The Cyclotron resonance as a smoking gun for U(1) spin liquids with gapless fermions

Certain U(1) spin liquids with gapless neutral fermions are expected to have the mind-boggling property that their optical conductivity vanishes as a power law of frequency. Thus, they are insulators to DC electric fields but without a "hard" optical gap, allowing them to absorb light at low frequencies. Additionally, they can also develop Landau levels in a magnetic field. In this work, we show that they can also have cyclotron resonance peaks in their optical spectrum analogous to metals, even though they are charge insulators. Interestingly, we have found that in contrast to metals, the principal Kohn harmonic of the cyclotron resonance is missing. The cyclotron resonance could therefore serve as a beautiful smoking gun test for the existence of these states which have been proposed in 2D organic materials and SmB₆.