what determines speaker efficiency? Is it the materials used, or is it something else?
At a fixed frequency, how it is loaded (i.e. horn or not), magnet size, strength and structure, moving mass and radiating surface, as well as suspension.
You'll notice the speakers with ridiculously high efficiency (i.e. 100 dB+) are almost always horn loaded, and/or or very large bass drivers.
Focal has recently (last 10 years) reintroduced the electro magnet. That is, instead of using a permanent magnet, their subs use a second coil to generate a startlingly strong magnetic field against which the voice coil pushes. This gives the subs amazing amplifier efficiency measured from the amp side alone.
Of course, the total driver efficiency is now different, since the speaker itself has a power supply, but it’s a great example of how the strength of the magnetic field affects efficiency.