Kohn's theorem places strong constraints on the cyclotron response of Fermi liquids. Recent observations of a doping dependence in the cyclotron mass of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ [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 that we compute. This is the same theory that yields linear-in-temperature resistivity and other properties of strange metals at zero fields [Patel et al., Science 381, 790 (2023)].

• Received 11 August 2023
• Accepted 11 January 2024

DOI:https://doi.org/10.1103/PhysRevB.109.075162