Cyclotron resonance and quantum oscillations of critical Fermi surfaces

Kohn's theorem places strong constraints on the cyclotron response of Fermi liquids. Recent observations of a doping dependence in the cyclotron mass of La$_{2-x}$Sr$_x$CuO$_4$ (Legros et al., Phys. Rev. B 106, 195110 (2022)) are therefore surprising because the cyclotron mass can only be renormalized by large momentum umklapp interactions which are not expected to vary significantly with doping. We show that a version of Kohn's theorem continues to apply to disorder-free non-Fermi liquids with a critical boson near zero momentum. However, marginal Fermi liquids arising from a spatially random Yukawa coupling between the electrons and bosons do give rise to significant corrections to the cyclotron mass which we compute. This is the same theory which yields linear-in-temperature resistivity and other properties of strange metals at zero fields (Patel et al., Science 381, 790 (2023)).