I think you know what the Hirsch-index is: if you have n papers cited at least n times – then your h-index is n. For instance, if out of your 10 papers two were cited 4 times, and the rest three times, then your h-index is 3. The index was introduced by Jorge Hirsch in 2005, and became an accepted tool to rank scientists within about one year: community found it useful that a scientist's productivity may be described by a single number. However, the h-index does not take into account such important things as the number of co-authors and the self-citations.
Recently Jorge Hirsch himself wrote a preprint, where he proposed a new, ħ (hbar) - index, that is aimed to solve at least one of these problems, multiple co-athorship. Indeed, the "mass graves" (sorry), published by high-energy physicists and the institute policies to include everyone's name to any article, can unreasonably increase the Hirsch-index, with no extra work.
Some of the h-index terminology before describing the ħ-index. You have the h-index n, if n of your papers belong to the "h core". The paper belongs to the h-core if it was cited n times or more. Your co-authors will probably have other h cores, and a given paper may belong there or not.
The ħ - index is defined in a similar way: you have the ħ - index m if m of your papers belong to the ħ-core. But, the paper belongs to the ħ-core if it was cited m times or more and it also belongs to the h-core of your co-authors. (Actually, the latter h should be also ħ, but since the index would be extremely difficult to compute in this case, Hirsch decided to relax the condition a bit)
In other words, only if the paper improves the h-index of all the authors, it will contribute to your ħ-index. Imagine that you have the h-index of 20, and you have a paper cited 25 times, co-authored by a student with a h-index of 5. Then, it will be included in your and the student's ħ-index, because it belongs to the h-cores of both of you. But, if you add a third author to this paper, say, a director of your institute with a h-index of 45, the paper will not count for any of you, because it doesn't belong to the director's h-core.
So, if you have 200 papers, cited 44 times each and co-authored by your director, who has the h-index of 45, none of them will count, and your ħ-index will be zero. Hirsch expects this to stimulate young scientists to work independently. However, he mentions, that the ħ-index will be definitely useless for postdocs, since they are used to include senior scientists in their papers.
I wonder whether it will be possible to eliminate self-citations at some point.