Avalanche photodiodes already exist and convert a single incident photon into multiple charge carriers. They do this using an externally-applied electric field. This externally-applied electric field enables "impact ionization" which means that one mobile charge carrier seems to be able to knock another one loose.
(As a thought experiment: imagine a bed of pebbles. Toss in another pebble, and it's likely to kick one of the existing pebbles free. Now, pretend the bed of pebbles is at a 45-degree angle to gravity. Toss a pebble in and it's more likely that the ejected pebble will itself kick another pebble loose when it lands. Make the angle steep enough and you get an "avalanche", hence the name.)
As far as I can tell, the novelty here is that the high electric field is created by the geometry and materials at the surface of the nanoscale needle structure, so some version of the avalanche effect happens without needing to apply an external electric field.
In the headline, efficiency refers to quantum efficiency (electrons per photon); conservation of energy still applies.
But in all seriousness, thanks for such a detailed explanation! It'll be a while before I understand it, but it's pretty great.
More electrons per photon means more accurate detection of low amounts of light and also lower power requirements for light sensors in general. That would include, for example, the cells that make up a digital camera's sensor grid. Economics permitting, this could lead to better low-light performance or more efficient optical equipment (e.g. fiber optic transceivers).
I would think so, since the reason the efficiency was less than 100% before was that some of the electrons were being recaptured rather than emitted from the detector. On the other hand, the article didn't say anything about the amount of energy captured. It could be that more of the photon's energy is converted into heat, with the remainder being spread across more electrons.
* Since current is charge per time, technically it creates more than one electron per second of current per incoming photon per second.