Gotta love statistics

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And you sir are a bigger troll. The paper I cited was not the original paper, but rather a follow up that puts the memristor in a better context. If you allow for various combinations of the derivatives and integrals of just current and voltage you can get a capacitor, resistor, inductor, and memristor. However you can also get the memductor and memacitor as well. This is all explained in that paper.

Why are combinations of voltage, current, charge and flux fundamental?

According to Websters fundamental is:
"a: serving as an original or generating source : primary (a discovery fundamental to modern computers) b: serving as a basis supporting existence or determining essential structure or function : basic"

The memristor is is just a way to model nonlinear circuit elements and is one of many components in a nonlinear expansion for circuit modeling. See this paper by Leon Chua, the memristor's inventor. Note that in this paper the fourth element of the four element torus is negative resistance and not the memristor. All of the publicity over the memristor has been (sucessfull) marketing by some researchers at HP. .

From the talk page for the memristor on wikipedia

"Resistance, Capacitance and Inductance are regarded as fundamental because to each there corresponds a different picture of what is going on with the energy. Resistance refers to the loss of energy to Joule heating. Capacitance refers to storage of energy in the electric field. Inductance refers to storage of energy in the magnetic field.

If memristance is the "fourth fundamental" circuit element then memristors must do something with the energy they are imparted other than turn it into heat, or store it in electric or magnetic fields. So what do memristor supporters have to say about this? nothing. This is not surprising, since the concept of memristance stems from a purely mathematical argument bent on taming the current/voltage relationships of nonlinear circuit elements. The concept of memristance was invented out of convenience to avoid dealing with frequency-dependent (time-dependent) resistance, inductance, and capacitance. Thus the memeristor is not "fundamental", unless in your book fundamental is synonymous with convenient."

If you read the journal articles http://dx.doi.org/10.1016/j.mseb.2006.10.002 you'll find that this process esentially creates a large number of impurity states at the center of the band gap, creating an impurity band. What this means is that light is absorbed very very fast, but then its also turned to to heat very very fast. In other words you can excite electrons but that electron will decay back down before it creates any current. This could still work for a photodetector because you can apply a voltage to sweep out the excited carriers before they recombine/decay but not for a solar cell since you want to generate power.