Hi Jerry,

The approach of PRR is what you should use if you want the Chern marker at a single energy. Note, however, that explicit methods will scale similarly in 2D—those are often competitive with KPM, and that's why we chose a 3D application. I'm not sure what's the most efficient way if you want the answer at all energies. Off the top of my head, the KPM correlator will scale as the resolution squared, which is something you almost never want.

Best, Anton

On Sun, 7 Aug 2022 at 09:16, Jerry xhm xiaoxiao.zhang@riken.jp wrote:

Hello Kwant community, After posting the question, I got no reply but came across another paper by some of Kwant's authors [PHYSICAL REVIEW RESEARCH 2, 013229 (2020), Computation of topological phase diagram of disordered Pb1−xSnxTe using the kernel polynomial method]. This paper uses kwant to calculate the Chern marker I asked although with mirror symmetry and disorder. These additional features aside, its code still seems to be rather different from just applying kwant.kpm.correlator as in my code. I am a bit confused now.

I initially thought the topological marker could be directly calculated using kwant.kpm.correlator. Is it true at all? If yes, what's the relation with this 2020 paper? If no, so this 2020 paper is the correct and probably optimized calculation of topological marker in kwant?

Any comment will be appreciated!