Good morning, We are writing this email as we would like to ask about the application of the bound state algorithm (described in https://scipost.org/10.21468/SciPostPhys.4.5.026) to higher-dimensional systems. In particular, we are trying to apply the algorithm to solve for proximitised 3DTIs, and for reference have been trying to understand the example cases of the quantum billiards and 2D topological insulator in the paper. Essentially, we would like to clarify if the reduction of higher-dimensional systems to quasi-1D is necessary for the bound state algorithm to work correctly.
To solve for the 2D BHZ model (Section 5.2), the system was reduced to a quasi-1D system through the use of the Bloch theorem, and was then fed into the bound state algorithm. In section 4 however, a system of quantum billiards was considered without any mention of reduction to a quasi-1D system. As we are trying to apply the algorithm to a 3D system, we are wondering if this is a necessary step for the algorithm to work as intended. In the proximitised 3DTI systems we are considering, the leads are translationally invariant only in 1 direction, so we are wondering if the algorithm can be applied if we do need to reduce the system like in section 5.2. Thank you very much! Regards, Ryan and Chi
