Why is it twenty minutes for a “Power Nap?”
News Item: Power Nap in the News
Reference: Metro Naps NYC
Real help or raw hype?
Because it’s how long you can stay at the bottom of the Marianas Trench? (At least once, in 1960) 
Seriously, a very good question. My WAG is that it’s the minimum needed to go into “deep sleep” and make any serious reduction in fatigue. But I’d love to hear from a physiologist or other person familar with the thinking here.
My suspicion is that it’s because 20 minutes is 1/3 of an hour and 3 is a magic number.
A nap of 20 minutes or less generally results in sleep no deeper than stage 1 or 2, while longer naps result in entering the deeper stages of sleep. Once stage 3 or 4 are reached, then rousing from sleep becomes a more difficult process, with more symptoms of “sleep hangover”.
IIRC, Thomas Edison was known for doing the same thing: taking 15-30 minute naps during the workday.