Can a Cochlear implant impart superhuman hearing? The bandwidth of human hearing determined by empirical data is $20 \; Hz$ to $20 \; kHz$. A cochlear implant stimulates the auditory or acoustic or Cochlear  nerve directly so that the hearing can be improved in the case of stimulation mechanism upstream of the Cochlear nerve has degraded.
Let us assume that the ear mechanism has not degraded (such as in a young and healthy adult). The Cochlear implant can likely improve hearing even in this case by increasing the bandwidth by amplifying the effect of the ear drum vibration (sensor actuation). However the neurons connecting the Cochlear nerve to the hearing region of the brain will still have an upper limit to the sampling rate.

Does the the Nyquist sampling theorem limit the superhuman hearing capability made possible by a Cochlear implant?


 A: Human hearing is not really limited by the Nyquist sampling theorem, since we do not reconstruct the sound signal in the brain like it assumes. So the enhancement an implant can give is not due to frequency range.
The theorem shows what signals can be perfectly reconstructed from bandwidth-limited measurements, but the goal of hearing is extracting useful information from sound. The cochlea implements a kind of mechanical Fourier transform of sound where intensities at different frequencies are transmitted by neural spikes with signal frequencies <100 Hz (and some phase information in spike timing, maybe). But this nerve bandwidth is not a major Nyquist limiter since different axons transmit information about intensities in different parts of the spectrum: they are separate channels. However, changes in spectrum faster than 100 Hz will not be represented accurately.
In implant taking a few of these axon channels and giving them intensity information from a wider spectrum will reduce the fidelity of their original part of the spectrum slightly, but the brain can likely adapt to the new meaning of these inputs.  So you could expand the range tremendously and hear things normal ears cannot. But note that the total bandwidth of information about what you are hearing is unchanged: the data rate of each axon is still about 100 Hz, no matter what the data is about.
Michael Chorost, in his excellent book Rebuilt (about the experience of cochlear implants) describes listening to music from a MP3 player with his implant, and recognizing that there is no sound in the room - information is electronically unpacked, repackaged and eventually ends up in his auditory nerve without ever having been vibrations in air. This is a form of superhuman hearing.
It is not hard to imagine sensors and implants allowing hearing other normally inaudible things through direct axon stimulation. Yet the data rate of the auditory nerve (and auditory cortex) are set by the signal processing limits of neurons. We can never get superhuman timing information of hearing, for example (unless we cheat and amplify phase differences - but then we still need time enough to notice, we will not react faster than 100 Hz).
