Quantum oscillations in Dirac magnetoplasmons

The plasmon frequency in standard electron gases with a parabolic single-particle dispersion is a purely classical quantity that is not sensitive to electron interactions or the equation of state. We demonstrate that this canonical result no longer holds for plasmons in three-dimensional semimetals, which can thus be used to probe many-body effects. In particular, we show that the plasmon frequency in an external magnetic field displays quantum oscillations, which is not the case for the electron gas. Using the random phase approximation, results are presented for the magnetoplasmon dispersion and the loss function in Dirac semimetals. We include a full discussion of the loss function in a magnetic field as a function of the direction of propagation with respect to the magnetic field direction and discuss the transition from large magnetic fields to the low-field limit.