2H, B^Mo/Mo, B^S/S).

Fair point. Only using S or Mo atoms for both layers will not distinguish between the order parameters. For example,  the Order Parameters (OP) for AA' and AB' are the same. However, for the relaxed structures, the areas of these stackings are different. So, you may still be able to figure out the the stackings by looking at the OP.

Here's a simple suggestion:

If you want to distinguish between AA' and AB', you may want to use a weighted combination of Mo atoms for the Order parameters. Note that with S atoms you already are able to distinguish between A'B and the other high-symmetry stackings.

Best regards,

Indrajit

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[Jiaheng Li]

Hello Indrajit!

Your advice seems useful for such systems. And I will try to figure out the displacement field u(r) accordingly, what stacking fault energy can be easily obtained.

Thanks again!

Best,

Jiaheng