Preservation of optical selection rules in an amorphous semiconductor

In amorphous solids, distinguishable regions of order exist that can be modeled by regular polytopes in curved (non-euclidean) spaces1,2. We propose that selection rules govern hypothetical physical processes, e.g., optical absorption, in such high symmetry non-euclidean structures. We show an analogy between curved space azimuthal angular momentum m and crystal momentum k. The selection rule ▵m=0 corresponds to a vertical ▵k = 0 transition in a crystal. In amorphous Si, a remnant of the crystalline k selection rule exists near the 1.1 eV absorption edge.