Low-frequency quantum oscillations from interactions in layered metals

Metals composed of weakly coupled, stacked layers possess a Fermi surface that slightly varies in size along the stacking direction. This appears in de Haas–van Alphen (dHvA) oscillations of the magnetization with a magnetic field as two close frequencies, corresponding to the two extremal Fermi-surface cross-sectional areas. We show that, for layered materials of sufficiently high mobility, Coulomb interactions can have a dramatic effect on the form of the dHvA oscillations: There is also generically an oscillation at the small difference of the two large frequencies. We determine the size and form of this effect, and show that it probes the short-range part of the Coulomb interactions within the layered material. We argue that this interaction effect may explain recent experimental observations of anomalous low-frequency dHvA oscillations in the ultrapure delafossites.

Figure 1

The Fourier spectra of the (a) kinetic energy $F_{\text{3D}}^{\left(0\right)}$ and (b) Fock interaction energy $F_{\text{3D}}^{\left(1\right)}$ for the 3D multilayer system. The red dashed lines show the same spectra for the case of a fixed chemical potential [36]. Frequencies are given in units of $f_{\text{avg}}=(f_{+}+f_{-})/2=m^{*}\mu /e\hslash$. We use $\delta f/f_{\text{avg}}=4t_{\perp }/\mu =0.0189$, consistent with the parameters of ${\text{PtCoO}}_2$ [20]. Vertical and horizontal guidelines mark the location and size of the largest difference-frequency peak in each panel. The insets of each panel expand the boxed sections of the main figures. The vertical scale of each panel is set by the appropriate amplitude in Eq. (11) or (12).