The quantum Hall effect has the well-known signature of plateaus in the Hall conductivity $\sigma_{xy}=n e^2/h$ that occur at integer values of $n$. This quantization is extremely precise, up to one part in $10^{-9}$. SI units uses this quantization to define the "von Klitzing" constant.
The modern understanding of the Quantum Hall effect is due to topologically-protected chiral edge states playing the dominant role.
My question is: What does the frequency-dependent (AC) version of the Quantum Hall conductivity look like from quasi-DC to THz? Do we have a theory for its behavior in general, and are there experimental proofs of that behavior?
At large enough frequencies, the Hall conductivity must no longer be quantized. But I'm interested in understanding how the topological protection fails. Does it happen smoothly, or suddenly go away as soon as you hit the cyclotron frequency? Depending on the answer to that, is it possible to measure the quantized conductance $e^2/h$ with light (well microwaves or Rf waves more likely), rather than with electrodes?
