The specific effect of Ansel's "Black Sun" is identical to the way Harman Direct Positive photo paper works -- except theirs is very well controlled. There have also been direct positive cine copy films (typical ISO speed from <1 to 6 or so) sold in 35mm on occasion; Kodak used to make them, wouldn't surprise me if ORWO (or Inoviscoat, which I understand handles their actual coating) has or does as well.
For direct positive imaging, the entire emulsion receives a carefully calibrated exposure to push it exactly to the peak of the characteristic curve, or more likely to a precisely determined point past (so that the slope of density reduction becomes useful). For effects like "Black Sun" it's a lot simpler, in some ways; you need a film that actually has a reversed section of the H&D curve, and then you need to set up your exposure so some extreme highlights get enough light to push far past that point (so you wind up with clear or nearly clear film in that region) without burning out the rest of the negative.
The complication is that a number of modern film stocks have been adjusted to make them "easier to use" -- the more commonly noted effect of these adjustments has been that the range of Zone expansions and contractions is much less broad; instead of N-3 to N+7, with a modern film like T-Max you're limited to N-1 to N+3 or so. A side effect of this "baked in" contrast range is that the reversal portion of the H&D curve is just gone; there's no amount of exposure you can give, short of literally burning a hole in the film, that will give that reversal effect. So, you need to know what films will do the job you want, and in general, it's going to be the oldest technology films -- Fomapan probably can, Ilford's cubic grain stocks (Pan F, FP4+, and HP5+) are reported to work this way, and it's possible Tri-X does. Double-X Negative cine stock probably does (this film is almost unchanged since it came out in 1959), and there are very likely some other stocks produced by Inoviscoat for Maco/Rollei or ORWO, or by Tasma that will work this way; Lucky? Who knows. Beyond that sort of "this is an old-tech film, so it ought to work" you're likely on your own to establish how much exposure you need to get past the peak, since published H&D curves almost never go much past the shoulder, and the peak is usually far past that exposure level (in normal use, anything beyond the shoulder is a "blocked highlight" and is to be avoided).
Ansel is on record as saying the effect was more or less accidental -- the composition he wanted couldn't avoid the sun in frame, so he took what he could get in that respect to get the rest of the photo he wanted.