Now I encountered a popular article (see this) telling about this strange halving of photon angular momentum unit two years after writing the above comments. I found nothing new but my immediate reaction was that the finding could be seen as a direct proof for heff=nh0 hierarchy, where h0 is the minimal value of Planck constants, which need not be ordinary Planck constant h as I have often assumed in previous writings.
Various arguments indeed support for h=6h0. This hypothesis would explain the strange findings about hydrogen atom having what Mills calls hydrino states having larger binding energy than normal hydrogen atom (see this): the increase of the binding energy would follow from the proportionality of the binding energy to 1/heff2. For n0=6→ n<6 the binding energy is scale up as (n/6)2. The values of n=1,2,3 dividing n are preferred. Second argument supporting h=6h0 comes from the model for the color vision (see this).
What is the interpretation of the ordinary photon angular momentum for n=n0= 6? Quantization for angular momentum as multiples of hbar0 reads as l= l0hbar0= (l0/6)hbar, l0=1,2... so that fractional angular momenta are possible. l0=6 gives the ordinary quantization for which the wave function has same value for all 6 sheets of the covering. l0=3 gives the claimed half-quantization.
See the article Badly behaving photons and space-time as 4-surface.
For a summary of earlier postings see Latest progress in TGD.