Cyclotron resonance and quantum oscillations of critical Fermi surfaces

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