Fermi liquid theory of $d$-wave altermagnets: demon modes and Fano-demon states

Abstract

We develop a Fermi liquid theory of $d$-wave altermagnets and apply it to describe their collective excitation spectrum. We predict that in addition to a conventional undamped plasmon mode, where both spin components oscillate in phase, there is an acoustic plasmon (or {\em demon}) mode with out-of-phase spin dynamics. By analyzing the dynamical structure factor, we reveal a strong dependence of the demon's frequency and spectral weight both on the Landau parameters and on the direction of propagation. Notably, as a function of the propagation angle, we show that the acoustic mode evolves from a {\em hidden state}, which has zero spectral weight in the density excitation spectrum, to a weakly damped propagating demon mode and then (below a critical interaction parameter) to a {\em Fano-demon mixed state}, which is marked by a strong hybridization with particle-hole excitations and a corresponding asymmetric line shape in the structure factor. Our Letter paves the way for applications of altermagnetic materials in optospintronics by harnessing collective electron spin oscillations beyond traditional magnon spin waves.

Figures (3)

• Figure 1: Microscopic Fermi surface deformations (green shaded areas) of (a) the demon mode and (b) the plasmon mode for propagation near the nodal direction. The corresponding spin-$\uparrow$ and spin-$\downarrow$ Fermi surfaces are shown as blue and red ellipses, respectively. The demon mode involves an out-of-phase oscillation of both spin components, whereas for the plasmon mode both components oscillate in phase. (c) Dynamical structure factor $S_{nn}({\bf q},\omega)$ as a function of frequency $\omega$ at fixed wave number $q a_B = 0.4$ for three different directions of propagation $\phi = 0, 0.95 \pi/4$, and $\pi/4$. The plasmon is nearly isotropic, but there is a strong directional dependence of the demon mode contribution to the density fluctuations: For propagation exactly along the diagonal $\phi=\pi/4$ (blue line), the demon has zero residue and is hidden in the density excitations. Near this nodal direction, the demon mode is weakly damped and present in the density excitations (green line). Finally, for propagation near the nematic axis (gray line), it hybridizes with the particle-hole continuum and forms a strongly asymmetric line shape, a Fano resonance.
• Figure 2: Dynamical density and spin structure factors $S_{nn}(\mathbf{q},\omega)$ and $S_{zz}(\mathbf{q},\omega)$ as a function of wave number $q$ and frequency $\omega$ for propagation directions (a)–(c) $\phi=0,0.9\pi/4,\pi/4$ and (d) $\phi=0.9\pi/4$. Red and blue dashed lines mark the particle-hole continuum boundary for the two spin surfaces. The top row shows the spectral density and the bottom row shows cuts at a fixed energy $\omega = 0.15 v_F/a_B$ (indicated by the dashed cyan line in the top panels). As $\phi$ increases from $0$ to $\pi/4$, the spectral weight of the demon branch becomes more concentrated, and the initially broad Fano-demon mode [panel (a)] sharpens into a well-defined Lorentzian peak [panel (b)]. At $\phi = \pi/4$ [panel (c)], the spectral weight of the demon mode is suppressed in the density spectrum. By contrast, the spin structure factor (panel (d)) shows a strong demon peak and a faint plasmon peak. The parameters are $\alpha = 0.4$, $\gamma = 10^{-4} v_F/a_B$, $F^{s}_{0} = 1$, and $F^{a}_{0} = 0.5$.
• Figure 3: Density plot of the dynamical structure factor $S_{nn}({\bf q}, \omega)$ in the wave-vector plane $(q_x, q_y)$ for $\omega = 0.4 v_F/a_B, \alpha = 0.4$, and $F_0^{s}=1$ for two different values of the Landau parameter (a) $F_0^{a}=0.5$ and (b) $F_0^{a}=1.5$. Both panels show a weakly anisotropic plasmon mode (inner blue circle). Panel (a) shows a strongly anisotropic demon mode with (i) a broad Fano–demon resonance region (intermediate blue spectral weight), (ii) a narrow region with a demon excitation (red), and (iii) a hidden branch along the nodal directions $\phi=\pm\pi/4,\,\pm 3\pi/4$. The transition point from the demon to the Fano–demon regime is marked by the red dot. In panel (b), the Fano–demon disappears and the demon mode lies entirely outside the particle–hole continuum with anisotropic dispersion. (c) Trajectories of the Fano-demon and demon modes in the complex frequency plane as a function of propagation angle $\phi \in [0, \pi/4]$ for three values of $F^a_0 = 0.25, 0.5$, and $0.75$. The red dashed line marks the branch cut of particle-hole excitations, where the real part is rescaled. The red shaded area highlights the region between the Fano-demon and hidden modes (at $\phi = \pi/4$).