How to build a supercell model

[kabume]

How can we build a supercell model to calculate the edge states? like below:

----------
AAAAABBBBB
----------

e.g., A is a topological non-trivial photonic cell and B is trivial, and "----" means Bloch boundary conditions.

By the way, it seems that we cannot build a rectangular lattice, such as a1=[1, 0], a2=[0, 2], an error would appear:

ERROR: AssertionError: norm(b1) ≈ norm(b2)

Thanks!

[sp94]

Hi @kabume

There are two functions to make a solver:

solver = Solver(geometry, P) will make a solver with the k-vectors of the plane waves roughly in a circle around k=[0,0]. It assumes that b1 == b2

solver = Solver(geometry, P, Q) will make a solver with the k-vectors of the plane waves in a rhombus from k=±P*b1±Q*b2

For your problem, you probably want to use the second method since b1 != b2

(See the source here: https://github.com/sp94/Peacock.jl/blob/master/src/plane_wave_basis.jl#L57)

[kabume]

Thanks! I'm sorry for forgetting it. Would you mind showing an example of the supercell in the documentation? It would be friendly for a wider audience.

[sp94]

Hi @kabume
Sorry for the long delay. Did you make any progress? I may be able to share an example if you don't have one already